Research ArticleParticle Filtering for Obstacle Tracking inUAS Sense and Avoid Applications

Anna Elena Tirri Giancarmine Fasano Domenico Accardo and Antonio Moccia

University of Naples ldquoFederico IIrdquo I80125 Naples Italy

Correspondence should be addressed to Anna Elena Tirri annaelenatirriuninait

Received 16 January 2014 Revised 13 June 2014 Accepted 13 June 2014 Published 1 July 2014

Academic Editor Liang Lin

Copyright copy 2014 Anna Elena Tirri et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Obstacle detection and tracking is a key function for UAS sense and avoid applications In fact obstacles in the flight path mustbe detected and tracked in an accurate and timely manner in order to execute a collision avoidance maneuver in case of collisionthreat The most important parameter for the assessment of a collision risk is the Distance at Closest Point of Approach thatis the predicted minimum distance between own aircraft and intruder for assigned current position and speed Since assessedmethodologies can cause some loss of accuracy due to nonlinearities advanced filtering methodologies such as particle filters canprovide more accurate estimates of the target state in case of nonlinear problems thus improving system performance in terms ofcollision risk estimationThe paper focuses on algorithm development and performance evaluation for an obstacle tracking systembased on a particle filter The particle filter algorithm was tested in off-line simulations based on data gathered during flight testsIn particular radar-based tracking was considered in order to evaluate the impact of particle filtering in a single sensor frameworkThe analysis shows some accuracy improvements in the estimation of Distance at Closest Point of Approach thus reducing thedelay in collision detection

1 Introduction

Unmanned aircraft systems (UAS)must guarantee an equiva-lent level of safety compared tomanned aircraft in order to beallowed flying in both controlled and uncontrolled airspace[1] Thus they must have the ability to ldquosee and avoidrdquo otheraircraft andor obstacles in the flight path and they need tobe equipped with an autonomous detect sense and avoid(DSampA) system [2 3] The primary functions of this systemconsist in detecting obstacles in the own trajectory trackingthe detected objects and executing a collision avoidancemaneuver if an intruder is closely approaching thus becom-ing a collision threat ANearMid-Air Collision is determinedwhen the distance between own aircraft and an intruder is lessthan 500 ft [3] thus the prediction of the Distance at ClosestPoint of Approach (DCPA) is considered as a fundamentalparameter for the estimation of a collision risk In order toobtain an accurate DCPA estimate an adequate sensor setuphas to be chosen In fact the autonomous avoidance functioncan be performed installing onboardUAS cooperative andornon-cooperative technologies [4ndash6]

In the framework of TECVOL project carried out bythe Italian Aerospace Research Centre and the Universityof Naples ldquoFederico IIrdquo non-cooperative technology basedon an integrated radarelectro-optical (EO) architecture hasbeen considered as the optimal solution since the projectaimed at demonstrating the full autonomy of the system incase of absenceloss of data link between the aircraft [4 7]The prototype sensing setup has been installed onboard anoptionally piloted very light aircraft named FLARE (flyinglaboratory for aeronautical research) The hardwaresoftwarearchitecture is comprised of radar and four electro-opticalcameras and a central-level fusion algorithm based on anextended Kalman filter (EKF) An intensive flight test cam-paign has been performed taking into account several relativeflight geometries including chasing and frontal encounters[8 9] and considering a non-cooperative intruder of the sameclass of FLARE

In general while EKF is awell-assessed technique suitablefor real time implementation nonlinearities in obstacledynamics andor in the measurement equation can cause

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 280478 12 pageshttpdxdoiorg1011552014280478

2 The Scientific World Journal

some loss of accuracy in obstacle tracking performance Onthe other hand innovative filtering techniques developed fornonlinear systems such as particle filters are expected toprovide more accurate estimates of obstacle dynamics thanEKF thus improving the accuracy of the DCPA estimate andpotentially reducing the delay in collision detection [10]

Thus a research effort has been carried out in orderto assess the impact of particle filtering approaches in theconsidered application

In general tracking problems comprise several applica-tions such as ocean surveillance submarine tracking carpositioning video surveillance and airborne target trackingDifferent solutions and methods have been proposed andimplemented [11ndash16]

One of the key components of a tracking system isthe filtering and prediction block where target motion ismodeled using a state vector and a dynamic system andsensor observations are related to the state vector by aproper measurement equation Within this framework mostpopular solutions are based onKalmanfiltering [17ndash19]whichcan be demonstrated to be the theoretically optimal approachfor linear systems corrupted by gaussian noise In the latestyears particle filtering techniques have found increasingdiffusion in problems involving nonlinear and non-Gaussiannoise processes [20ndash23]

Particle filtering has been applied to various nonlinearproblems such as bearing-only tracking trackingmultitargetin clutter and jump Markov linear system

In [24] the tracking problem is examined in the contextof autonomous bearing-only tracking of a single appear-ingdisappearing target in the presence of clutter measure-ments The same problem is also analyzed in [21] where acomparison between EKF a pseudo measurement trackingfilter and a PF is pointed out The study aims at tracking atarget from an airborne sensor at an approximately knownaltitude The analysis shows the PF algorithm to be morerobust than EKF Karlsson and Gustafsson [25] make acomparison between the two filters for angle-only trackingin several applications such as air-to-air air-to-sea and sea-to-sea scenarios In the study experimental data are used totest the algorithm in the sea-to-sea caseThe results show thatthe PF outperforms the EKF algorithm Besides PF has beenalso applied to solve problems of tracking multiple targetsin clutter environment [26ndash28] These works provide someimplementation suggestions to improve the PF performancewith extension to bootstrap filter

This paper describes a customized particle filtering algo-rithm based on spherical coordinates and aimed at flyingobstacle detection and tracking for non-cooperative senseand avoid On the basis of application needs the algorithmhas been developed to understand PF potential especially interms of reliability and latency in collision risk estimationThus the predicted DCPA between aircraft has been consid-ered as the key variable of the problem

Besides the application field main innovation aspectsof the developed PF algorithm comprise the treatment andcompensation of sensor latencies in view of real time softwareimplementation with the negative timemeasurement updateproblem dealt with keeping in memory a sliding window

B r

VB

VA

AdAB

VAB = VA minus VB

Figure 1 Definition ofminimum separation distance vector 119889119860119861

and using a Monte Carlo sampling approach and the directparticle-based prediction of minimum separation distance

The paper is organized as follows First a brief descriptionof problem geometry and hardware architecture of the systemused in flight tests is provided Then the tracking algorithmis presented in detail Finally results obtained in off-linesimulations based on flight data gathered during TECVOLtest campaign are presented and discussed

2 Obstacle Detection and Tracking forUAS Sense and Avoid

ADSampA systemhas to be endowedwith an obstacle detectionand tracking system that performs the ldquosenserdquo function anda collision avoidance subsystem that performs a collisionavoidance maneuver as soon as a collision risk is detectedIn order to realize a suitable and reliable sense and avoidsystem a series of requirements concerning the field ofregard range resolution angular resolution detection rangetime to collision and system data rate have to be satisfied inthe case of non-cooperative technologies In particular flightregulations define the scanning volume for collision threatdetection and the maximum relative speed between the twoaircraft Moreover they prescribe that the own aircraft andthe intruder must never be closer than 500 ft that is the so-called bubble distance [3]

Considering the above-mentioned requirements they areessentially relevant to the ability to estimate the Distance atClosest Point of Approach and the Time to Closest Point ofApproach often named ldquotime to gordquo in the literature Theformer parameter indicates the minimum distance that willbe measured between two planes that keep their currentvelocity constant it can be calculated from [4]

119889119860119861=119903 sdot 119881119860119861

100381710038171003817100381711988111986011986110038171003817100381710038172119881119860119861minus 119903 (1)

where 119889119860119861

is the minimum separation distance (whose normis the DCPA) [29]119881

119860119861is the relative speed vector (119881

119860minus119881119861)

between the intruder (aircraft 119860) and the ownship (aircraft119861) and 119903 is the relative position between the aircraft (seeFigure 1) If the intruder is modeled as a spherical object withradius 119877 it can be demonstrated [4] that assuming constantvelocity vectors 119881

119860and 119881

119861 respectively the two aircraft are

headed for collision if and only if the following conditions aresatisfied

10038171003817100381710038171198891198601198611003817100381710038171003817 le 119877 119903 lt 0 (2)

The Scientific World Journal 3

These values are a measure of the collision risk if theseconditions are satisfied a Near Mid-Air Collision threat isconsidered

It is worth noting that in order to obtain an accurateestimate of the DCPA an adequate sensor setup has to beproperly chosen In general this function can be performedinstalling onboard UAS cooperative andor non-cooperativesystems that include both active and passive sensors thechoice depends on size speed maneuverability andmissionsfor which theUASwill be used In case of largeUAS platformsand fully autonomous systems integrated radarelectro-optical architecture seems to be a good option to increasethe collision threat awareness In fact radars provide accuraterange estimates and can operate in all-time all-weatherconditions while EO sensors offer the potential of accurateangular measurements at fast update rates in addition thesesystems do not rely on information from external sources todetect and track other aircraft thus avoiding problems due tothe loss of communication links

As anticipated above within TECVOL project a con-figuration with radar as main sensor and EO as auxiliarysensors has been chosen as the optimal solution in view of theapplication In fact this project aimed at the development andflight demonstration of the technologies needed to supporthigh altitude long endurance UAS flight autonomy Thechoice of a multisensor configuration allows a compensationof single sensor shortcomings by integrating informationfrom heterogeneous sources In the next section for the sakeof clarity the flight system architecture is briefly described

3 Flight System Architecture

During the TECVOL flight test campaign the prototypehardwaresoftware sensing system installed onboard FLARE(Figure 2) was comprised of a Ka-band pulse radar and fourelectro-optical cameras (two visible cameras and two infraredcameras) a CPU devoted to image processing (IP-CPU) anda CPU devoted to real time tracking by sensor data fusion(RTT-CPU) This unit is connected to the onboard flightcontrol computer that performs autonomous navigation andflight control including autonomous collision avoidancemaneuvers [4 7 30] A hierarchical architecture in which theradar is the main sensor that must perform initial detectionand tracking and the EO sensors are used as auxiliary infor-mation sources in order to increase accuracy and data ratehas been consideredThe choice of a hierarchical architectureis determined by different levels of sensor performance infact the conventional EO sensors perform initial detectionat closer ranges than radar The standalone radar trackingestimates can be effective in reducing the computation timeand false alarm rate of EO image processing by selecting prop-erly defined search windows to apply the obstacle detectionprocess

In Figure 3 the adopted hardware system is depictedFor more details on the hardware and logical architecturesadopted within TECVOL project the reader is referred to[4 7]

Figure 2 Sensing system onboard FLARE

AHRS

Radar Panchro vis Color vis Infrared Infrared

Ethernet

EthernetFirewire link

Can BUS

GNC systemGPS

AIR

ALT

Navigation sensors

Image processingcomputer

Real timecomputer

Figure 3 The onboard hardware architecture

The tracking system can operate in two different modes

(1) standalone radar tracking mode that performs cur-rent estimates of obstacle relative position and veloc-ity on the basis of measurements from radar and theinertial unit

(2) radarEO tracking mode where current estimates ofobstacle relative position and velocity are determinedalso on the basis of EO sensor measurements

In this paper the radar-only tracking configuration wasconsidered in order to evaluate the impact of particle filteringtechniques first in a single sensor framework Indeed giventhe hierarchical architecture of the considered system radar-only tracking performance has a significant impact on datafusion operation In particular while in TECVOL projectthe tracking module was based on an EKF-based central-level fusion system for real time applications this paperdiscusses the development of a particle filter technique whichhas been tested in off-line simulations in fact innovativetechniques are expected to provide more accurate estimatesof obstacle dynamics than EKF in case of nonlinear systemsthus reducing the delay in collision detection

4 The Scientific World Journal

4 Developed Software Description

In general the tracking software allows effective fusion ofinformation provided by different sensors such as radar andinertial unit moreover it performs the gatingassociationfunctions in order to associate at the same intruder mea-surements gathered in different scans and to eliminate falsealarms and clutter returns In fact the inputs to the algorithmare sensor measurements which represent in general objectof interest false alarm and clutter In this case most ofthe clutter return will likely come from ground echoesTrackmeasurement association is carried out using ellip-soidal gating and a centralized statistic [31] defined as

120585 = [119910 minus 119910]1015840[119877 + 119867119875119867

1015840]minus1

[119910 minus 119910] (3)

where 119910 is the measurement vector at the time of detection 119910is the predicted measurement vector at the time of detection119875 is the predicted covariance matrix 119867 is the measurementtransition matrix and 119877 is the measurement covariancematrix This statistics is a normalized distance betweenmeasurement and prediction which takes into account allthe relevant uncertainties Assuming a statistical distributionfor 120585 it is then possible to define a threshold based onthe probability of a correct measurement falling inside thegate As an example in common radar applications 120585 isassumed to be distributed as a chi-square variable with anumber of degrees of freedom equal to the dimension of themeasurement vector

After the association phase based on a common nearestneighbour approach since a dense multitarget environmentis unlikely to be found in the considered civil collision avoid-ance scenario the track status must be properly handled Inparticular tracks are divided in three categories one-plot(single observation not associated with any existing track)tentative (at least two observations but confirmation logicis still required) and firm (confirmed track) The transitiontentative firm can be based on different techniques Tracks aredeleted if they are not updated within a reasonable interval

The filtering and prediction phase allows combining trackprediction and sensormeasurements and produces new trackpredictions The tracking system is based on a particle filterwith nonlinear dynamic model and linear measurementequation The state vector is comprised of 6 componentsthat are the obstacle positions in terms of range azimuthand elevation in north-east-down (NED) reference frame andtheir first time derivatives Besides the PF tracker providesalso an estimate of the Distance at Closest Point of ApproachThe obstacle dynamic model is based on a nearly constantvelocity model better described in the following sectionImportant points are related to the sensor latency and theproper inclusion of aircraft navigation measurements Thusproper data registration techniques have been considered asa prerequisite for the developed algorithm [32] Regardingtime registration the radar sends its measurements at theend of each pass with maximum latency of the order of 1 sSince the tracker works at 10Hz in the developed system ameasurement is assigned a time stamp which is the nearesttime on the tracker 01 s scale Since the radar delay is typically

larger than the 01 s scale it is likely that a measurementrelative to time 119905

1arrives when the state has already been

propagated to a later time 119905119899 In this case the state and

covariance must be updated at time 1199051 Also the gating and

association processes have to be performed with values ofstate and covariance at time 119905

1 Then the problem is how to

produce updated parameters from measurement at time 1199051

In order to perform gating association and track updat-ing the solution is to keep inmemory a slidingwindowwherenavigation and track data are stored The considered timewindow dimensions correspond to the largest possible radardata latency Given that state and covariance at time 119905

1have

to be known and stored in the developed PF tracker the keyidea is to consider all the variables at time 119905

1 to perform the

filtering step taking into account the radar measurement atthat time and then update the state (and covariance) untiltime 119905

119899by means of a Monte Carlo approach

41 Particle Filter Algorithm Particle filters are Bayesianestimators that resolve the state estimation problems bydetermining the probability density function (PDF) of anunknown random vector using a weighted sum of delta func-tionsThese filters have less limitations than the Kalman filterIndeed they can exploit nonlinear process and measurementmodels and they can be used with any form of system noisestatistical distribution

The implemented particle filter is based on the samplingimportance resampling algorithm [33] constituted by threemain steps generation of particles calculation of the weightsassociated with the particles and resampling procedureThen the state space is propagated through a nonlineardynamic equation A brief overview of the PF phases isreported

Let us consider a set of points and associated weights inthe target state space 119908(119894)

119896minus1 119909(119894)

119896minus1 for 119894 = 1 119873

119904 which

represent samples from the updated target state PDF at time119896minus1The latter can be represented by a weighted sum of deltafunctions as

119901 (119909119896minus1| 119885119896minus1) asymp

119873

sum

119894=1

119908(119894)

119896minus1120575 (119909119896minus1minus 119909(119894)

119896minus1) (4)

where 119908(119894)119896minus1

is the weight associated with the 119894th particle andsum119873

119894=1119908(119894)

119896minus1= 1

In the developed algorithm the target state space (iethe points and related weights) is initialized generating theparticles from a multivariate normal distribution with meanequal to the first radar measurements and specified standarddeviation values In particular the uncertainties have beenestimated on the basis of obstacle dynamic behavior and radaraccuracy (120590

119903= 9m 120590

120599= 2∘ 120590

120601= 2∘) Choosing a large

initial uncertainty on obstacle position allows letting a goodnumber of particles representing the state in important orhigh likelihood regions Consequently radar measurementshave non-negligible importance in the track initializationphase At the first step all the particles are generated withthe same weight set equal to 1N After that the set of pointsrepresenting 119901(119909

119896minus1| 119885119896minus1) have to be transformed into a set

The Scientific World Journal 5

Estimate at k + 1

State at k + 1

PF initialization

Transition to k + 1

xik+1 = f(xik) + nk

Measurement at k + 1

zik+1 = H(xik+1) + k+1

Prediction at k + 1

xi(k+1|k) = f(xi(k|k)) + nk

Measurement prediction at k + 1

zi(k+1|k) = H(xi(k+1|k)) + k

Weights update at k + 1

Resamplingxi(k+1|k+1) = resampling(xi(k+1|k) wi

k+1)

Generation of particles xikand weights wi

k

exp

Figure 4 Particle filtering algorithm

of points 119908(119894)119896 119909(119894)

119896 representing 119901(119909

119896| 119885119896) This is done by

PF in two steps prediction and filteringThe prediction step exploits the system model to predict

the state distribution function from one measurement timeto another one It transforms the updated density at time119896 minus 1 into a set of points representing the predicted density119901(119909119896| 119885119896minus1) by substituting each sample 119909(119894)

119896minus1in the dynamic

equation Since the state is subject to a process noise modeledas an independent and identically distributed process noisesequence the prediction step translates deforms and spreadsthe state distribution

The filtering step utilizes a measurement at time 119896 toupdate the set of particles representing the propagated density119901(119909119896| 119885119896minus1) to a set of particles 119908(119894)

119896 119909(119894)

119896 sim 119901(119909

119896| 119885119896) with

updated weights The optimal choice is to sample from theupdated density 119901(119909

119896| 119885119896) directly since this is impossible

because it is unknown the solution is to sample from thepropagated density (as in this specific analysis)Then given ameasurement 119911

119896and the set of propagated points 119908(119894)

119896minus1 119909(119894)

119896

the updated set of particles is given by

119908(119894)

119896=

119908(119894)

119896minus1119901 (119911119896| 119909(119894)

119896)

sum119873

119895=1119908(119895)

119896minus1119901 (119911119896| 119909(119895)

119896)

(5)

where 119901(119911119896| 119909(119894)

119896) is the measurement likelihood in this

application it has been defined as

119901 (119911119896| 119909119896) =

1

radic21205871198772

exp(minus(119911119896minus 119896)1015840119877minus1(119911119896minus 119896)

2)

(6)where

119896is the predicted measurement at the time of

detection and 119877 is the measurement covariance matrix

In the software the resampling procedure is based on asystematic resampling scheme [33] which is performed ateach time step and not only when the number of particleswith non-negligible weight falls below a threshold valueThe resampling phase enables a great quantity of particlesto survive during the propagation of the state space thusavoiding the degeneracy phenomenon

The software outputs based on range azimuth elevationand their first time derivatives are then calculated on the basisof the state estimates weighted on all particles

In Figure 4 a particle filtering scheme is reported in orderto better clarify how the developed software has been con-ceived The scheme exploits the main steps of the algorithminitialization prediction filtering and resampling In partic-ular the filtering phase is based on weights update obtainedconsidering measurement prediction sensor outputs andmeasurement covariance matrix 119877

42 Obstacle Tracking Dynamic Model The selection of adynamic model is a nontrivial problem for airborne obstacletracking systems since an accurate estimate of the obstacleposition is considered fundamental for the evaluation of theDistance at Closest Point of Approach In the developedsoftware a nearly constant velocity model in spherical coor-dinates has been implemented to represent the target relativetrajectory [34 35] The target state is propagated through anonlinear dynamic equation since the state variables are inspherical coordinates and thus closer to sensormeasurementsoutputs

The state vector is comprised of obstacle position interms of range azimuth and elevation in north-east-downreference frame and their first time derivatives Hereinafterthe obstacle dynamic model is reported for the sake of clarity

6 The Scientific World Journal

52505

52505

52505

52505

52506

52506

52506

times104

1080

1070

1060

1050

1040

1030

1020

1010

1000

990

GPS time of day (s)

Rang

e (m

)

Spherical PF

GPSRadar

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104

4000

3000

2000

1000

0

GPS time of day (s)

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Rang

e (m

)

GPSRadar

RadarPF tracker

20

0

minus20

minus40

Erro

r in

rang

e (m

)

Spherical PF

Figure 5 Range as estimated by GPS by radar and by radar-only tracker and estimation error as a function of GPS time of day The upperfigure highlights the trajectory of each particle

The target state vector in spherical coordinates is definedas

119909 = [119903 119903 120599 120599 120601 120601] (7)

where 119903 is the range 120599 is the azimuth 120601 is the elevation angleand 119903 120599 120601 are their first time derivatives

In order to evaluate the velocity components let usconsider

V = [

[

V119903

V120599

V120601

]

]

= [

[

119903

119903 120599 cos120601119903 120601

]

]

(8)

where the velocity vector has been defined as V = [V119903 V120599 V120601]

for the sake of simplicity

For a spherical constant velocity dynamic model repre-senting the objectmotion it is assumed that V

119903= V120599= V120601= 0

Taking the time derivative of each component in (8) yields

V119903= 119903 = 0

V120599= 119903 120599 cos 120593 + 119903 120599 cos 120593 minus 119903 120599 sin 120593 = 0

V120601= 119903 + 119903 = 0

(9)

Rearranging the above expressions in terms of angu-lar velocities and considering discrete-time domain with

The Scientific World Journal 7

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PF

100

0

minus100

minus200Azi

mut

h in

NED

refe

renc

e fra

me (

∘ )PF tracker

6

4

2

Erro

r in

stab

ilize

daz

imut

h (∘

)

Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

sampling time 119879 the components of the dynamic motionequation are given by

119903119899= 119903119899minus1+ 119879 119903119899minus1

119903119899= 119903119899minus1

120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +

119879

2119903119899minus1

(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]

120599119899= 120599119899minus1[1 + 119879( 120601

119899minus1119905119892120601119899minus1minus119903119899minus1

119903119899minus1

)]

120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

120601119899= 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

(10)

The nonlinear dynamicmotion equation for the sphericalstate vector can be written as

119909119899= 119891 (119909

119899minus1) + 119899119899minus1 (11)

with the zero-mean Gaussian dynamic acceleration noisedistribution

119899119899sim 119873(0 119876

120588) (12)

The components of 119891(119909119899minus1) are given by the nonlinear

equation (10) and the process noise matrix is

119876120588= [

[

119902119903119876102

02

02119902ℎ119876102

02

02119902V1198761

]

]

(13)

with

1198761=

[[[[

[

1198793

3

1198792

2

1198792

2119879

]]]]

]

(14)

where 119902119903 119902ℎ and 119902V must be set depending on the target

maneuvers [34]Since the model is in spherical coordinates the measure-

ment equation is linear and it can be expressed as

119911119899= 119867119909119899+ 119908119899 (15)

with

119867 = [

[

1 0 0 0 0 0

0 0 1 0 0 0

0 0 0 0 1 0

]

]

(16)

and 119908119899is the observation noise which is considered to be

independent zero-mean Gaussian noise defined by

119908119899sim 119873 (0 119877

119899) (17)

8 The Scientific World Journal

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PFEl

evat

ion

in N

EDre

fere

nce f

ram

e (∘ )

PF tracker

40

minus4minus8minus12

1505

minus05minus15minus25Er

ror i

n st

abili

zed

elev

atio

n (∘

)

Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

minus72

minus76

minus80

minus84

Rang

e rat

e(m

s)

6

2

minus2

minus6Erro

r in

rang

era

te (m

s)

Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day

where 119877119899is the measurement covariance matrix as stated

aboveThe developed obstacle detection and tracking software

provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from

position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as

DCPA119899=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119903 sdot 119881

1003817100381710038171003817100381711988110038171003817100381710038171003817

2119881 minus 119903

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(18)

This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm

The Scientific World Journal 9

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

0

minus1

minus2

minus3

050301

minus01minus03

Azi

mut

h ra

te in

NED

refe

renc

e fra

me (

∘ s)

Erro

r in

stab

ilize

daz

imut

h ra

te (∘

s)

Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day

This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself

5 Results

The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities

(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system

(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage

(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]

(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements

(e) a downlink between intruder and GCS used for flightmonitoring

During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view

In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is

estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system

The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output

The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m

In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)

Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases

10 The Scientific World Journal

Table 1 PF performance in the selected scenario in terms of RMSerror

RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08

have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach

The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation

Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step

In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas

RMS = radic 1119873

119873

sum

119905=1

(119909119905minus 119909119905)2 (19)

where 119873 is the number of measurements 119909119905is the generic

PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909

119905is the

reference value computed on the basis of FLARE and intruderGPS measurements

The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar

In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate

In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

Elev

atio

nh ra

te in

NED

refe

renc

e fra

me (

∘ s)

08

04

0

minus04

minus01minus02minus03minus04minus05Er

ror i

n st

abili

zed

elev

atio

n ra

te (∘

s)

Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day

450

400

350

300

250

200

150

100

50

Distance at Closest Point of Approach (DCPA) (m)

PF trackerEKF trackerGPS

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day

phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase

The Scientific World Journal 11

6 Conclusion and Future Works

This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework

The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as

(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance

(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project

References

[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007

[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008

[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007

[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system

for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008

[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002

[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007

[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013

[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman

filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997

[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013

[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009

[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011

[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012

[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013

[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002

[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001

[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001

[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001

[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960

[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000

[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data

12 The Scientific World Journal

Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002

[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002

[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001

[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013

[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005

[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995

[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000

[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005

[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993

[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010

[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999

[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010

[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004

[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012

[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000

[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008

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2 The Scientific World Journal

some loss of accuracy in obstacle tracking performance Onthe other hand innovative filtering techniques developed fornonlinear systems such as particle filters are expected toprovide more accurate estimates of obstacle dynamics thanEKF thus improving the accuracy of the DCPA estimate andpotentially reducing the delay in collision detection [10]

Thus a research effort has been carried out in orderto assess the impact of particle filtering approaches in theconsidered application

In general tracking problems comprise several applica-tions such as ocean surveillance submarine tracking carpositioning video surveillance and airborne target trackingDifferent solutions and methods have been proposed andimplemented [11ndash16]

One of the key components of a tracking system isthe filtering and prediction block where target motion ismodeled using a state vector and a dynamic system andsensor observations are related to the state vector by aproper measurement equation Within this framework mostpopular solutions are based onKalmanfiltering [17ndash19]whichcan be demonstrated to be the theoretically optimal approachfor linear systems corrupted by gaussian noise In the latestyears particle filtering techniques have found increasingdiffusion in problems involving nonlinear and non-Gaussiannoise processes [20ndash23]

Particle filtering has been applied to various nonlinearproblems such as bearing-only tracking trackingmultitargetin clutter and jump Markov linear system

In [24] the tracking problem is examined in the contextof autonomous bearing-only tracking of a single appear-ingdisappearing target in the presence of clutter measure-ments The same problem is also analyzed in [21] where acomparison between EKF a pseudo measurement trackingfilter and a PF is pointed out The study aims at tracking atarget from an airborne sensor at an approximately knownaltitude The analysis shows the PF algorithm to be morerobust than EKF Karlsson and Gustafsson [25] make acomparison between the two filters for angle-only trackingin several applications such as air-to-air air-to-sea and sea-to-sea scenarios In the study experimental data are used totest the algorithm in the sea-to-sea caseThe results show thatthe PF outperforms the EKF algorithm Besides PF has beenalso applied to solve problems of tracking multiple targetsin clutter environment [26ndash28] These works provide someimplementation suggestions to improve the PF performancewith extension to bootstrap filter

This paper describes a customized particle filtering algo-rithm based on spherical coordinates and aimed at flyingobstacle detection and tracking for non-cooperative senseand avoid On the basis of application needs the algorithmhas been developed to understand PF potential especially interms of reliability and latency in collision risk estimationThus the predicted DCPA between aircraft has been consid-ered as the key variable of the problem

Besides the application field main innovation aspectsof the developed PF algorithm comprise the treatment andcompensation of sensor latencies in view of real time softwareimplementation with the negative timemeasurement updateproblem dealt with keeping in memory a sliding window

B r

VB

VA

AdAB

VAB = VA minus VB

Figure 1 Definition ofminimum separation distance vector 119889119860119861

and using a Monte Carlo sampling approach and the directparticle-based prediction of minimum separation distance

The paper is organized as follows First a brief descriptionof problem geometry and hardware architecture of the systemused in flight tests is provided Then the tracking algorithmis presented in detail Finally results obtained in off-linesimulations based on flight data gathered during TECVOLtest campaign are presented and discussed

2 Obstacle Detection and Tracking forUAS Sense and Avoid

ADSampA systemhas to be endowedwith an obstacle detectionand tracking system that performs the ldquosenserdquo function anda collision avoidance subsystem that performs a collisionavoidance maneuver as soon as a collision risk is detectedIn order to realize a suitable and reliable sense and avoidsystem a series of requirements concerning the field ofregard range resolution angular resolution detection rangetime to collision and system data rate have to be satisfied inthe case of non-cooperative technologies In particular flightregulations define the scanning volume for collision threatdetection and the maximum relative speed between the twoaircraft Moreover they prescribe that the own aircraft andthe intruder must never be closer than 500 ft that is the so-called bubble distance [3]

Considering the above-mentioned requirements they areessentially relevant to the ability to estimate the Distance atClosest Point of Approach and the Time to Closest Point ofApproach often named ldquotime to gordquo in the literature Theformer parameter indicates the minimum distance that willbe measured between two planes that keep their currentvelocity constant it can be calculated from [4]

119889119860119861=119903 sdot 119881119860119861

100381710038171003817100381711988111986011986110038171003817100381710038172119881119860119861minus 119903 (1)

where 119889119860119861

is the minimum separation distance (whose normis the DCPA) [29]119881

119860119861is the relative speed vector (119881

119860minus119881119861)

between the intruder (aircraft 119860) and the ownship (aircraft119861) and 119903 is the relative position between the aircraft (seeFigure 1) If the intruder is modeled as a spherical object withradius 119877 it can be demonstrated [4] that assuming constantvelocity vectors 119881

119860and 119881

119861 respectively the two aircraft are

headed for collision if and only if the following conditions aresatisfied

10038171003817100381710038171198891198601198611003817100381710038171003817 le 119877 119903 lt 0 (2)

The Scientific World Journal 3

These values are a measure of the collision risk if theseconditions are satisfied a Near Mid-Air Collision threat isconsidered

It is worth noting that in order to obtain an accurateestimate of the DCPA an adequate sensor setup has to beproperly chosen In general this function can be performedinstalling onboard UAS cooperative andor non-cooperativesystems that include both active and passive sensors thechoice depends on size speed maneuverability andmissionsfor which theUASwill be used In case of largeUAS platformsand fully autonomous systems integrated radarelectro-optical architecture seems to be a good option to increasethe collision threat awareness In fact radars provide accuraterange estimates and can operate in all-time all-weatherconditions while EO sensors offer the potential of accurateangular measurements at fast update rates in addition thesesystems do not rely on information from external sources todetect and track other aircraft thus avoiding problems due tothe loss of communication links

As anticipated above within TECVOL project a con-figuration with radar as main sensor and EO as auxiliarysensors has been chosen as the optimal solution in view of theapplication In fact this project aimed at the development andflight demonstration of the technologies needed to supporthigh altitude long endurance UAS flight autonomy Thechoice of a multisensor configuration allows a compensationof single sensor shortcomings by integrating informationfrom heterogeneous sources In the next section for the sakeof clarity the flight system architecture is briefly described

3 Flight System Architecture

During the TECVOL flight test campaign the prototypehardwaresoftware sensing system installed onboard FLARE(Figure 2) was comprised of a Ka-band pulse radar and fourelectro-optical cameras (two visible cameras and two infraredcameras) a CPU devoted to image processing (IP-CPU) anda CPU devoted to real time tracking by sensor data fusion(RTT-CPU) This unit is connected to the onboard flightcontrol computer that performs autonomous navigation andflight control including autonomous collision avoidancemaneuvers [4 7 30] A hierarchical architecture in which theradar is the main sensor that must perform initial detectionand tracking and the EO sensors are used as auxiliary infor-mation sources in order to increase accuracy and data ratehas been consideredThe choice of a hierarchical architectureis determined by different levels of sensor performance infact the conventional EO sensors perform initial detectionat closer ranges than radar The standalone radar trackingestimates can be effective in reducing the computation timeand false alarm rate of EO image processing by selecting prop-erly defined search windows to apply the obstacle detectionprocess

In Figure 3 the adopted hardware system is depictedFor more details on the hardware and logical architecturesadopted within TECVOL project the reader is referred to[4 7]

Figure 2 Sensing system onboard FLARE

AHRS

Radar Panchro vis Color vis Infrared Infrared

Ethernet

EthernetFirewire link

Can BUS

GNC systemGPS

AIR

ALT

Navigation sensors

Image processingcomputer

Real timecomputer

Figure 3 The onboard hardware architecture

The tracking system can operate in two different modes

(1) standalone radar tracking mode that performs cur-rent estimates of obstacle relative position and veloc-ity on the basis of measurements from radar and theinertial unit

(2) radarEO tracking mode where current estimates ofobstacle relative position and velocity are determinedalso on the basis of EO sensor measurements

In this paper the radar-only tracking configuration wasconsidered in order to evaluate the impact of particle filteringtechniques first in a single sensor framework Indeed giventhe hierarchical architecture of the considered system radar-only tracking performance has a significant impact on datafusion operation In particular while in TECVOL projectthe tracking module was based on an EKF-based central-level fusion system for real time applications this paperdiscusses the development of a particle filter technique whichhas been tested in off-line simulations in fact innovativetechniques are expected to provide more accurate estimatesof obstacle dynamics than EKF in case of nonlinear systemsthus reducing the delay in collision detection

4 The Scientific World Journal

4 Developed Software Description

In general the tracking software allows effective fusion ofinformation provided by different sensors such as radar andinertial unit moreover it performs the gatingassociationfunctions in order to associate at the same intruder mea-surements gathered in different scans and to eliminate falsealarms and clutter returns In fact the inputs to the algorithmare sensor measurements which represent in general objectof interest false alarm and clutter In this case most ofthe clutter return will likely come from ground echoesTrackmeasurement association is carried out using ellip-soidal gating and a centralized statistic [31] defined as

120585 = [119910 minus 119910]1015840[119877 + 119867119875119867

1015840]minus1

[119910 minus 119910] (3)

where 119910 is the measurement vector at the time of detection 119910is the predicted measurement vector at the time of detection119875 is the predicted covariance matrix 119867 is the measurementtransition matrix and 119877 is the measurement covariancematrix This statistics is a normalized distance betweenmeasurement and prediction which takes into account allthe relevant uncertainties Assuming a statistical distributionfor 120585 it is then possible to define a threshold based onthe probability of a correct measurement falling inside thegate As an example in common radar applications 120585 isassumed to be distributed as a chi-square variable with anumber of degrees of freedom equal to the dimension of themeasurement vector

After the association phase based on a common nearestneighbour approach since a dense multitarget environmentis unlikely to be found in the considered civil collision avoid-ance scenario the track status must be properly handled Inparticular tracks are divided in three categories one-plot(single observation not associated with any existing track)tentative (at least two observations but confirmation logicis still required) and firm (confirmed track) The transitiontentative firm can be based on different techniques Tracks aredeleted if they are not updated within a reasonable interval

The filtering and prediction phase allows combining trackprediction and sensormeasurements and produces new trackpredictions The tracking system is based on a particle filterwith nonlinear dynamic model and linear measurementequation The state vector is comprised of 6 componentsthat are the obstacle positions in terms of range azimuthand elevation in north-east-down (NED) reference frame andtheir first time derivatives Besides the PF tracker providesalso an estimate of the Distance at Closest Point of ApproachThe obstacle dynamic model is based on a nearly constantvelocity model better described in the following sectionImportant points are related to the sensor latency and theproper inclusion of aircraft navigation measurements Thusproper data registration techniques have been considered asa prerequisite for the developed algorithm [32] Regardingtime registration the radar sends its measurements at theend of each pass with maximum latency of the order of 1 sSince the tracker works at 10Hz in the developed system ameasurement is assigned a time stamp which is the nearesttime on the tracker 01 s scale Since the radar delay is typically

larger than the 01 s scale it is likely that a measurementrelative to time 119905

1arrives when the state has already been

propagated to a later time 119905119899 In this case the state and

covariance must be updated at time 1199051 Also the gating and

association processes have to be performed with values ofstate and covariance at time 119905

1 Then the problem is how to

produce updated parameters from measurement at time 1199051

In order to perform gating association and track updat-ing the solution is to keep inmemory a slidingwindowwherenavigation and track data are stored The considered timewindow dimensions correspond to the largest possible radardata latency Given that state and covariance at time 119905

1have

to be known and stored in the developed PF tracker the keyidea is to consider all the variables at time 119905

1 to perform the

filtering step taking into account the radar measurement atthat time and then update the state (and covariance) untiltime 119905

119899by means of a Monte Carlo approach

41 Particle Filter Algorithm Particle filters are Bayesianestimators that resolve the state estimation problems bydetermining the probability density function (PDF) of anunknown random vector using a weighted sum of delta func-tionsThese filters have less limitations than the Kalman filterIndeed they can exploit nonlinear process and measurementmodels and they can be used with any form of system noisestatistical distribution

The implemented particle filter is based on the samplingimportance resampling algorithm [33] constituted by threemain steps generation of particles calculation of the weightsassociated with the particles and resampling procedureThen the state space is propagated through a nonlineardynamic equation A brief overview of the PF phases isreported

Let us consider a set of points and associated weights inthe target state space 119908(119894)

119896minus1 119909(119894)

119896minus1 for 119894 = 1 119873

119904 which

represent samples from the updated target state PDF at time119896minus1The latter can be represented by a weighted sum of deltafunctions as

119901 (119909119896minus1| 119885119896minus1) asymp

119873

sum

119894=1

119908(119894)

119896minus1120575 (119909119896minus1minus 119909(119894)

119896minus1) (4)

where 119908(119894)119896minus1

is the weight associated with the 119894th particle andsum119873

119894=1119908(119894)

119896minus1= 1

In the developed algorithm the target state space (iethe points and related weights) is initialized generating theparticles from a multivariate normal distribution with meanequal to the first radar measurements and specified standarddeviation values In particular the uncertainties have beenestimated on the basis of obstacle dynamic behavior and radaraccuracy (120590

119903= 9m 120590

120599= 2∘ 120590

120601= 2∘) Choosing a large

initial uncertainty on obstacle position allows letting a goodnumber of particles representing the state in important orhigh likelihood regions Consequently radar measurementshave non-negligible importance in the track initializationphase At the first step all the particles are generated withthe same weight set equal to 1N After that the set of pointsrepresenting 119901(119909

119896minus1| 119885119896minus1) have to be transformed into a set

The Scientific World Journal 5

Estimate at k + 1

State at k + 1

PF initialization

Transition to k + 1

xik+1 = f(xik) + nk

Measurement at k + 1

zik+1 = H(xik+1) + k+1

Prediction at k + 1

xi(k+1|k) = f(xi(k|k)) + nk

Measurement prediction at k + 1

zi(k+1|k) = H(xi(k+1|k)) + k

Weights update at k + 1

Resamplingxi(k+1|k+1) = resampling(xi(k+1|k) wi

k+1)

Generation of particles xikand weights wi

k

exp

Figure 4 Particle filtering algorithm

of points 119908(119894)119896 119909(119894)

119896 representing 119901(119909

119896| 119885119896) This is done by

PF in two steps prediction and filteringThe prediction step exploits the system model to predict

the state distribution function from one measurement timeto another one It transforms the updated density at time119896 minus 1 into a set of points representing the predicted density119901(119909119896| 119885119896minus1) by substituting each sample 119909(119894)

119896minus1in the dynamic

equation Since the state is subject to a process noise modeledas an independent and identically distributed process noisesequence the prediction step translates deforms and spreadsthe state distribution

The filtering step utilizes a measurement at time 119896 toupdate the set of particles representing the propagated density119901(119909119896| 119885119896minus1) to a set of particles 119908(119894)

119896 119909(119894)

119896 sim 119901(119909

119896| 119885119896) with

updated weights The optimal choice is to sample from theupdated density 119901(119909

119896| 119885119896) directly since this is impossible

because it is unknown the solution is to sample from thepropagated density (as in this specific analysis)Then given ameasurement 119911

119896and the set of propagated points 119908(119894)

119896minus1 119909(119894)

119896

the updated set of particles is given by

119908(119894)

119896=

119908(119894)

119896minus1119901 (119911119896| 119909(119894)

119896)

sum119873

119895=1119908(119895)

119896minus1119901 (119911119896| 119909(119895)

119896)

(5)

where 119901(119911119896| 119909(119894)

119896) is the measurement likelihood in this

application it has been defined as

119901 (119911119896| 119909119896) =

1

radic21205871198772

exp(minus(119911119896minus 119896)1015840119877minus1(119911119896minus 119896)

2)

(6)where

119896is the predicted measurement at the time of

detection and 119877 is the measurement covariance matrix

In the software the resampling procedure is based on asystematic resampling scheme [33] which is performed ateach time step and not only when the number of particleswith non-negligible weight falls below a threshold valueThe resampling phase enables a great quantity of particlesto survive during the propagation of the state space thusavoiding the degeneracy phenomenon

The software outputs based on range azimuth elevationand their first time derivatives are then calculated on the basisof the state estimates weighted on all particles

In Figure 4 a particle filtering scheme is reported in orderto better clarify how the developed software has been con-ceived The scheme exploits the main steps of the algorithminitialization prediction filtering and resampling In partic-ular the filtering phase is based on weights update obtainedconsidering measurement prediction sensor outputs andmeasurement covariance matrix 119877

42 Obstacle Tracking Dynamic Model The selection of adynamic model is a nontrivial problem for airborne obstacletracking systems since an accurate estimate of the obstacleposition is considered fundamental for the evaluation of theDistance at Closest Point of Approach In the developedsoftware a nearly constant velocity model in spherical coor-dinates has been implemented to represent the target relativetrajectory [34 35] The target state is propagated through anonlinear dynamic equation since the state variables are inspherical coordinates and thus closer to sensormeasurementsoutputs

The state vector is comprised of obstacle position interms of range azimuth and elevation in north-east-downreference frame and their first time derivatives Hereinafterthe obstacle dynamic model is reported for the sake of clarity

6 The Scientific World Journal

52505

52505

52505

52505

52506

52506

52506

times104

1080

1070

1060

1050

1040

1030

1020

1010

1000

990

GPS time of day (s)

Rang

e (m

)

Spherical PF

GPSRadar

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104

4000

3000

2000

1000

0

GPS time of day (s)

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Rang

e (m

)

GPSRadar

RadarPF tracker

20

0

minus20

minus40

Erro

r in

rang

e (m

)

Spherical PF

Figure 5 Range as estimated by GPS by radar and by radar-only tracker and estimation error as a function of GPS time of day The upperfigure highlights the trajectory of each particle

The target state vector in spherical coordinates is definedas

119909 = [119903 119903 120599 120599 120601 120601] (7)

where 119903 is the range 120599 is the azimuth 120601 is the elevation angleand 119903 120599 120601 are their first time derivatives

In order to evaluate the velocity components let usconsider

V = [

[

V119903

V120599

V120601

]

]

= [

[

119903

119903 120599 cos120601119903 120601

]

]

(8)

where the velocity vector has been defined as V = [V119903 V120599 V120601]

for the sake of simplicity

For a spherical constant velocity dynamic model repre-senting the objectmotion it is assumed that V

119903= V120599= V120601= 0

Taking the time derivative of each component in (8) yields

V119903= 119903 = 0

V120599= 119903 120599 cos 120593 + 119903 120599 cos 120593 minus 119903 120599 sin 120593 = 0

V120601= 119903 + 119903 = 0

(9)

Rearranging the above expressions in terms of angu-lar velocities and considering discrete-time domain with

The Scientific World Journal 7

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PF

100

0

minus100

minus200Azi

mut

h in

NED

refe

renc

e fra

me (

∘ )PF tracker

6

4

2

Erro

r in

stab

ilize

daz

imut

h (∘

)

Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

sampling time 119879 the components of the dynamic motionequation are given by

119903119899= 119903119899minus1+ 119879 119903119899minus1

119903119899= 119903119899minus1

120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +

119879

2119903119899minus1

(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]

120599119899= 120599119899minus1[1 + 119879( 120601

119899minus1119905119892120601119899minus1minus119903119899minus1

119903119899minus1

)]

120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

120601119899= 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

(10)

The nonlinear dynamicmotion equation for the sphericalstate vector can be written as

119909119899= 119891 (119909

119899minus1) + 119899119899minus1 (11)

with the zero-mean Gaussian dynamic acceleration noisedistribution

119899119899sim 119873(0 119876

120588) (12)

The components of 119891(119909119899minus1) are given by the nonlinear

equation (10) and the process noise matrix is

119876120588= [

[

119902119903119876102

02

02119902ℎ119876102

02

02119902V1198761

]

]

(13)

with

1198761=

[[[[

[

1198793

3

1198792

2

1198792

2119879

]]]]

]

(14)

where 119902119903 119902ℎ and 119902V must be set depending on the target

maneuvers [34]Since the model is in spherical coordinates the measure-

ment equation is linear and it can be expressed as

119911119899= 119867119909119899+ 119908119899 (15)

with

119867 = [

[

1 0 0 0 0 0

0 0 1 0 0 0

0 0 0 0 1 0

]

]

(16)

and 119908119899is the observation noise which is considered to be

independent zero-mean Gaussian noise defined by

119908119899sim 119873 (0 119877

119899) (17)

8 The Scientific World Journal

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PFEl

evat

ion

in N

EDre

fere

nce f

ram

e (∘ )

PF tracker

40

minus4minus8minus12

1505

minus05minus15minus25Er

ror i

n st

abili

zed

elev

atio

n (∘

)

Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

minus72

minus76

minus80

minus84

Rang

e rat

e(m

s)

6

2

minus2

minus6Erro

r in

rang

era

te (m

s)

Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day

where 119877119899is the measurement covariance matrix as stated

aboveThe developed obstacle detection and tracking software

provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from

position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as

DCPA119899=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119903 sdot 119881

1003817100381710038171003817100381711988110038171003817100381710038171003817

2119881 minus 119903

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(18)

This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm

The Scientific World Journal 9

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

0

minus1

minus2

minus3

050301

minus01minus03

Azi

mut

h ra

te in

NED

refe

renc

e fra

me (

∘ s)

Erro

r in

stab

ilize

daz

imut

h ra

te (∘

s)

Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day

This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself

5 Results

The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities

(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system

(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage

(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]

(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements

(e) a downlink between intruder and GCS used for flightmonitoring

During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view

In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is

estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system

The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output

The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m

In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)

Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases

10 The Scientific World Journal

Table 1 PF performance in the selected scenario in terms of RMSerror

RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08

have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach

The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation

Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step

In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas

RMS = radic 1119873

119873

sum

119905=1

(119909119905minus 119909119905)2 (19)

where 119873 is the number of measurements 119909119905is the generic

PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909

119905is the

reference value computed on the basis of FLARE and intruderGPS measurements

The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar

In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate

In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

Elev

atio

nh ra

te in

NED

refe

renc

e fra

me (

∘ s)

08

04

0

minus04

minus01minus02minus03minus04minus05Er

ror i

n st

abili

zed

elev

atio

n ra

te (∘

s)

Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day

450

400

350

300

250

200

150

100

50

Distance at Closest Point of Approach (DCPA) (m)

PF trackerEKF trackerGPS

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day

phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase

The Scientific World Journal 11

6 Conclusion and Future Works

This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework

The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as

(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance

(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project

References

[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007

[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008

[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007

[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system

for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008

[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002

[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007

[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013

[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman

filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997

[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013

[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009

[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011

[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012

[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013

[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002

[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001

[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001

[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001

[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960

[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000

[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data

12 The Scientific World Journal

Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002

[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002

[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001

[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013

[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005

[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995

[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000

[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005

[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993

[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010

[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999

[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010

[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004

[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012

[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000

[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008

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International Journal of

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DistributedSensor Networks

International Journal of

The Scientific World Journal 3

These values are a measure of the collision risk if theseconditions are satisfied a Near Mid-Air Collision threat isconsidered

It is worth noting that in order to obtain an accurateestimate of the DCPA an adequate sensor setup has to beproperly chosen In general this function can be performedinstalling onboard UAS cooperative andor non-cooperativesystems that include both active and passive sensors thechoice depends on size speed maneuverability andmissionsfor which theUASwill be used In case of largeUAS platformsand fully autonomous systems integrated radarelectro-optical architecture seems to be a good option to increasethe collision threat awareness In fact radars provide accuraterange estimates and can operate in all-time all-weatherconditions while EO sensors offer the potential of accurateangular measurements at fast update rates in addition thesesystems do not rely on information from external sources todetect and track other aircraft thus avoiding problems due tothe loss of communication links

As anticipated above within TECVOL project a con-figuration with radar as main sensor and EO as auxiliarysensors has been chosen as the optimal solution in view of theapplication In fact this project aimed at the development andflight demonstration of the technologies needed to supporthigh altitude long endurance UAS flight autonomy Thechoice of a multisensor configuration allows a compensationof single sensor shortcomings by integrating informationfrom heterogeneous sources In the next section for the sakeof clarity the flight system architecture is briefly described

3 Flight System Architecture

During the TECVOL flight test campaign the prototypehardwaresoftware sensing system installed onboard FLARE(Figure 2) was comprised of a Ka-band pulse radar and fourelectro-optical cameras (two visible cameras and two infraredcameras) a CPU devoted to image processing (IP-CPU) anda CPU devoted to real time tracking by sensor data fusion(RTT-CPU) This unit is connected to the onboard flightcontrol computer that performs autonomous navigation andflight control including autonomous collision avoidancemaneuvers [4 7 30] A hierarchical architecture in which theradar is the main sensor that must perform initial detectionand tracking and the EO sensors are used as auxiliary infor-mation sources in order to increase accuracy and data ratehas been consideredThe choice of a hierarchical architectureis determined by different levels of sensor performance infact the conventional EO sensors perform initial detectionat closer ranges than radar The standalone radar trackingestimates can be effective in reducing the computation timeand false alarm rate of EO image processing by selecting prop-erly defined search windows to apply the obstacle detectionprocess

In Figure 3 the adopted hardware system is depictedFor more details on the hardware and logical architecturesadopted within TECVOL project the reader is referred to[4 7]

Figure 2 Sensing system onboard FLARE

AHRS

Radar Panchro vis Color vis Infrared Infrared

Ethernet

EthernetFirewire link

Can BUS

GNC systemGPS

AIR

ALT

Navigation sensors

Image processingcomputer

Real timecomputer

Figure 3 The onboard hardware architecture

The tracking system can operate in two different modes

(1) standalone radar tracking mode that performs cur-rent estimates of obstacle relative position and veloc-ity on the basis of measurements from radar and theinertial unit

(2) radarEO tracking mode where current estimates ofobstacle relative position and velocity are determinedalso on the basis of EO sensor measurements

In this paper the radar-only tracking configuration wasconsidered in order to evaluate the impact of particle filteringtechniques first in a single sensor framework Indeed giventhe hierarchical architecture of the considered system radar-only tracking performance has a significant impact on datafusion operation In particular while in TECVOL projectthe tracking module was based on an EKF-based central-level fusion system for real time applications this paperdiscusses the development of a particle filter technique whichhas been tested in off-line simulations in fact innovativetechniques are expected to provide more accurate estimatesof obstacle dynamics than EKF in case of nonlinear systemsthus reducing the delay in collision detection

4 The Scientific World Journal

4 Developed Software Description

In general the tracking software allows effective fusion ofinformation provided by different sensors such as radar andinertial unit moreover it performs the gatingassociationfunctions in order to associate at the same intruder mea-surements gathered in different scans and to eliminate falsealarms and clutter returns In fact the inputs to the algorithmare sensor measurements which represent in general objectof interest false alarm and clutter In this case most ofthe clutter return will likely come from ground echoesTrackmeasurement association is carried out using ellip-soidal gating and a centralized statistic [31] defined as

120585 = [119910 minus 119910]1015840[119877 + 119867119875119867

1015840]minus1

[119910 minus 119910] (3)

where 119910 is the measurement vector at the time of detection 119910is the predicted measurement vector at the time of detection119875 is the predicted covariance matrix 119867 is the measurementtransition matrix and 119877 is the measurement covariancematrix This statistics is a normalized distance betweenmeasurement and prediction which takes into account allthe relevant uncertainties Assuming a statistical distributionfor 120585 it is then possible to define a threshold based onthe probability of a correct measurement falling inside thegate As an example in common radar applications 120585 isassumed to be distributed as a chi-square variable with anumber of degrees of freedom equal to the dimension of themeasurement vector

After the association phase based on a common nearestneighbour approach since a dense multitarget environmentis unlikely to be found in the considered civil collision avoid-ance scenario the track status must be properly handled Inparticular tracks are divided in three categories one-plot(single observation not associated with any existing track)tentative (at least two observations but confirmation logicis still required) and firm (confirmed track) The transitiontentative firm can be based on different techniques Tracks aredeleted if they are not updated within a reasonable interval

The filtering and prediction phase allows combining trackprediction and sensormeasurements and produces new trackpredictions The tracking system is based on a particle filterwith nonlinear dynamic model and linear measurementequation The state vector is comprised of 6 componentsthat are the obstacle positions in terms of range azimuthand elevation in north-east-down (NED) reference frame andtheir first time derivatives Besides the PF tracker providesalso an estimate of the Distance at Closest Point of ApproachThe obstacle dynamic model is based on a nearly constantvelocity model better described in the following sectionImportant points are related to the sensor latency and theproper inclusion of aircraft navigation measurements Thusproper data registration techniques have been considered asa prerequisite for the developed algorithm [32] Regardingtime registration the radar sends its measurements at theend of each pass with maximum latency of the order of 1 sSince the tracker works at 10Hz in the developed system ameasurement is assigned a time stamp which is the nearesttime on the tracker 01 s scale Since the radar delay is typically

larger than the 01 s scale it is likely that a measurementrelative to time 119905

1arrives when the state has already been

propagated to a later time 119905119899 In this case the state and

covariance must be updated at time 1199051 Also the gating and

association processes have to be performed with values ofstate and covariance at time 119905

1 Then the problem is how to

produce updated parameters from measurement at time 1199051

In order to perform gating association and track updat-ing the solution is to keep inmemory a slidingwindowwherenavigation and track data are stored The considered timewindow dimensions correspond to the largest possible radardata latency Given that state and covariance at time 119905

1have

to be known and stored in the developed PF tracker the keyidea is to consider all the variables at time 119905

1 to perform the

filtering step taking into account the radar measurement atthat time and then update the state (and covariance) untiltime 119905

119899by means of a Monte Carlo approach

41 Particle Filter Algorithm Particle filters are Bayesianestimators that resolve the state estimation problems bydetermining the probability density function (PDF) of anunknown random vector using a weighted sum of delta func-tionsThese filters have less limitations than the Kalman filterIndeed they can exploit nonlinear process and measurementmodels and they can be used with any form of system noisestatistical distribution

The implemented particle filter is based on the samplingimportance resampling algorithm [33] constituted by threemain steps generation of particles calculation of the weightsassociated with the particles and resampling procedureThen the state space is propagated through a nonlineardynamic equation A brief overview of the PF phases isreported

Let us consider a set of points and associated weights inthe target state space 119908(119894)

119896minus1 119909(119894)

119896minus1 for 119894 = 1 119873

119904 which

represent samples from the updated target state PDF at time119896minus1The latter can be represented by a weighted sum of deltafunctions as

119901 (119909119896minus1| 119885119896minus1) asymp

119873

sum

119894=1

119908(119894)

119896minus1120575 (119909119896minus1minus 119909(119894)

119896minus1) (4)

where 119908(119894)119896minus1

is the weight associated with the 119894th particle andsum119873

119894=1119908(119894)

119896minus1= 1

In the developed algorithm the target state space (iethe points and related weights) is initialized generating theparticles from a multivariate normal distribution with meanequal to the first radar measurements and specified standarddeviation values In particular the uncertainties have beenestimated on the basis of obstacle dynamic behavior and radaraccuracy (120590

119903= 9m 120590

120599= 2∘ 120590

120601= 2∘) Choosing a large

initial uncertainty on obstacle position allows letting a goodnumber of particles representing the state in important orhigh likelihood regions Consequently radar measurementshave non-negligible importance in the track initializationphase At the first step all the particles are generated withthe same weight set equal to 1N After that the set of pointsrepresenting 119901(119909

119896minus1| 119885119896minus1) have to be transformed into a set

The Scientific World Journal 5

Estimate at k + 1

State at k + 1

PF initialization

Transition to k + 1

xik+1 = f(xik) + nk

Measurement at k + 1

zik+1 = H(xik+1) + k+1

Prediction at k + 1

xi(k+1|k) = f(xi(k|k)) + nk

Measurement prediction at k + 1

zi(k+1|k) = H(xi(k+1|k)) + k

Weights update at k + 1

Resamplingxi(k+1|k+1) = resampling(xi(k+1|k) wi

k+1)

Generation of particles xikand weights wi

k

exp

Figure 4 Particle filtering algorithm

of points 119908(119894)119896 119909(119894)

119896 representing 119901(119909

119896| 119885119896) This is done by

PF in two steps prediction and filteringThe prediction step exploits the system model to predict

the state distribution function from one measurement timeto another one It transforms the updated density at time119896 minus 1 into a set of points representing the predicted density119901(119909119896| 119885119896minus1) by substituting each sample 119909(119894)

119896minus1in the dynamic

equation Since the state is subject to a process noise modeledas an independent and identically distributed process noisesequence the prediction step translates deforms and spreadsthe state distribution

The filtering step utilizes a measurement at time 119896 toupdate the set of particles representing the propagated density119901(119909119896| 119885119896minus1) to a set of particles 119908(119894)

119896 119909(119894)

119896 sim 119901(119909

119896| 119885119896) with

updated weights The optimal choice is to sample from theupdated density 119901(119909

119896| 119885119896) directly since this is impossible

because it is unknown the solution is to sample from thepropagated density (as in this specific analysis)Then given ameasurement 119911

119896and the set of propagated points 119908(119894)

119896minus1 119909(119894)

119896

the updated set of particles is given by

119908(119894)

119896=

119908(119894)

119896minus1119901 (119911119896| 119909(119894)

119896)

sum119873

119895=1119908(119895)

119896minus1119901 (119911119896| 119909(119895)

119896)

(5)

where 119901(119911119896| 119909(119894)

119896) is the measurement likelihood in this

application it has been defined as

119901 (119911119896| 119909119896) =

1

radic21205871198772

exp(minus(119911119896minus 119896)1015840119877minus1(119911119896minus 119896)

2)

(6)where

119896is the predicted measurement at the time of

detection and 119877 is the measurement covariance matrix

In the software the resampling procedure is based on asystematic resampling scheme [33] which is performed ateach time step and not only when the number of particleswith non-negligible weight falls below a threshold valueThe resampling phase enables a great quantity of particlesto survive during the propagation of the state space thusavoiding the degeneracy phenomenon

The software outputs based on range azimuth elevationand their first time derivatives are then calculated on the basisof the state estimates weighted on all particles

In Figure 4 a particle filtering scheme is reported in orderto better clarify how the developed software has been con-ceived The scheme exploits the main steps of the algorithminitialization prediction filtering and resampling In partic-ular the filtering phase is based on weights update obtainedconsidering measurement prediction sensor outputs andmeasurement covariance matrix 119877

42 Obstacle Tracking Dynamic Model The selection of adynamic model is a nontrivial problem for airborne obstacletracking systems since an accurate estimate of the obstacleposition is considered fundamental for the evaluation of theDistance at Closest Point of Approach In the developedsoftware a nearly constant velocity model in spherical coor-dinates has been implemented to represent the target relativetrajectory [34 35] The target state is propagated through anonlinear dynamic equation since the state variables are inspherical coordinates and thus closer to sensormeasurementsoutputs

The state vector is comprised of obstacle position interms of range azimuth and elevation in north-east-downreference frame and their first time derivatives Hereinafterthe obstacle dynamic model is reported for the sake of clarity

6 The Scientific World Journal

52505

52505

52505

52505

52506

52506

52506

times104

1080

1070

1060

1050

1040

1030

1020

1010

1000

990

GPS time of day (s)

Rang

e (m

)

Spherical PF

GPSRadar

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525

52502

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52512

52514

times104

4000

3000

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1000

0

GPS time of day (s)

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times104GPS time of day (s)

Rang

e (m

)

GPSRadar

RadarPF tracker

20

0

minus20

minus40

Erro

r in

rang

e (m

)

Spherical PF

Figure 5 Range as estimated by GPS by radar and by radar-only tracker and estimation error as a function of GPS time of day The upperfigure highlights the trajectory of each particle

The target state vector in spherical coordinates is definedas

119909 = [119903 119903 120599 120599 120601 120601] (7)

where 119903 is the range 120599 is the azimuth 120601 is the elevation angleand 119903 120599 120601 are their first time derivatives

In order to evaluate the velocity components let usconsider

V = [

[

V119903

V120599

V120601

]

]

= [

[

119903

119903 120599 cos120601119903 120601

]

]

(8)

where the velocity vector has been defined as V = [V119903 V120599 V120601]

for the sake of simplicity

For a spherical constant velocity dynamic model repre-senting the objectmotion it is assumed that V

119903= V120599= V120601= 0

Taking the time derivative of each component in (8) yields

V119903= 119903 = 0

V120599= 119903 120599 cos 120593 + 119903 120599 cos 120593 minus 119903 120599 sin 120593 = 0

V120601= 119903 + 119903 = 0

(9)

Rearranging the above expressions in terms of angu-lar velocities and considering discrete-time domain with

The Scientific World Journal 7

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GPS

Radar

RadarPF tracker

Spherical PF

Spherical PF

100

0

minus100

minus200Azi

mut

h in

NED

refe

renc

e fra

me (

∘ )PF tracker

6

4

2

Erro

r in

stab

ilize

daz

imut

h (∘

)

Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

sampling time 119879 the components of the dynamic motionequation are given by

119903119899= 119903119899minus1+ 119879 119903119899minus1

119903119899= 119903119899minus1

120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +

119879

2119903119899minus1

(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]

120599119899= 120599119899minus1[1 + 119879( 120601

119899minus1119905119892120601119899minus1minus119903119899minus1

119903119899minus1

)]

120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

120601119899= 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

(10)

The nonlinear dynamicmotion equation for the sphericalstate vector can be written as

119909119899= 119891 (119909

119899minus1) + 119899119899minus1 (11)

with the zero-mean Gaussian dynamic acceleration noisedistribution

119899119899sim 119873(0 119876

120588) (12)

The components of 119891(119909119899minus1) are given by the nonlinear

equation (10) and the process noise matrix is

119876120588= [

[

119902119903119876102

02

02119902ℎ119876102

02

02119902V1198761

]

]

(13)

with

1198761=

[[[[

[

1198793

3

1198792

2

1198792

2119879

]]]]

]

(14)

where 119902119903 119902ℎ and 119902V must be set depending on the target

maneuvers [34]Since the model is in spherical coordinates the measure-

ment equation is linear and it can be expressed as

119911119899= 119867119909119899+ 119908119899 (15)

with

119867 = [

[

1 0 0 0 0 0

0 0 1 0 0 0

0 0 0 0 1 0

]

]

(16)

and 119908119899is the observation noise which is considered to be

independent zero-mean Gaussian noise defined by

119908119899sim 119873 (0 119877

119899) (17)

8 The Scientific World Journal

52494

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times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PFEl

evat

ion

in N

EDre

fere

nce f

ram

e (∘ )

PF tracker

40

minus4minus8minus12

1505

minus05minus15minus25Er

ror i

n st

abili

zed

elev

atio

n (∘

)

Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

52494

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GPS

PF tracker

Spherical PF

Spherical PFPF tracker

minus72

minus76

minus80

minus84

Rang

e rat

e(m

s)

6

2

minus2

minus6Erro

r in

rang

era

te (m

s)

Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day

where 119877119899is the measurement covariance matrix as stated

aboveThe developed obstacle detection and tracking software

provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from

position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as

DCPA119899=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119903 sdot 119881

1003817100381710038171003817100381711988110038171003817100381710038171003817

2119881 minus 119903

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(18)

This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm

The Scientific World Journal 9

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GPS

PF tracker

Spherical PF

Spherical PFPF tracker

0

minus1

minus2

minus3

050301

minus01minus03

Azi

mut

h ra

te in

NED

refe

renc

e fra

me (

∘ s)

Erro

r in

stab

ilize

daz

imut

h ra

te (∘

s)

Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day

This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself

5 Results

The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities

(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system

(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage

(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]

(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements

(e) a downlink between intruder and GCS used for flightmonitoring

During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view

In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is

estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system

The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output

The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m

In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)

Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases

10 The Scientific World Journal

Table 1 PF performance in the selected scenario in terms of RMSerror

RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08

have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach

The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation

Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step

In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas

RMS = radic 1119873

119873

sum

119905=1

(119909119905minus 119909119905)2 (19)

where 119873 is the number of measurements 119909119905is the generic

PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909

119905is the

reference value computed on the basis of FLARE and intruderGPS measurements

The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar

In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate

In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial

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PF tracker

Spherical PF

Spherical PFPF tracker

Elev

atio

nh ra

te in

NED

refe

renc

e fra

me (

∘ s)

08

04

0

minus04

minus01minus02minus03minus04minus05Er

ror i

n st

abili

zed

elev

atio

n ra

te (∘

s)

Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day

450

400

350

300

250

200

150

100

50

Distance at Closest Point of Approach (DCPA) (m)

PF trackerEKF trackerGPS

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Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day

phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase

The Scientific World Journal 11

6 Conclusion and Future Works

This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework

The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as

(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance

(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project

References

[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007

[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008

[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007

[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system

for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008

[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002

[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007

[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013

[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman

filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997

[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013

[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009

[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011

[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012

[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013

[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002

[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001

[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001

[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001

[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960

[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000

[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data

12 The Scientific World Journal

Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002

[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002

[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001

[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013

[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005

[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995

[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000

[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005

[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993

[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010

[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999

[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010

[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004

[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012

[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000

[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008

International Journal of

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation

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DistributedSensor Networks

International Journal of

4 The Scientific World Journal

4 Developed Software Description

In general the tracking software allows effective fusion ofinformation provided by different sensors such as radar andinertial unit moreover it performs the gatingassociationfunctions in order to associate at the same intruder mea-surements gathered in different scans and to eliminate falsealarms and clutter returns In fact the inputs to the algorithmare sensor measurements which represent in general objectof interest false alarm and clutter In this case most ofthe clutter return will likely come from ground echoesTrackmeasurement association is carried out using ellip-soidal gating and a centralized statistic [31] defined as

120585 = [119910 minus 119910]1015840[119877 + 119867119875119867

1015840]minus1

[119910 minus 119910] (3)

where 119910 is the measurement vector at the time of detection 119910is the predicted measurement vector at the time of detection119875 is the predicted covariance matrix 119867 is the measurementtransition matrix and 119877 is the measurement covariancematrix This statistics is a normalized distance betweenmeasurement and prediction which takes into account allthe relevant uncertainties Assuming a statistical distributionfor 120585 it is then possible to define a threshold based onthe probability of a correct measurement falling inside thegate As an example in common radar applications 120585 isassumed to be distributed as a chi-square variable with anumber of degrees of freedom equal to the dimension of themeasurement vector

After the association phase based on a common nearestneighbour approach since a dense multitarget environmentis unlikely to be found in the considered civil collision avoid-ance scenario the track status must be properly handled Inparticular tracks are divided in three categories one-plot(single observation not associated with any existing track)tentative (at least two observations but confirmation logicis still required) and firm (confirmed track) The transitiontentative firm can be based on different techniques Tracks aredeleted if they are not updated within a reasonable interval

The filtering and prediction phase allows combining trackprediction and sensormeasurements and produces new trackpredictions The tracking system is based on a particle filterwith nonlinear dynamic model and linear measurementequation The state vector is comprised of 6 componentsthat are the obstacle positions in terms of range azimuthand elevation in north-east-down (NED) reference frame andtheir first time derivatives Besides the PF tracker providesalso an estimate of the Distance at Closest Point of ApproachThe obstacle dynamic model is based on a nearly constantvelocity model better described in the following sectionImportant points are related to the sensor latency and theproper inclusion of aircraft navigation measurements Thusproper data registration techniques have been considered asa prerequisite for the developed algorithm [32] Regardingtime registration the radar sends its measurements at theend of each pass with maximum latency of the order of 1 sSince the tracker works at 10Hz in the developed system ameasurement is assigned a time stamp which is the nearesttime on the tracker 01 s scale Since the radar delay is typically

larger than the 01 s scale it is likely that a measurementrelative to time 119905

1arrives when the state has already been

propagated to a later time 119905119899 In this case the state and

covariance must be updated at time 1199051 Also the gating and

association processes have to be performed with values ofstate and covariance at time 119905

1 Then the problem is how to

produce updated parameters from measurement at time 1199051

In order to perform gating association and track updat-ing the solution is to keep inmemory a slidingwindowwherenavigation and track data are stored The considered timewindow dimensions correspond to the largest possible radardata latency Given that state and covariance at time 119905

1have

to be known and stored in the developed PF tracker the keyidea is to consider all the variables at time 119905

1 to perform the

filtering step taking into account the radar measurement atthat time and then update the state (and covariance) untiltime 119905

119899by means of a Monte Carlo approach

41 Particle Filter Algorithm Particle filters are Bayesianestimators that resolve the state estimation problems bydetermining the probability density function (PDF) of anunknown random vector using a weighted sum of delta func-tionsThese filters have less limitations than the Kalman filterIndeed they can exploit nonlinear process and measurementmodels and they can be used with any form of system noisestatistical distribution

The implemented particle filter is based on the samplingimportance resampling algorithm [33] constituted by threemain steps generation of particles calculation of the weightsassociated with the particles and resampling procedureThen the state space is propagated through a nonlineardynamic equation A brief overview of the PF phases isreported

Let us consider a set of points and associated weights inthe target state space 119908(119894)

119896minus1 119909(119894)

119896minus1 for 119894 = 1 119873

119904 which

represent samples from the updated target state PDF at time119896minus1The latter can be represented by a weighted sum of deltafunctions as

119901 (119909119896minus1| 119885119896minus1) asymp

119873

sum

119894=1

119908(119894)

119896minus1120575 (119909119896minus1minus 119909(119894)

119896minus1) (4)

where 119908(119894)119896minus1

is the weight associated with the 119894th particle andsum119873

119894=1119908(119894)

119896minus1= 1

In the developed algorithm the target state space (iethe points and related weights) is initialized generating theparticles from a multivariate normal distribution with meanequal to the first radar measurements and specified standarddeviation values In particular the uncertainties have beenestimated on the basis of obstacle dynamic behavior and radaraccuracy (120590

119903= 9m 120590

120599= 2∘ 120590

120601= 2∘) Choosing a large

initial uncertainty on obstacle position allows letting a goodnumber of particles representing the state in important orhigh likelihood regions Consequently radar measurementshave non-negligible importance in the track initializationphase At the first step all the particles are generated withthe same weight set equal to 1N After that the set of pointsrepresenting 119901(119909

119896minus1| 119885119896minus1) have to be transformed into a set

The Scientific World Journal 5

Estimate at k + 1

State at k + 1

PF initialization

Transition to k + 1

xik+1 = f(xik) + nk

Measurement at k + 1

zik+1 = H(xik+1) + k+1

Prediction at k + 1

xi(k+1|k) = f(xi(k|k)) + nk

Measurement prediction at k + 1

zi(k+1|k) = H(xi(k+1|k)) + k

Weights update at k + 1

Resamplingxi(k+1|k+1) = resampling(xi(k+1|k) wi

k+1)

Generation of particles xikand weights wi

k

exp

Figure 4 Particle filtering algorithm

of points 119908(119894)119896 119909(119894)

119896 representing 119901(119909

119896| 119885119896) This is done by

PF in two steps prediction and filteringThe prediction step exploits the system model to predict

the state distribution function from one measurement timeto another one It transforms the updated density at time119896 minus 1 into a set of points representing the predicted density119901(119909119896| 119885119896minus1) by substituting each sample 119909(119894)

119896minus1in the dynamic

equation Since the state is subject to a process noise modeledas an independent and identically distributed process noisesequence the prediction step translates deforms and spreadsthe state distribution

The filtering step utilizes a measurement at time 119896 toupdate the set of particles representing the propagated density119901(119909119896| 119885119896minus1) to a set of particles 119908(119894)

119896 119909(119894)

119896 sim 119901(119909

119896| 119885119896) with

updated weights The optimal choice is to sample from theupdated density 119901(119909

119896| 119885119896) directly since this is impossible

because it is unknown the solution is to sample from thepropagated density (as in this specific analysis)Then given ameasurement 119911

119896and the set of propagated points 119908(119894)

119896minus1 119909(119894)

119896

the updated set of particles is given by

119908(119894)

119896=

119908(119894)

119896minus1119901 (119911119896| 119909(119894)

119896)

sum119873

119895=1119908(119895)

119896minus1119901 (119911119896| 119909(119895)

119896)

(5)

where 119901(119911119896| 119909(119894)

119896) is the measurement likelihood in this

application it has been defined as

119901 (119911119896| 119909119896) =

1

radic21205871198772

exp(minus(119911119896minus 119896)1015840119877minus1(119911119896minus 119896)

2)

(6)where

119896is the predicted measurement at the time of

detection and 119877 is the measurement covariance matrix

In the software the resampling procedure is based on asystematic resampling scheme [33] which is performed ateach time step and not only when the number of particleswith non-negligible weight falls below a threshold valueThe resampling phase enables a great quantity of particlesto survive during the propagation of the state space thusavoiding the degeneracy phenomenon

The software outputs based on range azimuth elevationand their first time derivatives are then calculated on the basisof the state estimates weighted on all particles

In Figure 4 a particle filtering scheme is reported in orderto better clarify how the developed software has been con-ceived The scheme exploits the main steps of the algorithminitialization prediction filtering and resampling In partic-ular the filtering phase is based on weights update obtainedconsidering measurement prediction sensor outputs andmeasurement covariance matrix 119877

42 Obstacle Tracking Dynamic Model The selection of adynamic model is a nontrivial problem for airborne obstacletracking systems since an accurate estimate of the obstacleposition is considered fundamental for the evaluation of theDistance at Closest Point of Approach In the developedsoftware a nearly constant velocity model in spherical coor-dinates has been implemented to represent the target relativetrajectory [34 35] The target state is propagated through anonlinear dynamic equation since the state variables are inspherical coordinates and thus closer to sensormeasurementsoutputs

The state vector is comprised of obstacle position interms of range azimuth and elevation in north-east-downreference frame and their first time derivatives Hereinafterthe obstacle dynamic model is reported for the sake of clarity

6 The Scientific World Journal

52505

52505

52505

52505

52506

52506

52506

times104

1080

1070

1060

1050

1040

1030

1020

1010

1000

990

GPS time of day (s)

Rang

e (m

)

Spherical PF

GPSRadar

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104

4000

3000

2000

1000

0

GPS time of day (s)

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Rang

e (m

)

GPSRadar

RadarPF tracker

20

0

minus20

minus40

Erro

r in

rang

e (m

)

Spherical PF

Figure 5 Range as estimated by GPS by radar and by radar-only tracker and estimation error as a function of GPS time of day The upperfigure highlights the trajectory of each particle

The target state vector in spherical coordinates is definedas

119909 = [119903 119903 120599 120599 120601 120601] (7)

where 119903 is the range 120599 is the azimuth 120601 is the elevation angleand 119903 120599 120601 are their first time derivatives

In order to evaluate the velocity components let usconsider

V = [

[

V119903

V120599

V120601

]

]

= [

[

119903

119903 120599 cos120601119903 120601

]

]

(8)

where the velocity vector has been defined as V = [V119903 V120599 V120601]

for the sake of simplicity

For a spherical constant velocity dynamic model repre-senting the objectmotion it is assumed that V

119903= V120599= V120601= 0

Taking the time derivative of each component in (8) yields

V119903= 119903 = 0

V120599= 119903 120599 cos 120593 + 119903 120599 cos 120593 minus 119903 120599 sin 120593 = 0

V120601= 119903 + 119903 = 0

(9)

Rearranging the above expressions in terms of angu-lar velocities and considering discrete-time domain with

The Scientific World Journal 7

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PF

100

0

minus100

minus200Azi

mut

h in

NED

refe

renc

e fra

me (

∘ )PF tracker

6

4

2

Erro

r in

stab

ilize

daz

imut

h (∘

)

Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

sampling time 119879 the components of the dynamic motionequation are given by

119903119899= 119903119899minus1+ 119879 119903119899minus1

119903119899= 119903119899minus1

120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +

119879

2119903119899minus1

(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]

120599119899= 120599119899minus1[1 + 119879( 120601

119899minus1119905119892120601119899minus1minus119903119899minus1

119903119899minus1

)]

120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

120601119899= 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

(10)

The nonlinear dynamicmotion equation for the sphericalstate vector can be written as

119909119899= 119891 (119909

119899minus1) + 119899119899minus1 (11)

with the zero-mean Gaussian dynamic acceleration noisedistribution

119899119899sim 119873(0 119876

120588) (12)

The components of 119891(119909119899minus1) are given by the nonlinear

equation (10) and the process noise matrix is

119876120588= [

[

119902119903119876102

02

02119902ℎ119876102

02

02119902V1198761

]

]

(13)

with

1198761=

[[[[

[

1198793

3

1198792

2

1198792

2119879

]]]]

]

(14)

where 119902119903 119902ℎ and 119902V must be set depending on the target

maneuvers [34]Since the model is in spherical coordinates the measure-

ment equation is linear and it can be expressed as

119911119899= 119867119909119899+ 119908119899 (15)

with

119867 = [

[

1 0 0 0 0 0

0 0 1 0 0 0

0 0 0 0 1 0

]

]

(16)

and 119908119899is the observation noise which is considered to be

independent zero-mean Gaussian noise defined by

119908119899sim 119873 (0 119877

119899) (17)

8 The Scientific World Journal

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PFEl

evat

ion

in N

EDre

fere

nce f

ram

e (∘ )

PF tracker

40

minus4minus8minus12

1505

minus05minus15minus25Er

ror i

n st

abili

zed

elev

atio

n (∘

)

Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

minus72

minus76

minus80

minus84

Rang

e rat

e(m

s)

6

2

minus2

minus6Erro

r in

rang

era

te (m

s)

Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day

where 119877119899is the measurement covariance matrix as stated

aboveThe developed obstacle detection and tracking software

provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from

position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as

DCPA119899=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119903 sdot 119881

1003817100381710038171003817100381711988110038171003817100381710038171003817

2119881 minus 119903

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(18)

This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm

The Scientific World Journal 9

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

0

minus1

minus2

minus3

050301

minus01minus03

Azi

mut

h ra

te in

NED

refe

renc

e fra

me (

∘ s)

Erro

r in

stab

ilize

daz

imut

h ra

te (∘

s)

Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day

This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself

5 Results

The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities

(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system

(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage

(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]

(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements

(e) a downlink between intruder and GCS used for flightmonitoring

During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view

In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is

estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system

The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output

The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m

In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)

Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases

10 The Scientific World Journal

Table 1 PF performance in the selected scenario in terms of RMSerror

RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08

have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach

The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation

Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step

In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas

RMS = radic 1119873

119873

sum

119905=1

(119909119905minus 119909119905)2 (19)

where 119873 is the number of measurements 119909119905is the generic

PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909

119905is the

reference value computed on the basis of FLARE and intruderGPS measurements

The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar

In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate

In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

Elev

atio

nh ra

te in

NED

refe

renc

e fra

me (

∘ s)

08

04

0

minus04

minus01minus02minus03minus04minus05Er

ror i

n st

abili

zed

elev

atio

n ra

te (∘

s)

Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day

450

400

350

300

250

200

150

100

50

Distance at Closest Point of Approach (DCPA) (m)

PF trackerEKF trackerGPS

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day

phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase

The Scientific World Journal 11

6 Conclusion and Future Works

This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework

The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as

(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance

(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project

References

[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007

[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008

[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007

[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system

for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008

[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002

[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007

[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013

[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman

filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997

[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013

[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009

[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011

[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012

[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013

[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002

[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001

[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001

[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001

[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960

[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000

[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data

12 The Scientific World Journal

Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002

[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002

[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001

[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013

[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005

[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995

[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000

[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005

[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993

[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010

[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999

[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010

[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004

[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012

[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000

[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008

International Journal of

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Active and Passive Electronic Components

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Submit your manuscripts athttpwwwhindawicom

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DistributedSensor Networks

International Journal of

The Scientific World Journal 5

Estimate at k + 1

State at k + 1

PF initialization

Transition to k + 1

xik+1 = f(xik) + nk

Measurement at k + 1

zik+1 = H(xik+1) + k+1

Prediction at k + 1

xi(k+1|k) = f(xi(k|k)) + nk

Measurement prediction at k + 1

zi(k+1|k) = H(xi(k+1|k)) + k

Weights update at k + 1

Resamplingxi(k+1|k+1) = resampling(xi(k+1|k) wi

k+1)

Generation of particles xikand weights wi

k

exp

Figure 4 Particle filtering algorithm

of points 119908(119894)119896 119909(119894)

119896 representing 119901(119909

119896| 119885119896) This is done by

PF in two steps prediction and filteringThe prediction step exploits the system model to predict

the state distribution function from one measurement timeto another one It transforms the updated density at time119896 minus 1 into a set of points representing the predicted density119901(119909119896| 119885119896minus1) by substituting each sample 119909(119894)

119896minus1in the dynamic

equation Since the state is subject to a process noise modeledas an independent and identically distributed process noisesequence the prediction step translates deforms and spreadsthe state distribution

The filtering step utilizes a measurement at time 119896 toupdate the set of particles representing the propagated density119901(119909119896| 119885119896minus1) to a set of particles 119908(119894)

119896 119909(119894)

119896 sim 119901(119909

119896| 119885119896) with

updated weights The optimal choice is to sample from theupdated density 119901(119909

119896| 119885119896) directly since this is impossible

because it is unknown the solution is to sample from thepropagated density (as in this specific analysis)Then given ameasurement 119911

119896and the set of propagated points 119908(119894)

119896minus1 119909(119894)

119896

the updated set of particles is given by

119908(119894)

119896=

119908(119894)

119896minus1119901 (119911119896| 119909(119894)

119896)

sum119873

119895=1119908(119895)

119896minus1119901 (119911119896| 119909(119895)

119896)

(5)

where 119901(119911119896| 119909(119894)

119896) is the measurement likelihood in this

application it has been defined as

119901 (119911119896| 119909119896) =

1

radic21205871198772

exp(minus(119911119896minus 119896)1015840119877minus1(119911119896minus 119896)

2)

(6)where

119896is the predicted measurement at the time of

detection and 119877 is the measurement covariance matrix

In the software the resampling procedure is based on asystematic resampling scheme [33] which is performed ateach time step and not only when the number of particleswith non-negligible weight falls below a threshold valueThe resampling phase enables a great quantity of particlesto survive during the propagation of the state space thusavoiding the degeneracy phenomenon

The software outputs based on range azimuth elevationand their first time derivatives are then calculated on the basisof the state estimates weighted on all particles

In Figure 4 a particle filtering scheme is reported in orderto better clarify how the developed software has been con-ceived The scheme exploits the main steps of the algorithminitialization prediction filtering and resampling In partic-ular the filtering phase is based on weights update obtainedconsidering measurement prediction sensor outputs andmeasurement covariance matrix 119877

42 Obstacle Tracking Dynamic Model The selection of adynamic model is a nontrivial problem for airborne obstacletracking systems since an accurate estimate of the obstacleposition is considered fundamental for the evaluation of theDistance at Closest Point of Approach In the developedsoftware a nearly constant velocity model in spherical coor-dinates has been implemented to represent the target relativetrajectory [34 35] The target state is propagated through anonlinear dynamic equation since the state variables are inspherical coordinates and thus closer to sensormeasurementsoutputs

The state vector is comprised of obstacle position interms of range azimuth and elevation in north-east-downreference frame and their first time derivatives Hereinafterthe obstacle dynamic model is reported for the sake of clarity

6 The Scientific World Journal

52505

52505

52505

52505

52506

52506

52506

times104

1080

1070

1060

1050

1040

1030

1020

1010

1000

990

GPS time of day (s)

Rang

e (m

)

Spherical PF

GPSRadar

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104

4000

3000

2000

1000

0

GPS time of day (s)

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Rang

e (m

)

GPSRadar

RadarPF tracker

20

0

minus20

minus40

Erro

r in

rang

e (m

)

Spherical PF

Figure 5 Range as estimated by GPS by radar and by radar-only tracker and estimation error as a function of GPS time of day The upperfigure highlights the trajectory of each particle

The target state vector in spherical coordinates is definedas

119909 = [119903 119903 120599 120599 120601 120601] (7)

where 119903 is the range 120599 is the azimuth 120601 is the elevation angleand 119903 120599 120601 are their first time derivatives

In order to evaluate the velocity components let usconsider

V = [

[

V119903

V120599

V120601

]

]

= [

[

119903

119903 120599 cos120601119903 120601

]

]

(8)

where the velocity vector has been defined as V = [V119903 V120599 V120601]

for the sake of simplicity

For a spherical constant velocity dynamic model repre-senting the objectmotion it is assumed that V

119903= V120599= V120601= 0

Taking the time derivative of each component in (8) yields

V119903= 119903 = 0

V120599= 119903 120599 cos 120593 + 119903 120599 cos 120593 minus 119903 120599 sin 120593 = 0

V120601= 119903 + 119903 = 0

(9)

Rearranging the above expressions in terms of angu-lar velocities and considering discrete-time domain with

The Scientific World Journal 7

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PF

100

0

minus100

minus200Azi

mut

h in

NED

refe

renc

e fra

me (

∘ )PF tracker

6

4

2

Erro

r in

stab

ilize

daz

imut

h (∘

)

Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

sampling time 119879 the components of the dynamic motionequation are given by

119903119899= 119903119899minus1+ 119879 119903119899minus1

119903119899= 119903119899minus1

120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +

119879

2119903119899minus1

(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]

120599119899= 120599119899minus1[1 + 119879( 120601

119899minus1119905119892120601119899minus1minus119903119899minus1

119903119899minus1

)]

120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

120601119899= 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

(10)

The nonlinear dynamicmotion equation for the sphericalstate vector can be written as

119909119899= 119891 (119909

119899minus1) + 119899119899minus1 (11)

with the zero-mean Gaussian dynamic acceleration noisedistribution

119899119899sim 119873(0 119876

120588) (12)

The components of 119891(119909119899minus1) are given by the nonlinear

equation (10) and the process noise matrix is

119876120588= [

[

119902119903119876102

02

02119902ℎ119876102

02

02119902V1198761

]

]

(13)

with

1198761=

[[[[

[

1198793

3

1198792

2

1198792

2119879

]]]]

]

(14)

where 119902119903 119902ℎ and 119902V must be set depending on the target

maneuvers [34]Since the model is in spherical coordinates the measure-

ment equation is linear and it can be expressed as

119911119899= 119867119909119899+ 119908119899 (15)

with

119867 = [

[

1 0 0 0 0 0

0 0 1 0 0 0

0 0 0 0 1 0

]

]

(16)

and 119908119899is the observation noise which is considered to be

independent zero-mean Gaussian noise defined by

119908119899sim 119873 (0 119877

119899) (17)

8 The Scientific World Journal

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PFEl

evat

ion

in N

EDre

fere

nce f

ram

e (∘ )

PF tracker

40

minus4minus8minus12

1505

minus05minus15minus25Er

ror i

n st

abili

zed

elev

atio

n (∘

)

Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

minus72

minus76

minus80

minus84

Rang

e rat

e(m

s)

6

2

minus2

minus6Erro

r in

rang

era

te (m

s)

Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day

where 119877119899is the measurement covariance matrix as stated

aboveThe developed obstacle detection and tracking software

provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from

position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as

DCPA119899=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119903 sdot 119881

1003817100381710038171003817100381711988110038171003817100381710038171003817

2119881 minus 119903

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(18)

This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm

The Scientific World Journal 9

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

0

minus1

minus2

minus3

050301

minus01minus03

Azi

mut

h ra

te in

NED

refe

renc

e fra

me (

∘ s)

Erro

r in

stab

ilize

daz

imut

h ra

te (∘

s)

Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day

This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself

5 Results

The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities

(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system

(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage

(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]

(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements

(e) a downlink between intruder and GCS used for flightmonitoring

During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view

In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is

estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system

The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output

The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m

In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)

Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases

10 The Scientific World Journal

Table 1 PF performance in the selected scenario in terms of RMSerror

RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08

have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach

The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation

Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step

In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas

RMS = radic 1119873

119873

sum

119905=1

(119909119905minus 119909119905)2 (19)

where 119873 is the number of measurements 119909119905is the generic

PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909

119905is the

reference value computed on the basis of FLARE and intruderGPS measurements

The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar

In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate

In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

Elev

atio

nh ra

te in

NED

refe

renc

e fra

me (

∘ s)

08

04

0

minus04

minus01minus02minus03minus04minus05Er

ror i

n st

abili

zed

elev

atio

n ra

te (∘

s)

Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day

450

400

350

300

250

200

150

100

50

Distance at Closest Point of Approach (DCPA) (m)

PF trackerEKF trackerGPS

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day

phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase

The Scientific World Journal 11

6 Conclusion and Future Works

This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework

The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as

(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance

(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project

References

[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007

[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008

[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007

[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system

for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008

[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002

[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007

[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013

[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman

filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997

[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013

[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009

[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011

[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012

[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013

[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002

[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001

[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001

[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001

[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960

[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000

[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data

12 The Scientific World Journal

Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002

[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002

[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001

[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013

[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005

[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995

[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000

[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005

[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993

[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010

[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999

[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010

[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004

[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012

[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000

[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 The Scientific World Journal

52505

52505

52505

52505

52506

52506

52506

times104

1080

1070

1060

1050

1040

1030

1020

1010

1000

990

GPS time of day (s)

Rang

e (m

)

Spherical PF

GPSRadar

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104

4000

3000

2000

1000

0

GPS time of day (s)

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Rang

e (m

)

GPSRadar

RadarPF tracker

20

0

minus20

minus40

Erro

r in

rang

e (m

)

Spherical PF

Figure 5 Range as estimated by GPS by radar and by radar-only tracker and estimation error as a function of GPS time of day The upperfigure highlights the trajectory of each particle

The target state vector in spherical coordinates is definedas

119909 = [119903 119903 120599 120599 120601 120601] (7)

where 119903 is the range 120599 is the azimuth 120601 is the elevation angleand 119903 120599 120601 are their first time derivatives

In order to evaluate the velocity components let usconsider

V = [

[

V119903

V120599

V120601

]

]

= [

[

119903

119903 120599 cos120601119903 120601

]

]

(8)

where the velocity vector has been defined as V = [V119903 V120599 V120601]

for the sake of simplicity

For a spherical constant velocity dynamic model repre-senting the objectmotion it is assumed that V

119903= V120599= V120601= 0

Taking the time derivative of each component in (8) yields

V119903= 119903 = 0

V120599= 119903 120599 cos 120593 + 119903 120599 cos 120593 minus 119903 120599 sin 120593 = 0

V120601= 119903 + 119903 = 0

(9)

Rearranging the above expressions in terms of angu-lar velocities and considering discrete-time domain with

The Scientific World Journal 7

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PF

100

0

minus100

minus200Azi

mut

h in

NED

refe

renc

e fra

me (

∘ )PF tracker

6

4

2

Erro

r in

stab

ilize

daz

imut

h (∘

)

Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

sampling time 119879 the components of the dynamic motionequation are given by

119903119899= 119903119899minus1+ 119879 119903119899minus1

119903119899= 119903119899minus1

120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +

119879

2119903119899minus1

(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]

120599119899= 120599119899minus1[1 + 119879( 120601

119899minus1119905119892120601119899minus1minus119903119899minus1

119903119899minus1

)]

120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

120601119899= 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

(10)

The nonlinear dynamicmotion equation for the sphericalstate vector can be written as

119909119899= 119891 (119909

119899minus1) + 119899119899minus1 (11)

with the zero-mean Gaussian dynamic acceleration noisedistribution

119899119899sim 119873(0 119876

120588) (12)

The components of 119891(119909119899minus1) are given by the nonlinear

equation (10) and the process noise matrix is

119876120588= [

[

119902119903119876102

02

02119902ℎ119876102

02

02119902V1198761

]

]

(13)

with

1198761=

[[[[

[

1198793

3

1198792

2

1198792

2119879

]]]]

]

(14)

where 119902119903 119902ℎ and 119902V must be set depending on the target

maneuvers [34]Since the model is in spherical coordinates the measure-

ment equation is linear and it can be expressed as

119911119899= 119867119909119899+ 119908119899 (15)

with

119867 = [

[

1 0 0 0 0 0

0 0 1 0 0 0

0 0 0 0 1 0

]

]

(16)

and 119908119899is the observation noise which is considered to be

independent zero-mean Gaussian noise defined by

119908119899sim 119873 (0 119877

119899) (17)

8 The Scientific World Journal

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PFEl

evat

ion

in N

EDre

fere

nce f

ram

e (∘ )

PF tracker

40

minus4minus8minus12

1505

minus05minus15minus25Er

ror i

n st

abili

zed

elev

atio

n (∘

)

Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

minus72

minus76

minus80

minus84

Rang

e rat

e(m

s)

6

2

minus2

minus6Erro

r in

rang

era

te (m

s)

Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day

where 119877119899is the measurement covariance matrix as stated

aboveThe developed obstacle detection and tracking software

provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from

position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as

DCPA119899=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119903 sdot 119881

1003817100381710038171003817100381711988110038171003817100381710038171003817

2119881 minus 119903

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(18)

This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm

The Scientific World Journal 9

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

0

minus1

minus2

minus3

050301

minus01minus03

Azi

mut

h ra

te in

NED

refe

renc

e fra

me (

∘ s)

Erro

r in

stab

ilize

daz

imut

h ra

te (∘

s)

Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day

This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself

5 Results

The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities

(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system

(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage

(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]

(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements

(e) a downlink between intruder and GCS used for flightmonitoring

During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view

In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is

estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system

The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output

The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m

In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)

Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases

10 The Scientific World Journal

Table 1 PF performance in the selected scenario in terms of RMSerror

RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08

have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach

The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation

Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step

In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas

RMS = radic 1119873

119873

sum

119905=1

(119909119905minus 119909119905)2 (19)

where 119873 is the number of measurements 119909119905is the generic

PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909

119905is the

reference value computed on the basis of FLARE and intruderGPS measurements

The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar

In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate

In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

Elev

atio

nh ra

te in

NED

refe

renc

e fra

me (

∘ s)

08

04

0

minus04

minus01minus02minus03minus04minus05Er

ror i

n st

abili

zed

elev

atio

n ra

te (∘

s)

Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day

450

400

350

300

250

200

150

100

50

Distance at Closest Point of Approach (DCPA) (m)

PF trackerEKF trackerGPS

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day

phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase

The Scientific World Journal 11

6 Conclusion and Future Works

This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework

The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as

(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance

(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project

References

[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007

[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008

[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007

[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system

for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008

[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002

[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007

[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013

[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman

filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997

[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013

[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009

[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011

[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012

[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013

[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002

[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001

[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001

[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001

[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960

[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000

[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data

12 The Scientific World Journal

Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002

[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002

[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001

[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013

[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005

[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995

[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000

[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005

[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993

[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010

[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999

[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010

[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004

[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012

[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000

[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

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International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

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Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

The Scientific World Journal 7

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PF

100

0

minus100

minus200Azi

mut

h in

NED

refe

renc

e fra

me (

∘ )PF tracker

6

4

2

Erro

r in

stab

ilize

daz

imut

h (∘

)

Figure 6 Azimuth in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

sampling time 119879 the components of the dynamic motionequation are given by

119903119899= 119903119899minus1+ 119879 119903119899minus1

119903119899= 119903119899minus1

120599119899= 120599119899minus1+ 119879 120599119899minus1[1 +

119879

2119903119899minus1

(119903119899minus1120601119899minus1119905119892120601119899minus1minus 119903119899minus1)]

120599119899= 120599119899minus1[1 + 119879( 120601

119899minus1119905119892120601119899minus1minus119903119899minus1

119903119899minus1

)]

120601119899= 120601119899minus1+ 119879 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

120601119899= 120601119899minus1[1 minus

119879

2119903119899minus1

119903119899minus1]

(10)

The nonlinear dynamicmotion equation for the sphericalstate vector can be written as

119909119899= 119891 (119909

119899minus1) + 119899119899minus1 (11)

with the zero-mean Gaussian dynamic acceleration noisedistribution

119899119899sim 119873(0 119876

120588) (12)

The components of 119891(119909119899minus1) are given by the nonlinear

equation (10) and the process noise matrix is

119876120588= [

[

119902119903119876102

02

02119902ℎ119876102

02

02119902V1198761

]

]

(13)

with

1198761=

[[[[

[

1198793

3

1198792

2

1198792

2119879

]]]]

]

(14)

where 119902119903 119902ℎ and 119902V must be set depending on the target

maneuvers [34]Since the model is in spherical coordinates the measure-

ment equation is linear and it can be expressed as

119911119899= 119867119909119899+ 119908119899 (15)

with

119867 = [

[

1 0 0 0 0 0

0 0 1 0 0 0

0 0 0 0 1 0

]

]

(16)

and 119908119899is the observation noise which is considered to be

independent zero-mean Gaussian noise defined by

119908119899sim 119873 (0 119877

119899) (17)

8 The Scientific World Journal

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PFEl

evat

ion

in N

EDre

fere

nce f

ram

e (∘ )

PF tracker

40

minus4minus8minus12

1505

minus05minus15minus25Er

ror i

n st

abili

zed

elev

atio

n (∘

)

Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

minus72

minus76

minus80

minus84

Rang

e rat

e(m

s)

6

2

minus2

minus6Erro

r in

rang

era

te (m

s)

Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day

where 119877119899is the measurement covariance matrix as stated

aboveThe developed obstacle detection and tracking software

provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from

position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as

DCPA119899=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119903 sdot 119881

1003817100381710038171003817100381711988110038171003817100381710038171003817

2119881 minus 119903

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(18)

This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm

The Scientific World Journal 9

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

0

minus1

minus2

minus3

050301

minus01minus03

Azi

mut

h ra

te in

NED

refe

renc

e fra

me (

∘ s)

Erro

r in

stab

ilize

daz

imut

h ra

te (∘

s)

Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day

This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself

5 Results

The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities

(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system

(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage

(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]

(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements

(e) a downlink between intruder and GCS used for flightmonitoring

During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view

In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is

estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system

The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output

The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m

In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)

Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases

10 The Scientific World Journal

Table 1 PF performance in the selected scenario in terms of RMSerror

RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08

have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach

The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation

Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step

In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas

RMS = radic 1119873

119873

sum

119905=1

(119909119905minus 119909119905)2 (19)

where 119873 is the number of measurements 119909119905is the generic

PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909

119905is the

reference value computed on the basis of FLARE and intruderGPS measurements

The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar

In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate

In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

Elev

atio

nh ra

te in

NED

refe

renc

e fra

me (

∘ s)

08

04

0

minus04

minus01minus02minus03minus04minus05Er

ror i

n st

abili

zed

elev

atio

n ra

te (∘

s)

Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day

450

400

350

300

250

200

150

100

50

Distance at Closest Point of Approach (DCPA) (m)

PF trackerEKF trackerGPS

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day

phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase

The Scientific World Journal 11

6 Conclusion and Future Works

This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework

The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as

(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance

(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project

References

[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007

[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008

[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007

[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system

for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008

[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002

[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007

[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013

[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman

filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997

[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013

[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009

[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011

[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012

[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013

[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002

[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001

[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001

[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001

[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960

[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000

[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data

12 The Scientific World Journal

Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002

[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002

[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001

[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013

[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005

[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995

[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000

[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005

[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993

[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010

[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999

[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010

[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004

[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012

[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000

[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 The Scientific World Journal

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

Radar

RadarPF tracker

Spherical PF

Spherical PFEl

evat

ion

in N

EDre

fere

nce f

ram

e (∘ )

PF tracker

40

minus4minus8minus12

1505

minus05minus15minus25Er

ror i

n st

abili

zed

elev

atio

n (∘

)

Figure 7 Elevation in NED reference frame as estimated by GPS by radar and by radar-only tracker and estimation error as a function ofGPS time of day

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

minus72

minus76

minus80

minus84

Rang

e rat

e(m

s)

6

2

minus2

minus6Erro

r in

rang

era

te (m

s)

Figure 8 Range rate as estimated by GPS and by radar-only tracker and estimation error as a function of GPS time of day

where 119877119899is the measurement covariance matrix as stated

aboveThe developed obstacle detection and tracking software

provides also an estimate of the Distance at Closest Pointof Approach (see (1)) Since the particles are characterizedby own positions and velocities and given the nonlineardependencies between 119903119881 andDCPA the latter is calculatedfor each particle In this way in order to avoid furtherapproximations due to the evaluation of this distance from

position and velocitymean values DCPA has been calculatedas mean value of the different distances evaluated as

DCPA119899=

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119903 sdot 119881

1003817100381710038171003817100381711988110038171003817100381710038171003817

2119881 minus 119903

100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(18)

This is a form of ldquodeep integrationrdquo of a collision detectionsensor since an estimate of the level of collision threat isdetermined by means of the same data fusion algorithm

The Scientific World Journal 9

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

0

minus1

minus2

minus3

050301

minus01minus03

Azi

mut

h ra

te in

NED

refe

renc

e fra

me (

∘ s)

Erro

r in

stab

ilize

daz

imut

h ra

te (∘

s)

Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day

This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself

5 Results

The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities

(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system

(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage

(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]

(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements

(e) a downlink between intruder and GCS used for flightmonitoring

During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view

In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is

estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system

The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output

The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m

In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)

Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases

10 The Scientific World Journal

Table 1 PF performance in the selected scenario in terms of RMSerror

RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08

have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach

The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation

Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step

In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas

RMS = radic 1119873

119873

sum

119905=1

(119909119905minus 119909119905)2 (19)

where 119873 is the number of measurements 119909119905is the generic

PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909

119905is the

reference value computed on the basis of FLARE and intruderGPS measurements

The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar

In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate

In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

Elev

atio

nh ra

te in

NED

refe

renc

e fra

me (

∘ s)

08

04

0

minus04

minus01minus02minus03minus04minus05Er

ror i

n st

abili

zed

elev

atio

n ra

te (∘

s)

Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day

450

400

350

300

250

200

150

100

50

Distance at Closest Point of Approach (DCPA) (m)

PF trackerEKF trackerGPS

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day

phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase

The Scientific World Journal 11

6 Conclusion and Future Works

This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework

The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as

(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance

(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project

References

[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007

[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008

[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007

[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system

for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008

[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002

[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007

[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013

[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman

filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997

[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013

[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009

[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011

[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012

[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013

[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002

[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001

[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001

[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001

[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960

[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000

[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data

12 The Scientific World Journal

Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002

[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002

[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001

[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013

[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005

[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995

[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000

[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005

[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993

[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010

[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999

[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010

[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004

[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012

[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000

[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

The Scientific World Journal 9

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

0

minus1

minus2

minus3

050301

minus01minus03

Azi

mut

h ra

te in

NED

refe

renc

e fra

me (

∘ s)

Erro

r in

stab

ilize

daz

imut

h ra

te (∘

s)

Figure 9 Azimuth rate in NED reference frame as estimated by GPS and by radar-only tracker and estimation error as a function of GPStime of day

This is an additional advantage of using PF rather than EKFsince the need of linearized models in EKF does not allowestimating DCPA by the filter itself

5 Results

The developed obstacle tracking algorithm has been testedin off-line simulations based on flight data gathered duringan intensive test campaign Flight tests were carried out byexploiting the following configuration of test facilities

(a) FLARE aircraft piloted by a human pilot or by theautonomous flight control system

(b) a piloted intruder VLA aircraft in the same class ofFLARE equipped with GPS antennas and receiversand an onboard CPU for navigation data storage

(c) a ground control station (GCS) for real time flightcoordination and test monitoring [36]

(d) a full-duplex data link between FLARE and GCSused to send commands to initiate or terminate testsand to receive synthetic filter output and navigationmeasurements

(e) a downlink between intruder and GCS used for flightmonitoring

During the tests two types of maneuvers were executedsuch as chasing tests with FLARE pursuing the intruder andquasi-frontal encounters performed to estimate detectionand tracking performance in the most interesting scenariosfrom the application point of view

In particular the scenario selected in this paper forperformance analysis is a single quasi-frontal encounterbetween FLARE and the intruder The algorithm has beentested in standalone radar tracking configuration that is

estimates of obstacle relative position and velocity are basedon measurements from radar (update frequency of 1Hz) andthe own-ship navigation system

The number of particles has been set equal to 500 Thisnumber was selected since increasing it up to one orderof magnitude did not produced significant performanceincrease The algorithm is initialized taking into accountthe first radar sensor measurement the covariance matrix iscalculated on the basis of sensor measurements and then it isupdated with estimated values of software output

The algorithm outputs are based on obstacle position andvelocity in terms of range azimuth and elevation and DCPAin a stabilized north-east-down reference frame with originin FLARE center of mass The considered flight segment hasduration of about 20 s with an initial range of about 2000m

In Figure 5 obstacle range as estimated by radar radar-based tracker and GPS (reference) together with errorestimate with respect to GPS measurements is reportedAfter a firm track has been generated on the basis of radarmeasurements the tracker is able to characterize the obstacletrajectory The radar-only tracker provides a range estimatewith an accuracy of the order of few meters that derives fromthe good radar range accuracy and the absence of intrudermaneuvers In Figure 5 the upper plot illustrates the obstaclerange in a small interval time (of about 1 s) in order to showthe particles trajectories (colored lines)

Figures 6 and 7 report the obstacle angular dynamicsin terms of azimuth and elevation As expected the orderof magnitude of these errors is comparable to the radaraccuracy In particular the estimation uncertainty in termsof root mean square is of about 25∘ for azimuth and 13∘ forelevation Being computed in NED these RMS errors includeattitude measurement error biases In fact error biases in theestimation of magnetic heading are the main reason of thelarger error in azimuth It is worth noting that these biases

10 The Scientific World Journal

Table 1 PF performance in the selected scenario in terms of RMSerror

RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08

have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach

The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation

Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step

In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas

RMS = radic 1119873

119873

sum

119905=1

(119909119905minus 119909119905)2 (19)

where 119873 is the number of measurements 119909119905is the generic

PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909

119905is the

reference value computed on the basis of FLARE and intruderGPS measurements

The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar

In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate

In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

Elev

atio

nh ra

te in

NED

refe

renc

e fra

me (

∘ s)

08

04

0

minus04

minus01minus02minus03minus04minus05Er

ror i

n st

abili

zed

elev

atio

n ra

te (∘

s)

Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day

450

400

350

300

250

200

150

100

50

Distance at Closest Point of Approach (DCPA) (m)

PF trackerEKF trackerGPS

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day

phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase

The Scientific World Journal 11

6 Conclusion and Future Works

This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework

The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as

(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance

(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project

References

[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007

[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008

[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007

[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system

for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008

[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002

[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007

[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013

[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman

filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997

[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013

[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009

[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011

[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012

[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013

[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002

[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001

[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001

[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001

[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960

[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000

[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data

12 The Scientific World Journal

Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002

[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002

[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001

[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013

[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005

[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995

[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000

[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005

[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993

[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010

[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999

[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010

[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004

[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012

[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000

[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 The Scientific World Journal

Table 1 PF performance in the selected scenario in terms of RMSerror

RMS Particle filter EKFRange (m) 84 37Range rate (m∘) 30 23Azimuth (∘) 25 17Azimuth rate (∘s) 02 04Elevation (∘) 13 21Elevation rate (∘s) 02 08

have a little effect on the estimation of angular rates and ofDistance at Closest Point of Approach

The range and angular rates as estimated by GPS (ref-erence) and particle filter tracker are reported in Figures 89 and 10 These variables are very important informationsources for collision detection assessment even though theyare not directly provided by the radar sensor The plots showthat the tracker estimates are very accurate with a very smallvalue in terms of standard deviation

Simulation results confirm how the resampling proce-dure is a key factor for tracking performance avoiding thedegeneracy phenomenon and thus enabling a great quantityof particles to survive to the prediction step

In order to better understand the particle filter trackingcapability PF and EKF estimation errors are reported inTable 1 in terms of root mean square (RMS) errors computedas

RMS = radic 1119873

119873

sum

119905=1

(119909119905minus 119909119905)2 (19)

where 119873 is the number of measurements 119909119905is the generic

PF tracker estimate (computed after resampling and repre-senting the mean value over all the particles) and 119909

119905is the

reference value computed on the basis of FLARE and intruderGPS measurements

The results show that PF tracker performance is com-parable to EKF in terms of order of magnitude Of coursethe introduction of electro-optical data can improve angularaccuracy since these sensors have a faster update rate thanradar In particular while the range rate error is very similarfor the two filters obstacle angular velocities provided byPF algorithm are slightly more accurate than EKF in theconsidered scenario These variables are very importantinformation sources for collision detection assessment eventhough they are not directly provided by the radar

In fact in near collision conditions angular rates are themost important variables influencing collision detection Asshown in [7] in these conditions DCPA uncertainty for givenrange and range rate shows a linear dependence on angularrate errors while range rate essentially impacts the time-to-go estimate

In the considered scenario DCPA as computed on thebasis of GPS measurement has been used as a reference forcomparing DCPA estimated by EKF tracker and PF trackerFigure 11 shows that the PF algorithm is more accuratethan EKF for the estimation of the DCPA in the initial

52494

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

GPS

PF tracker

Spherical PF

Spherical PFPF tracker

Elev

atio

nh ra

te in

NED

refe

renc

e fra

me (

∘ s)

08

04

0

minus04

minus01minus02minus03minus04minus05Er

ror i

n st

abili

zed

elev

atio

n ra

te (∘

s)

Figure 10 Elevation rate in NED reference frame as estimated byGPS and by radar-only tracker and estimation error as a function ofGPS time of day

450

400

350

300

250

200

150

100

50

Distance at Closest Point of Approach (DCPA) (m)

PF trackerEKF trackerGPS

52494

52496

52498

525

52502

52504

52506

52508

5251

52512

52514

times104GPS time of day (s)

Figure 11 Distance at Closest Point of Approach as estimated byGPS (reference) by radar and by radar-only tracker as function ofGPS time of the day

phase of firm tracking (at larger range) thus providing animprovement in collision risk assessment and a potentialreduction in the delay in declaring a collision threat Analysisof GPS data demonstrates that the considered encounterrepresents a real Near Mid-Air Collision (NMAC) scenariosince the reference DCPA keeps a very small value and liesbelow the bubble distance threshold almost in the whole firmtracking phase

The Scientific World Journal 11

6 Conclusion and Future Works

This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework

The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as

(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance

(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project

References

[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007

[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008

[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007

[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system

for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008

[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002

[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007

[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013

[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman

filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997

[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013

[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009

[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011

[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012

[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013

[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002

[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001

[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001

[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001

[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960

[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000

[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data

12 The Scientific World Journal

Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002

[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002

[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001

[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013

[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005

[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995

[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000

[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005

[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993

[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010

[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999

[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010

[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004

[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012

[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000

[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

The Scientific World Journal 11

6 Conclusion and Future Works

This paper focused on algorithm and test results fromobstacle tracking software based on particle filter and aimedat demonstrating UAS autonomous collision detection capa-bility in terms of reliable estimation of Distance at ClosestPoint of Approach The algorithm performance has beeninitially evaluated in radar-only configuration since the maininterest was addressed to the analysis of the potential impactof nonlinear filters on tracking capabilities with respect toassessed EKF first in a single sensor framework

The software has been tested in off-line simulations basedon real data recorded during a flight test campaign and aquasi-frontal encounter between the own aircraft and theintruder has been presented as test case The results pointedout that the developed algorithm is able to detect and trackthe obstacle trajectory with accuracy comparable to the EKFIn particular some advantages were highlighted in the directdetermination of Distance at Closest Point of Approach witha potential reduction of the delay for collision detectionThis result permits planning additional future investigationactivities such as

(i) performing the comparison on a larger experimentaldata set thus increasing the statistical significance

(ii) developing a multisensor-based analysis to confirmthe results obtained by the developed PF tracker whenadditional data sources are available such as electro-optical sensors indeed they can provide higheraccuracy in angular measurements and better datarate than radar sensors with a great impact on DCPAperformance

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The PhD grant of Miss Anna Elena Tirri is cofunded byEUROCONTROL through the research network HALA inthe framework of the WP-E of SESAR project

References

[1] EUROCONTROL in Proceedings of the EUROCONTROL Spec-ifications for the Use of Military Unmanned Aerial Vehicles asOperational Air Traffic Outside Segregated Airspace Version10 DocNo EUROCONTROL-SPEC-0102 Bruxelles BelgiumJuly 2007

[2] US Federal Aviation Administration (FAA) ldquoAirworthinesscertification of unmanned aircraft systemsrdquo Order 813034US Federal Aviation Administration (FAA) Washington DCUSA 2008

[3] US Federal Aviation Administration (FAA) ldquoInvestigate aNear Mid Air Collisionrdquo FAA Order 89001 vol 7 chapter 4Washington DC USA 2007

[4] G Fasano D Accardo A Moccia et al ldquoMulti-sensor-basedfully autonomous non-cooperative collision avoidance system

for unmanned air vehiclesrdquo Journal of Aerospace ComputingInformation and Communication vol 5 no 10 pp 338ndash3602008

[5] MTSI ldquoNon-cooperative detect see amp avoid (DSA) sensorstudyrdquo Tech Rep NASA ERAST 2002

[6] O Shakernia W Chen S Graham et al ldquoSense and Avoid(SAA) flight test and lessons learnedrdquo in Proceedings of the 2ndAIAA InfotechAerospace Conference and Exhibit (AIAA rsquo07)pp 2781ndash2795 Rohnert Park Calif USA May 2007

[7] D Accardo G Fasano L Forlenza A Moccia and A RispolildquoFlight test of a radar-based tracking system for UAS sense andavoidrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 49 no 2 pp 1139ndash1160 2013

[8] USFAA SpecialOperations FAAOrder 76104M January 2007[9] S J Julier and J K Uhlmann ldquoA new extension of the Kalman

filter to nonlinear systemsrdquo in Signal Processing Sensor Fusionand Target Recognition VI vol 3068 of Proceedings of SPIE pp182ndash193 Orlando Fla USA 1997

[10] N E Smith R G Cobb S J Pierce and V M Raska ldquoOptimalcollision avoidance trajectories for unmannedremotely pilotedaircraftrdquo in Proceedings of the AIAA Guidance Navigation andControl Conference (GNC 13) AIAA 2013-4619 Boston MassUSA August 2013

[11] L Lin Y Wang Y Liu C Xiong and K Zeng ldquoMarker-lessregistration based on template tracking for augmented realityrdquoMultimedia Tools and Applications vol 41 no 2 pp 235ndash2522009

[12] X Liu L Lin S Yan H Jin and W Jiang ldquoAdaptive objecttracking by learning hybrid template onlinerdquo IEEE Transactionson Circuits and Systems for Video Technology vol 21 no 11 pp1588ndash1599 2011

[13] L Lin Y Lu Y Pan and X Chen ldquoIntegrating graph partition-ing and matching for trajectory analysis in video surveillancerdquoIEEE Transactions on Image Processing vol 21 no 12 pp 4844ndash4857 2012

[14] L Xia P Li Y Guo and Z Shen ldquoResearch of maneuveringtarget tracking based on particle filterrdquo in Proceedings of the Chi-nese Automation Congress (CAC rsquo13) pp 567ndash570 ChangshaChina 2013

[15] F Gustafsson F Gunnarsson N Bergman et al ldquoParticle filtersfor positioning navigation and trackingrdquo IEEE Transactions onSignal Processing vol 50 no 2 pp 425ndash437 2002

[16] S Challa and G W Pulford ldquoJoint target tracking and classi-fication using radar and ESM sensorsrdquo IEEE Transactions onAerospace and Electronic Systems vol 37 no 3 pp 1039ndash10552001

[17] M S Grewal and A P Andrews Kalman Filtering Theory andPractice Using Matlab John Wiley amp Sons 2nd edition 2001

[18] S Haykin Kalman Filtering and Neural Networks John Wileyand Sons 2001

[19] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Transactions of the ASME Series D Journal of BasicEngineering vol 82 no 1 pp 35ndash45 1960

[20] S Arulampalam and B Ristic ldquoComparison of the particle filterwith range-parameterised and modified polar EKFs for angle-only trackingrdquo in Signal and Data Processing of Small Targetsvol 4048 of Proceedings of SPIE pp 288ndash299 Orlando FlaUSA April 2000

[21] X Lin T Kirubarajan Y Bar-Shalom and S Maskell ldquoCom-parison of EKF pseudomeasurement and particle filters fora bearing-only target tracking problemrdquo in Signal and Data

12 The Scientific World Journal

Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002

[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002

[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001

[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013

[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005

[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995

[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000

[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005

[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993

[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010

[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999

[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010

[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004

[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012

[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000

[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 The Scientific World Journal

Processing of Small Targets vol 4728 of Proceedings of SPIE pp240ndash250 April 2002

[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002

[23] A Doucet N de Freitas and N Gordon ldquoAn introduction tosequential Monte Carlo methodsrdquo in Sequential Monte CarloMethods in Practice Statistics for Engineering and InformationScience pp 3ndash14 Springer New York NY USA 2001

[24] B Liu andCHao ldquoSequential bearings-only-tracking initiationwith particle filteringmethodrdquoThe ScientificWorld Journal vol2013 Article ID 489121 7 pages 2013

[25] R Karlsson and F Gustafsson ldquoRecursive Bayesian estimationbearings-only applicationsrdquo IEE Proceedings Radar Sonar andNavigation vol 152 no 5 pp 305ndash313 2005

[26] N Gordon ldquoHybrid bootstrap filter for target tracking inclutterrdquo in Proceedings of the American Control Conference vol1 pp 628ndash632 June 1995

[27] S Mcginnity and G W Irwin ldquoMultiple model bootstrapfilter for maneuvering target trackingrdquo IEEE Transactions onAerospace and Electronic Systems vol 36 no 3 pp 1006ndash10122000

[28] M R Morelande and S Challa ldquoManoeuvring target trackingin clutter using particle filtersrdquo IEEE Transactions on Aerospaceand Electronic Systems vol 41 no 1 pp 252ndash270 2005

[29] D Lerro and Y Bar-Shalom ldquoTracking with de-biased consis-tent converted measurements versus EKFrdquo IEEE TransactionsonAerospace and Electronic Systems vol 29 no 3 pp 1015ndash10221993

[30] G Fasano L Forlenza D Accardo A Moccia and A RispolildquoIntegrated obstacle detection system based on radar andoptical sensorsrdquo inProceedings of the AIAA Infotech at Aerospace(AIAA rsquo10) Atlanta Ga USA April 2010

[31] S S Blackman and R F Popoli Design and Analysis of ModernTracking Systems Artech House Norwood Mass USA 1999

[32] G Fasano D Accardo A Moccia and A Rispoli ldquoAn inno-vative procedure for calibration of strapdown electro-opticalsensors onboard unmanned air vehiclesrdquo Sensors vol 10 no 1pp 639ndash654 2010

[33] B Ristic S Arulampalam and N Gordon Beyond the KalmanFilter Particle Filter for Tracking Applications Artech HouseNew York NY USA 2004

[34] A Haug and L Williams ldquoA spherical constant velocity modelfor target tracking in three dimensionsrdquo in IEEE AerospaceConference pp 1ndash15 Big Sky Mont USA March 2012

[35] X R Li and V P Jilkov ldquoA survey of maneuvering target track-ing dynamic modelsrdquo in Proceedings of the SPIE Conference onsignal and Data Processing of Small Targets vol 39 pp 1333ndash1364 Orlando Fla USA April 2000

[36] G Fasano A Moccia D Accardo and A Rispoli ldquoDevelop-ment and test of an integrated sensor system for autonomouscollision avoidancerdquo in Proceedings of the 26th Congress ofInternational Council of the Aeronautical Sciences (ICAS rsquo08) pp3625ndash3634 Anchorage Alaska USA September 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of