micromotion feature extraction of space target based on...

Research ArticleMicromotion Feature Extraction of Space TargetBased on Track-Before-Detect

Yijun Chen12 Qun Zhang123 Ying Luo123 and Tat Soon Yeo4

1 Institute of Information and Navigation Air Force Engineering University Xirsquoan 710077 China2Collaborative Innovation Center of Information Sensing and Understanding Xirsquoan 710077 China3Key Laboratory for Information Science of ElectromagneticWaves Ministry of Education FudanUniversity Shanghai 200433 China4Department of Electrical and Computer Engineering National University of Singapore Singapore 11576

Correspondence should be addressed to Qun Zhang zhangqunnusgmailcom

Received 29 May 2017 Accepted 16 July 2017 Published 22 August 2017

Academic Editor Hyung-Sup Jung

Copyright copy 2017 Yijun Chen et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The micromotion feature of space target provides an effective approach for target recognition The existing micromotion featureextraction is implemented after target detection and tracking thus the radar resources need to be allocated for target detectiontracking and feature extraction successively If the feature extraction can be implemented by utilizing the target detecting andtracking pulses the radar efficiency can be improved In this paper by establishing a feedback loop between micromotionfeature extraction and track-before-detect (TBD) of target a novel feature extraction method for space target is proposed TheTBD technology is utilized to obtain the range-slow-time curves of target scatterers Then micromotion feature parameters areestimated from the acquired curve information In return the state transition set of TBD is updated adaptively according to theseextracted feature parameters As a result the micromotion feature parameters of space target can be extracted concurrently withimplementing the target detecting and tracking Simulation results show the effectiveness of the proposed method

1 Introduction

Themonitoring and recognition of space targets have becomemore and more important since these space targets such asfragments of satellites rocket bodies and other space debrisare hazardous to aerospace activities with the increasing outerspace explorations [1] Generally a space target has complexmicromotion such as spinning precession and rolling inaddition to the body translation [2]Thesemicromotions willinduce themicro-Doppler (m-D) effect which can be regard-ed as a unique signature providing additional informationfor classification recognition and identification of the target[3]Therefore since the concept of micro-Doppler was intro-duced to the radar signal processing field [4 5] themicromo-tion feature extraction of space target has drawn extensiveattention of scholars [6ndash16]

Based on the fixed scatterer model [7] the micromotionfeature of space target was usually analyzed with the time-frequency distribution technique and the micromotion fea-ture of target was extracted with parameter transformation

method [7] However the time-frequency methods havesome limitations due to the fact that the change of micro-Doppler frequency with time is highly nonlinear [8] Afeature extraction method based on empirical-mode decom-position (EMD) was proposed to estimate the oscillation fre-quency of the truckrsquos surface in [9] To get the higher potentialpayoffs from the exploitation ofm-D effect in wideband radarsystem the micromotion feature extraction for widebandradar based on complex image orthogonal matching pursuitdecomposition is proposed in [10]

However many space targets are of conical and cone-cylinder shapes these rotationally symmetric targets cannotbe described exactly with the fixed scatterer model Theirscattering centers of the edge of the conic bottom slidewith the radar line of sight (LOS) that means the scatteringcenters local at the two intersections of the conic bottomedge and the radar wave incident plane [11] Based on theslide scatterer model the mathematical expression of micro-Doppler is derived which is validated by the darkroom datain [12 13] However these works did not provide effective

HindawiJournal of SensorsVolume 2017 Article ID 8723042 14 pageshttpsdoiorg10115520178723042

2 Journal of Sensors

micromotion feature extraction methods for the slide scat-terermodel Unfortunately most of the existingmicromotionfeature extraction methods for the fixed scatterer modelwill not function properly because the micro-Doppler curveof a slide scatterer is much different from that of a fixedscatterer Although some methods based on the complexgeneralizedRadon transform and extendedHough transformare proposed for micromotion feature extraction based onthe slide scatterer model [14 15] the computation load ofthese methods is heavy and the methods need high pulserepetition frequency (PRF) to avoid the frequency domainaliasing phenomenon In this case a lot of radar resourcesneeds to be allocated for micromotion feature extraction

In fact the existingmicromotion feature extractionmeth-ods of space target are implemented after target detection andtracking It is necessary to allocate the limited radar resourcesfor target detecting tracking and feature extraction succes-sively In the case of multitarget monitoring the allocationcontradiction of radar resources will be serious To overcomethis problem we intend to seek a novel approach whichcan implement target detecting and tracking simultaneouslywhen extracting the micromotion features of a space targetwhich can be available for both the fixed scatterer model andthe slide scatterer model

In recent years the track-before-detect (TBD) technol-ogy has shown good performance in weak target detectingand tracking Unlike traditional techniques that declare thepresence of a target at each scan the TBD technology pro-cesses more consecutive scans jointly and then it declaresthe presence of a target and its track [16ndash18] Through theinterscan accumulation the TBD technology can improvethe probability of target detection The idea of establishing afeedback loop between feature extraction and TBD of targethas been provided in our previous preliminary work [19] Inthis paper a micromotion feature extractionmethod of spacetarget based on TBD technology is further proposed In themethod the tracks of target scatterers can be obtained duringthe TBD of target and the tracks are the range-slow-timecurves of target scatterers indeed We call the range-slow-time curve as ldquorange trajectoryrdquo in this paper On this basiswe attempt to add the micromotion feature extraction intothe process of target detecting and tracking by establishing afeedback loop namely that the micromotion feature param-eters are extracted via fitting the obtained range trajectoryaccording to the mathematical expression of m-D effect andin turn the extracted micromotion feature parameters areutilized to update the parameters of TBD adaptively As aresult the micromotion feature extraction detecting andtracking of space target can be implemented simultaneouslywith the information feedback which can provide real-timeand effective information for target recognition By changingthe mathematical expressions of different kinds of m-Deffects for range trajectory fitting the fixed scatterer modelthe slide scatterer model and any kinds of micromotionforms can be processed with the proposed method

This paper is organized as follows Taking the conicaltarget contains a fixed scatterer and two slide scatterers as anexample the micromotion feature of the target precession isanalyzed in Section 2 Combining with the TBD technology

z

an

O y

c

bd

x

r0

Υ

Figure 1 The geometry of conical target with precession

the micromotion feature extraction method is presented indetail in Section 3 Simulations are presented in Section 4 andsome conclusions are made in the last section

2 Micromotion Feature of ConicalTarget with Precession

When the space target is flying outside the atmosphere itneeds to spin around its own axis of symmetry to main-tain stability Meanwhile it needs to cone around a spatialdirectional axis due to the lateral force caused by projectileseparation and bait release These two types of rotationformed the precession of target For a conical target itusually consists of three dominant scatterers (ie one tip-cone scatterer and two cone-base scatterers) where the tip-cone scatterer can be treated as a fixed tip-cone scattererand the cone-base scatterers are slide cone-base scatterersThe geometry of conical target with precession is shownin Figure 1 where 119874 is the target center and the target isrotating around 119911-axis with precession angle 120599 and precessionfrequency 120596 rads The distance between the radar and thetarget center is denoted as 119877119888 The radar LOS is denoted as997888n 119910-axis is in the plane determined by 997888n and 119911-axis and119909-axis is established according to the right-hand rule TheLOS can be represented as 997888n = sin120573997888rarry + cos120573997888rarrz where120573 is the angle between LOS and 119911-axis The target consistsof three scatterers denoted as 119886 119888 and 119889 respectively Theradius of the base circle is 1199030 the distance between the targetcentroid and scatterer 119886 is denoted as |119900119886| and the verticaldistance between the target centroid and the bottom circle isrepresented as |119900119887| According to the rigid body dynamicsthe velocity of target should be along 119911-axis and the velocityis given as V

Assume that the angle between 119909-axis and the projectionof vector997888rarroa on the119909119900119910 plane is1206010 at time 119905 = 0 then the angle

Journal of Sensors 3

between LOS and 997888rarroa is denoted as 120593 and it can be calculatedby

cos120593 = sin120573 sin 120599 sin (120596119905 + 1206010) + cos120573 cos 120599 (1)

The projection of 997888rarroa 997888rarroc and 997888rarrod in the line-of-sight

direction at time 119905 can be represented as 119903119886(119905) 119903119888(119905) and 119903119889(119905)respectively that is

119903119886 (119905) = minus |119900119886| sdot cos120593 minus cos120573 sdot V sdot 119905 + 119877119888 = minus |119900119886| (sin120573 sin 120599 sin (120596119905 + 1206010) + cos120573 cos 120599) minus cos120573 sdot V sdot 119905 + 119877119888 (2)

119903119888 (119905) = 1199030 sdot sin120593 + |119900119887| sdot cos120593 minus cos120573 sdot V sdot 119905 + 119877119888= 1199030radic1 minus cos2120573cos2120599 minus sin2120573sin2120599sin2 (120596119905 + 1206010) minus 2 cos120573 cos 120599 sin120573 sin 120599 sin (120596119905 + 1206010)+ |119900119887| (sin120573 sin 120599 sin (120596119905 + 1206010) + cos120573 cos 120599) minus cos120573 sdot V sdot 119905 + 119877119888

(3)

119903119889 (119905) = minus1199030 sdot sin120593 + |119900119887| sdot cos120593 minus cos120573 sdot V sdot 119905 + 119877119888= minus1199030radic1 minus cos2120573cos2120599 minus sin2120573sin2120599sin2 (120596119905 + 1206010) minus 2 cos120573 cos 120599 sin120573 sin 120599 sin (120596119905 + 1206010)+ |119900119887| (sin120573 sin 120599 sin (120596119905 + 1206010) + cos120573 cos 120599) minus cos120573 sdot V sdot 119905 + 119877119888

(4)

Reference [1] points out that in the wideband radarsystem the micromotion feature of target can be describedby range-slow-time image where the peak of range profileappears to be a range-slow-time curve (range trajectory)which is determined by the scatterer range 119903(119905) And the rangetrajectory reflects the micromotion feature of target scattererTherefore from (2)-(4) the micromotion feature of cone-tipscatterer 119886 is sinusoid while that of the cone-base scatterers119888 and 119889 is quasisinusoid which deviates from the standardsinusoid

During the target observation the shielded effect shouldbe considered Assume that the cone half angle of target is ΥObviously 120593 is changing with time 119905 and 120593 isin [|120573 minus 120599| 120573 +120599] The observable scatterers are different when 120593 locates indifferent interval range of [0 120587] Therefore we divide [0 120587]into four observation areas as follows

Area 1 0 le 120593 lt Υ the observable scatterers are 119886 119888and 119889Area 2 Υ le 120593 lt 1205872 the observable scatterers are 119886and 119889Area 3 1205872 le 120593 lt 120587 minusΥ the observable scatterers are119886 119888 and 119889Area 4 120587 minus Υ le 120593 lt 120587 the observable scatterers are 119888and 119889

The impact of the shielded effect on the proposedmicromotion feature extraction method will be discussed inSection 3

Next a simple simulation is given to validate the cor-rectness of theoretical analysis The pulse duration is 119879119901 =1 120583s carrier frequency is 119891119888 = 10GHz signal bandwidth is119861 = 3GHz pulse repetition frequencies is PRF = 60Hzand the coherent processing time is 119879119888 = 1 s The radius ofthe base circle is 1199030 = 1m the distance between the targetcenter and cone-tip scatterer 119886 is |119900119886| = 3m and the verticaldistance between the target center and the bottom circle is|119900119887| = 03m

To observe the micromotion feature of target more intui-tively we assume that119877119888 = 0mand V = 0msThe precessionangle is 120599 = 15∘ precession frequency is 120596 = 8120587 rads theangle between LOS and 119911-axis is 120573 = 145∘ and the initialangle is 1206010 = 120587100 rad We can obtain the range-slow-timeimage as shown in Figure 2

From Figure 2 we can see that the range profile peak ofscatterer 119886 changes with slow-time following the sinusoidalform while those of the sliding scatterers 119888 and 119889 are quasis-inusoids (deviating from the standard sinusoid form) whichconfirms the theoretical analysis

3 Micromotion Feature ExtractionBased on TBD

Due to the requirement of additional observation pulsesafter target detection and tracking the existing micromo-tion feature extraction methods usually occupy much radarresources Also the real-time performance and radar effi-ciency are not satisfied So we intend to combine the micro-motion feature extraction with target detecting and trackingin the way of information feedback and then implement themicromotion feature extraction detecting and tracking ofspace target simultaneously It will save the radar resourcesand improve the radar efficiency and real-time performanceof micromotion feature extraction

In this section we establish a feedback loop betweenmicromotion feature extraction and TBD of target Firstlybased on TBD technology the target scatterer range tra-jectory information is backtracked along with the energyaccumulation process and then the micromotion featureparameters of target can be fitted with these obtained tra-jectory information In return the extracted micromotionfeature parameters are used to update the state transition setof TBD adaptively and the results of micromotion featureextraction are considered into the declaration of the targetpresence As a result micromotion feature extraction targetdetecting and tracking can be completed simultaneously


Scatterer a

Scatterer d

Scatterer c

minus6

minus4

minus2

0

2

4

6

Rang

e (m

)

0 0402 06 08Slow-time (t)

Figure 2 Range-slow-time image of precession target

31 Range Trajectory Backtracking and Micromotion FeatureExtraction For simpleness the range trajectory backtrackingfor single scatterer based on TBD is described firstly Themonitoring area is divided into 119873119903 times 119873120579 grids according tothe range and azimuthal angle and each grid is denoted asa state (119894 119895) 119894 = 1 119873119903 119895 = 1 119873120579 which representsthe position ((119894 minus 1198731199032) sdot Δ119903 + 1198770 (119895 minus 1198731205792)Δ120579 + 1205790) whereΔ119903 and Δ120579 are the stepped increasement of the range andazimuthal angle and (1198770 1205790) is the center of the monitoringarea Assume the radar transmits wideband signal 119901( ) Ateach scan the beams towards all the azimuthal angles (119873120579

angles) are formed by the radar The beam width is denotedas 120601119861 each state (119894 119895) will be hit by119872 + 1 successive beamswhere

119872 =

lfloor120601119861Δ120579rfloor lfloor 120601119861Δ120579rfloor is even

lfloor 120601119861Δ120579rfloor minus 1 lfloor 120601119861Δ120579rfloor is odd(5)

Obviously the sequence number of these119872+1 beams shouldbe (119895 minus 1198722 119895 minus 1198722 + 1 119895 + 1198722)

At the 119896th scan the echo signal of the state x119896 = (119894119896 119895119896) ofthe119898th beam can be represented as

119904119896119898x119896 () = 120590119896(119894119896119895119896)119866119898 (119895119896)sdot 119901( minus 2 (119894119896 minus 1198731199032) sdot Δ119903 + 21198770119888 )

isin [minus1198791199012 1198791199012 ] 119898 isin (1 119872 + 1)

(6)

where 119866119898(sdot) represents the beampattern of the 119898th beamand 119866119898(119895119896) represents the obtained transmit gain at the119895119896th azimuthal angle with the 119898th beam and 120590119896(119894119896 119895119896) is thebackscattered amplitude of the state (119894119896 119895119896) at the 119896th scan

After performing range compression the high-resolutionrange profile (HRRP) can be obtained as

119878119896119898x119896 (119865119891)= 119879119901 sdot 119866119898 (119895119896) sdot 120590119896(119894119896 119895119896)sdot sinc (119865119891 + 2 (119894119896 minus 1198731199032) sdot Δ119903 + 21198770119888 )

(7)

Thus at the 119896th scan the measured value of each statex119896 = (119894119896 119895119896) can be defined as

119885119896 (x119896) = 119872+1sum119898=1

1003816100381610038161003816100381610038161003816 119878119896119898x119896 (119865119891)10038161003816100381610038161003816119865119891=minus(2(119894119896minus1198731199032)sdotΔ119903+21198770)11988810038161003816100381610038161003816100381610038162

119894119896 = 1 119873119903 119895119896 = 1 119873120579

(8)

At the 119896th scan the cumulative energy of state x119896 isdenoted as 119868(x119896) and it can be calculated as

119868 (x119896) = 119885119896 (x119896) + maxx119896minus1isinΓ(x119896)

(119868 (x119896minus1)) (9)

where Γ(x119896) is the state transition set Γ(x119896) contains all thepossible state x119896minus1 which can transit to state x119896 Set an appro-priate detection threshold for the cumulative energy function119868(x119896) after 119870 scans accumulation and the state sequencewhose cumulative energy is larger than the threshold can bebacktracked according to

119861119896 (x119896) = arg maxx119896minus1isinΓ(x119896)

(119868 (x119896minus1)) (10)

where 119861119896(x119896) is the backtracking function which is used torecord the state corresponding to the maximum cumulativeenergy at each scan Assume that the recorded state of the 119896thscan is x119896 = (119894119896 119895119896) the estimated scatterer range trajectorycan be denoted as119877(119896) = (119894119896minus1198731199032)sdotΔ119903+1198770 119896 = 1 119870 andthe angle trajectory isΘ(119896) = (119895119896minus1198731205792)Δ120579+1205790 119896 = 1 119870

For the cone-tip scatterer 119886 the estimated range trajectory

119877 (119896) = 119903119886 (119896 sdot Δ119905) (11)

should be equal to (2) where Δ119905 is the time interval betweenthe two adjacent scans Without loss of generality it holdsΔ119905 = 1PRF Similarly for the cone-base scatterers 119888 and 119889the estimated range trajectories 119877(119896) should be equal to (3)and (4) respectively

However the TBD method described above can obtainonly one scatterer range trajectory which cannot meet therequirement of getting range trajectories of each scatterersAlthough some TBD methods for multitarget detecting andtracking have been proposed [20 21] they require that thestate of different targets can not be the same However inthis paper the different scatterers are usually at the sameazimuthal angle and may be of the same range at some scans(ie the range trajectories may be intersected) That meansthe different scatterers may have the same state which leadsto the existing method which can not be used To resolve thisproblem we improve the TBD method as follows


Assume the target consists of 119875 observable scatterers Atthe 119896th scan for each azimuthal angle 119895119896 select any 119875 statesto form an expanded state ((1198941198961 119895119896) (1198941198962 119895119896) (119894119896119875 119895119896))where the 119875 states can be the same that is 1198941198961199011 can be equalto 1198941198961199012 when 1199011 = 1199012 The measured value of the expandedstate y119896 = (1198941198961 119895119896) (1198941198962 119895119896) (119894119896119875 119895119896) is defined as

119885119896 (y119896) = 119875sum119901=1

119885119896 ((119894119896119901 119895119896)) (12)

On the basis the cumulative energy shown as (9) isconducted in terms of the expanded state where the statecorrelation is necessary For example there are 6 kinds ofstates correlation approaches when 119875 = 3 shown as Figure 3

Among these 6 kinds of states correlation approachesonly one is consistent with the actual scatterers trajectoriesIn [22] we have proposed a state correlation approach whichcan be used for states correlation

After 119870 scans the cumulative energy 119868(y119896) should becompared with a detection threshold 119879120572

119879120572 = 120574119870119875 (13)

where 120574 is a constant which will affect the target detectingperformance in this paper we call 120574 as ldquodetection thresholdcoefficientrdquo The state sequences whose cumulative energy islarger than the threshold can be backtracked according to(10)

It should be pointed out that the states correlation leads tothe dependence of the energy accumulation of each scattererA specific expression of the detection threshold coefficient isdifficult to be derivedwith a given false alarm probability Justas [20] the detection threshold coefficient can be chosen fromMonte-Carlo experiments

Assume that the number of the cumulative energy 119868(y119896)which is larger than the threshold is 119876 Thus 119876 statesequences will be obtained and each state sequence contains119875 range trajectories 119877119901(119896) = (119894119896 minus 1198731199032) sdot Δ119903 + 1198770 (119901 =1 119875 119896 = 1 119870) and 119875 angle trajectories Θ119901(119896) =(119895119896 minus 1198731205792)Δ120579 + 1205790 (119901 = 1 119875 119896 = 1 119870) Due to the

fact that intersections number of any two range trajectorieswill be small a condition for selecting the reasonable statesequence from the 119876 state sequences is defined as

119862 (1198771199011 (119896) = 1198771199012 (119896)) lt 120589119870 forall1199011 = 1199012 (14)

where 119862(1198771199011(119896) = 1198771199012(119896)) represents the intersectionsnumber of 1198771199011(119896) and 1198771199012(119896) and 120589 is a constant used tocontrol the ratio of intersections number to scans number119870 The state sequences which satisfy the condition shown as(14) are selected and the corresponding range trajectories andangle trajectories are obtained from the target scatterers

For each possible value of119875 the TBDprocedure proposedabove can be conducted to obtain the range trajectories of 119875scatterersThe shielded effect has been discussed in Section 2when 120593 falls with in Area 1 or Area 3 three scatterers areobservable (corresponding to 119875 = 3) when 120593 falls withinArea 2 orArea 4 two scatterers are observable (correspondingto 119875 = 2) Therefore the possible values of 119875 are 119875 = 3 and119875 = 2 Thus the TBD procedure of 119875 = 3 and 119875 = 2 shouldbe conducted

In the case of 119875 = 3 if there is state sequence whichsatisfies (14) which can be selected out three range trajec-tories (ie 1198771(119896) 1198772(119896) and 1198773(119896)) can be obtained Firstlywe assume that 1198771(119896) is the range trajectory of the cone-tipscatterer 119886 and 1198772(119896) and 1198773(119896) are the range trajectories ofthe cone-base scatterers 119888 and 119889 respectively 1198771(119896) 1198772(119896)and 1198773(119896) can be represented as

1198771 (119896) = 119903119886 (119896 sdot Δ119905) + 120576 (119896) 1198772 (119896) = 119903119888 (119896 sdot Δ119905) + 120576 (119896) 1198773 (119896) = 119903119889 (119896 sdot Δ119905) + 120576 (119896)

(15)

where 120576(119896) represents the error induced from the noise andTBD procedure We can estimate the micromotion featureparameter vector PA = [|119900119886| 1206010 120573 120599 120596 V |119900119887| 1199030 119877119888] by fitt-ing 1198771(119896) 1198772(119896) and 1198773(119896) according to the curve form ofstandard sinusoid shown as (2) and quasisinusoid shown as(3)-(4) with the least squares method

minPA

10038171003817100381710038171198771 (119896) + |119900119886| (sin120573 sin 120599 sin (120596119896 sdot Δ119905 + 1206010) + cos120573 cos 120599) + cos120573 sdot V119896 sdot Δ119905 minus 1198771198881003817100381710038171003817 + 10038171003817100381710038171003817100381710038171198772 (119896)

minus 1199030radic1 minus cos2120573cos2120599 minus sin2120573sin2120599sin2 (120596119896 sdot Δ119905 + 1206010) minus 2 cos120573 cos 120599 sin120573 sin 120599 sin (120596119896 sdot Δ119905 + 1206010)minus |119900119887| (sin120573 sin 120599 sin (120596119896 sdot Δ119905 + 1206010) + cos120573 cos 120599) + cos120573 sdot V119896 sdot Δ119905 minus 1198771198881003817100381710038171003817100381710038171003817 +

10038171003817100381710038171003817100381710038171198773 (119896)+ 1199030radic1 minus cos2120573cos2120599 minus sin2120573sin2120599sin2 (120596119896 sdot Δ119905 + 1206010) minus 2 cos120573 cos 120599 sin120573 sin 120599 sin (120596119896 sdot Δ119905 + 1206010)minus |119900119887| (sin120573 sin 120599 sin (120596119896 sdot Δ119905 + 1206010) + cos120573 cos 120599) + cos120573 sdot V119896 sdot Δ119905 minus 1198771198881003817100381710038171003817100381710038171003817

(16)

Equation (16) can be solved with the LevenbergndashMarquardt method [23] which is sensitive to the initial

values Therefore how to set the appropriate initial values isproposed as follows The EMD method [24] can be used to


Figure 3 State correlation approaches

separate 1198771(119896) into a set of intrinsic mode functions (IMF)which is descended by frequency Thus we can obtain

11986811198771 (119896) = 119861119886 + 11986211988611989611986821198771 (119896) = 119860119886 sin (120596119886119896 + 1206010119886)

119860119886 = minus |119900119886| sin120573 sin 120599 + 120585

119861119886 = minus |119900119886| cos120573 cos 120599 + 119877119888 + 120585119862119886 = minus cos120573 sdot V + 120585120596119886 = 120596 + 1205851206010119886 = 1206010 + 120585

(17)

where 120585 is the error from 120576(119896) and EMD method Accordingto (3) and (4) we can get

119877+ (119896) = 1198772 (119896) + 1198773 (119896) = 2 |119900119887| (sin120573 sin 120599 sin (120596119896 + 1206010) + cos120573 cos 120599) minus 2 cos120573 sdot V119896 + 2119877119888 + 120576 (119896)119877minus (119896) = 1198772 (119896) minus 1198773 (119896)

= 21199030radic1 minus cos2120573cos2120599 minus sin2120573sin2120599sin2 (120596119896 sdot Δ119905 + 1206010) minus 2 cos120573 cos 120599 sin120573 sin 120599 sin (120596119896 sdot Δ119905 + 1206010) + 120576 (119896) (18)

Similarly separating119877+(119896)with the EMDmethod we canobtain

1198681119877+ (119896) = 119861119888119889 + 1198621198881198891198961198682119877+ (119896) = 119860119888119889 sin (120596119888119889119896 + 1206010119888119889)

119860119888119889 = 2 |119900119887| sin120573 sin 120599 + 120585119861119888119889 = 2 |119900119887| cos120573 cos 120599 + 2119877119888 + 120585

119862119888119889 = minus2 cos120573 sdot V + 120585120596119888119889 = 120596 + 1205851206010119888119889 = 1206010 + 120585

(19)

The initial values |119900119886|ini 1206010ini 120573ini 120599ini 120596ini Vini |119900119887|ini1199030ini and119877119888ini for (19) can be obtained according the equationset

minus |119900119886|ini cos120573ini cos 120599ini + 119877119888ini = 11986811198771 (0)2 |119900119887|ini cos120573ini cos 120599ini + 2119877119888ini = 1198681119877+ (0)

cos120573ini sdot Vini = minus((11986811198771 (1198962) minus 11986811198771 (1198961)) (1198962 minus 1198961) + (1198681119877+ (1198962) minus 1198681119877+ (1198961)) (1198962 minus 1198961))21003816100381610038161003816|119900119886|ini sin120573ini sin 120599ini1003816100381610038161003816 = max (11986821198771) minusmin (11986821198771)210038161003816100381610038162 |119900119887|ini sin120573ini sin 120599ini1003816100381610038161003816 = max (1198681119877+) minusmin (1198681119877+)2


1206010ini

=

(119886119903 sin (11986821198771 (0) minus 1003816100381610038161003816|119900119886|ini sin120573ini sin 120599ini1003816100381610038161003816) + 119886119903 sin (1198682119877+ (0) 10038161003816100381610038162 |119900119887|ini sin120573ini sin 120599ini1003816100381610038161003816))2 sin120573ini sin 120599ini gt 0(119886119903 sin (11986821198771 (0) 1003816100381610038161003816|119900119886|ini sin120573ini sin 120599ini1003816100381610038161003816) + 119886119903 sin (1198682119877+ (0) minus 10038161003816100381610038162 |119900119887|ini sin120573ini sin 120599ini1003816100381610038161003816))2 sin120573ini sin 120599ini lt 0

120596ini = (argmax120596 (FFT (11986821198771)) + argmax120596 (FFT (1198682119877+ (119896))))221199030iniradic1 minus cos2120573inicos2120599ini minus sin2120573inisin2120599inisin2 (1206010ini) minus 2 cos120573ini cos 120599ini sin120573ini sin 120599ini sin (1206010ini) = 119877minus (0)

(20)

where 119886119903 sin(sdot) is the inverse function of sin (sdot) In (20)the equationsrsquo number is one less than unknown param-eters number Thus we defined the search interval andthe search stepped increasement of 1199030 as [119903min 119903max] andΔ1199030 respectively For each initial values 1199030ini(119904119899) = 119903min +(119904119899 minus 1) sdot Δ1199030 119904119899 = 1 2 119878119873 and 119878119873 = (119903max minus119903min)Δ1199030 a group of initial values of |119900119886|ini(119904119899) 1206010ini(119904119899)120573ini(119904119899) 120599ini(119904119899) 120596ini(119904119899) Vini(119904119899) |119900119887|ini(119904119899) and 119877119888ini(119904119899) canbe obtained according to (20) Based on the initial valuesthe corresponding micromotion feature parameter vectorPA(119904119899) = [|119900119886|(119904119899) 1206010(119904119899) 120573(119904119899) 120599(119904119899) 120596(119904119899) V(119904119899) |119900119887|(119904119899)1199030(119904119899) 119877119888(119904119899)] can be obtained by solving (16) with theLevenbergndashMarquardtmethodThefitting error with the 119904119899thgroup initial values is calculated as

119864 (119904119899) = 13119870 (10038171003817100381710038171198771 (119896) + |119900119886| (119904119899) 1198651 (119904119899)1003817100381710038171003817+ 10038171003817100381710038171003817100381710038171198772 (119896) minus 1199030 (119904119899)radic1198652 (119904119899) minus |119900119887| (119904119899) 1198651 (119904119899)

1003817100381710038171003817100381710038171003817+ 10038171003817100381710038171003817100381710038171198773 (119896) + 1199030 (119904119899)radic1198652 (119904119899) minus |119900119887| (119904119899) 1198651 (119904119899)

1003817100381710038171003817100381710038171003817) 1198651 (119904119899) = sin120573 (119904119899) sin 120599 (119904119899) sin (120596 (119904119899) 119896 + 1206010 (119904119899))+ cos120573 (119904119899) cos 120599 (119904119899) + cos120573 (119904119899) sdot V (119904119899) 119896minus 119877119888 (119904119899)

1198652 (119904119899) = 1 minus cos2120573 (119904119899) cos2120599 (119904119899) minus sin2120573 (119904119899)sdot sin2120599 (119904119899) sin2 (120596 (119904119899) 119896 + 1206010 (119904119899)) minus 2 cos120573 (119904119899)sdot cos 120599 (119904119899) sin120573 (119904119899) sin 120599 (119904119899)sdot sin (120596 (119904119899) 119896 + 1206010 (119904119899))

(21)

All 119864(119904119899) is compared with each other and the estimatedmicromotion feature parameter vector is defined as

PA ≜ PA (argmin119904119899119864 (119904119899)) (22)

The fitting error is denoted as

119864 ≜ min119904119899119864 (119904119899) (23)

It should be pointed that PA and119864 are obtained under theassumption that 1198771(119896) is the range trajectory of the cone-tipscatterer 119886 Therefore we rewrite them as PA(1198771) and 119864(1198771)

Next we assume 1198772(119896) and 1198773(119896) are the range trajectoryof the cone-tip scatterer respectively The micromotion fea-ture parameter vectors PA(1198772) and PA(1198773) can be obtainedand the corresponding fitting errors are denoted as 119864(1198772)and 119864(1198773) The micromotion feature parameter vector corre-sponding to the minimum fitting error is selected out as thefinal micromotion feature parameter vector

PA119891 ≜ PA (arg min11987711198772 1198773

119864) (24)


119864119891 ≜ min11987711198772 1198773

119864 (25)

Similarly in the case of 119875 = 2 the micromotion featureparameter vector can be obtained What should be pointedout is that if the two range trajectories are corresponding tothe cone-base scatterers 119888 and 119889 respectively the parameter|119900119886| can not be obtained

32 Adaptive Update of State Transition Set Just as men-tioned in (18) the state transition set contains all the possiblestate y119896minus1 which can transit to state y119896 and the construction ofstate transition set will significantly affect the efficiency and


performance of TBD and micromotion feature extraction Inthis paper the state transition set is updated adaptively byforecasting the state of scatterers in next scan according tothe extracted micromotion feature parameters

Assume that in the 119896th scan the cumulative energy119868(y119896) is larger than the threshold the extracted micromotionfeature parameter vector can be obtained with the methodproposed in Section 31 which is represented as

PA119891y119896

= [|119900119886|y119896 1206010y119896 120573y119896 120599y119896 120596y119896 Vy119896 |119900119887|y119896 1199030y119896 119877119888y119896] (26)

The corresponding fitting error is denoted as 119864119891y119896 The state transition set can be determined in light of the

extracted micromotion feature parameters The state y119896 willbelong to the state transition set Γ(y119896+1) (ie y119896 isin Γ(y119896+1))when it satisfies

10038161003816100381610038161003816100381610038161003816(119894119896+11 minus1198731199032 ) sdot Δ119903 + 1198770 minus Δ119903119886

10038161003816100381610038161003816100381610038161003816 lt 119891119877 (119862119904y119896) sdot Δ1199031003816100381610038161003816119895119896+1 minus 1198951198961003816100381610038161003816 lt 2for scatterer 119886





(27)

where

Δ119903119886 = minus |119900119886|y119896 (sin120573y119896 sin 120599y119896 sin (120596y119896 (119896 + 1) + 1206010y119896) + cos120573y119896 cos 120599y119896) minus cos120573y119896Vy119896 (119896 + 1) + 119877119888y119896Δ119903119888= 1199030y119896radic1 minus cos2120573y119896cos2120599y119896 minus sin2120573y119896sin2120599y119896sin2 (120596y119896 (119896 + 1) + 1206010y119896) minus 2 cos120573y119896 cos 120599y119896 sin120573y119896 sin 120599y119896 sin (120596y119896 (119896 + 1) + 1206010y119896)+ |119900119887|y119896 (sin120573y119896 sin 120599y119896 sin (120596y119896 (119896 + 1) + 1206010y119896) + cos120573y119896 cos 120599y119896) minus cos120573y119896 sdot Vy119896 (119896 + 1) + 119877119888y119896

Δ119903119889= minus1199030y119896radic1 minus cos2120573y119896cos2120599y119896 minus sin2120573y119896sin2120599y119896sin2 (120596y119896 (119896 + 1) + 1206010y119896) minus 2 cos120573y119896 cos 120599y119896 sin120573y119896 sin 120599y119896 sin (120596y119896 (119896 + 1) + 1206010y119896)+ |119900119887|y119896 (sin120573y119896 sin 120599y119896 sin (120596y119896 (119896 + 1) + 1206010y119896) + cos120573y119896 cos 120599y119896) minus cos120573y119896 sdot Vy119896 (119896 + 1) + 119877119888y119896

(28)

119862119904y119896 represents the consistency of the micromotion featureparameter vectors between 119896 minus 1th scan and 119896th scan and119891119877(sdot) is an adaptive adjustment function which is used tocontrol the size of searching range gate duringTBDaccordingto 119862119904y119896 In this paper 119862119904y119896 is defined as

119862119904y119896 = mean(10038161003816100381610038161003816PA119891y119896 minus PA119891y119896minus1

1003816100381610038161003816100381610038161003816100381610038161003816PA119891y119896minus110038161003816100381610038161003816 ) (29)

where mean (sdot) represents the mean value of a vector Obvi-ously the smaller 119862119904y119896 is the higher consistency is

Obviously if 119862119904y119896 is relatively small it shows that theconsistency of the extracted micromotion feature parametervectors is high we can consider that the precision of themicromotion feature extraction is well and the forecast ofstate information in the next scan is accurate In this casethe searching range gate can be decreased to reduce thecomputation load On the contrary if 119862119904y119896 is relatively largethe forecasted precision is low and the searching range gate

should be increased appropriately Therefore 119891119877(sdot) should bean increasing function which is defined as

119891119877 (119862119904y119896) = 119903119898 + 120582 sdot 119862119904y119896 (30)

where 120582 is a constant coefficient 119903119898 is the minimum ofsearching range gate which is set to be 5 in this paper andthe maximum value of 119891119877(sdot) is limited to 20

33 Adaptive Starting and Ending of Precession Feature Extrac-tion In TBD algorithms the detection threshold affects thetarget detecting performance directly However how to set anappropriate detection threshold is difficult especially in themultiscatterers environment

As the micromotion feature extraction has been includedinto the process of target detecting and tracking by estab-lishing a feedback loop the pertinent issue now is how todeclare the presence of a target and when to start and endthe micromotion feature extraction algorithm

In the proposed method the energy accumulation valueand the result of micromotion feature extraction are bothtaken into full consideration to address the problem above


which is different from the traditional signal processingmethod Just as we know in traditional method only whenthe energy accumulation value is larger than the threshold itdeclares the presence of a target and then the extraction ofits micromotion feature will be implemented by transmittingadditional observation pulses In comparison in the pro-posedmethod by adding themicromotion feature extractioninto the process of target detecting and tracking on conditionthat the precision of micromotion feature extraction is highenough it can declare the presence of a target and themicromotion feature is extracted successfully at the sametime although the energy accumulation value dose notachieve the required level

Assume the minimum and maximum total number ofscans that are jointly processed in TBD are 119870119873 and 119870119872respectively Firstly set two detection threshold coefficientsthe lower detection threshold coefficient 1205741 and the higherdetection threshold coefficient 1205742 In the 119896th (119896 ge 119870119873) scan ifthe cumulative energy 119868(y119896) is larger than 1198791205722 = 1205742 sdot 119896 sdot 119875 wedeclare the presence of a target and the micromotion featureparameters can be obtained with the proposed methoddescribed in Section 31 On the other hand if the cumulativeenergy 119868(y119896) is larger than 1198791205721 = 1205741 sdot 119896 sdot 119875 and smaller than1198791205722 backtracking the target scatterers trajectories accordingto (10) and (14) On this basis the extracted micromotionfeature parameter vector at 119896th scan can be obtained Go onto cumulate energy for the data of 119896 + 1th scan and extractthe micromotion feature parameters at 119896 + 1th scan Theconsistency of the extracted micromotion feature parametervectors 119862119904y119896 can be calculated according to (29) If 119862119904y119896 andfitting error 119864119891y119896 are both relatively small (satisfies119862119904y119896 lt 119879119862and119864119891y119896 lt 119879119864) we can declare the presence of a target and getthe micromotion feature parameters The energy accumula-tion is no longer needed Otherwise update the state tran-sition set according to (27) and the energy accumulation ofthe data of 119896 + 2th scan is needed Repeat the steps describedabove until it satisfies119862119904y119896 lt 119879119862 and119864119891y119896 lt 119879119864 or 119868(y119896) gt 1198791205722 or it reached the 119870119872th scan In conclusion the flowchart ofmicromotion feature extraction of space target based on TBDis shown in Figure 4

There are three points should be noticed for the proposedmethod

(1) The values of 1205741 and 1205742 are chosen from Monte-Carloexperiments with the given false alarm probability 119875FA1205741 and119875FA1205742 in the case the presence of a target is declared whenthe energy accumulation value is larger than the thresholdThe corresponding detection probabilities are denoted as1198751198631205741 and 1198751198631205742 However the result of micromotion featureextraction is taken into consideration to declare the presenceof a target in this paper thus the final false alarm probability119875FA and detection probability 119875119863 obtained from the proposedmethod are hard to be calculated from a specific expressionwith the variables of 119875FA1205741 1198751198631205741 119875FA1205742 and 1198751198631205742 Numerousexperiments have shown that 119875FA will be a little higherthan 119875FA1205742 Therefore the value of 119875FA1205742 can be chosenaccording to the desired false alarm probability which is setas 119875FA1205742 = 0005 in this paper The value of 119875FA1205741 will affectthe detection probability and computation load and it is setas119875FA1205741 = 05 in this paper from numerous experiments with

the consideration of maximizing the detection probabilityand minimizing the computation load

(2) When the value of 119875 is larger than the observablescatterers number the cumulative energy and the trajectorieswhich are corresponding to the target will not be differentfrom that corresponding to the noise Thus the target willnot be detected On the contrary if the value of 119875 is smallerthan the observable scatterers number only119875 trajectories canbe obtained Thus some scatterers trajectories will be lostand the corresponding micromotion feature parameters cannot be extracted Therefore the value of 119875 should be set asthe maximum possible value firstly which can be preset byexperience Then the value of 119875 decreases gradually until atarget is detected and the micromotion feature is extracted or119875 = 1

(3) The computational load of the proposed method isproportional to the search range Therefore to reduce thecomputational load we assume that target detecting andtracking with narrow-band radar is conducted firstly and alower threshold is used to detect the possible targets then theobtained coarse position and velocity information of targetsare utilized to determine the search range of the proposedmethod

4 Simulations

In this section some simulations are carried out to verify theefficiency of the proposed algorithm

Assume that the target center is located at (0 0 1000) kmat the beginning of observation (ie 119877119888 = 1000 km) and thevelocity of target is 500msThe other simulation parametersare the same with those described in Section 2The geometryof radar and target is illustrated as shown in Figure 5

The parameters of the TBD procedure are set as follows119870119873 = 15 119870119872 = 30 119873119903 = 119873120579 = 1000 Δ119903 = 005m Δ120579 =0005∘ 1198770 = 1000m 1205790 = 0∘ 120601119861 = 015∘ 120589 = 017 119879119862 = 01119879119864 = 2 sdot Δ119903 = 01m 119875FA1205741 = 05 and 119875FA1205742 = 0005 First weconsider the problem of the detection threshold coefficientsetting When the energy accumulation value is larger thanthe threshold it declares the presence of a target and then thefalse alarm probability versus detection threshold coefficientis reported in Figure 6 Therefore for the given 119875FA1205741 = 05and 119875FA1205742 = 0005 the detection threshold coefficients are setas 1205741 = 1 and 1205742 = 13

Themicromotion feature extraction based on TBD of119875 =3 is conducted with SNR = 8 dB which is added to the HRRPof the target Due to the fact that Fourier transform with 119873119903

(119873119903 = 1000) points is taken to obtain the HRRP the averagereceived SNR of the original echo is obtained by subtracting10 log(1000) = 30 dB from the reported value After119870119873 = 15scans among all the state sequenceswhose cumulative energyis larger than 1198791205721 and satisfying the condition shown as (14)one state sequence is corresponding to the target as shown inFigure 7(a) and the other state sequences are induced fromnoise one of them is shown as Figure 7(b) For conveniencethe ordinate value has reduced by a constant of 1 times 106


Echo signal Energy accumulation

Target exists gettingmicromotion feature No target

Target exists gettingmicromotion feature

Update of statetransition set

k = k + 1

k = k + 1

k lt KNI(y (k I(y (kgt T2

k ge KN

Csy lt TC

Efy lt TE

Csy gt TC

orEfy gt TE

to obtain I(y (k andT1T2

Comparing I(y (k with

lt T2 k = KM

lt T1 k lt KM

I(y (k lt T2 k lt KMT1

ltFitting micromotion feature parameters

and fittingcalculating consistency Csyerror Efy

I(y (k

Figure 4 Micromotion feature extraction of space target based on TBD

z

O(0 0 1000)km

= 500 ms

Figure 5 Geometry of radar and target

In the following text for the state of y119896 the cumulativeenergy range trajectories angle trajectories estimatedmicro-motion feature parameter vector fitting error consistencyof the extracted micromotion feature parameter vector statetransition set of target and noise in next scan are denotedas 119868119879(y119896) 119868119873(y119896) 119877y119896 119879 119877y119896119873 Θy119896119879 Θy119896119873 PA119891y119896119879 PA119891y119896119873119864119891y119896119879 119864119891y119896119873 119862119904y119896 119879 119862119904y119896 119873 Γ119879(y119896+1) and Γ119873(y119896+1) respec-tively

Using any two values of the range trajectory the probableslope can be obtained which can be utilized for the coarseslope compensation of trajectories as shown in Figure 8

Based on the range trajectories of target and noiserespectively the estimated micromotion feature parametervectors PA119891y119896119879 and PA119891y119896119873 can be obtained according to(13)ndash(22) At this time the energy accumulation values 119868119879(y119896)and 119868119873(y119896) are both smaller than threshold 1198791205722 and theconsistencies 119862119904y119896 119879 and 119862119904y119896 119873 can not be obtained dueto the inexistence of the extracted micromotion featureparameter vector at the former scanTherefore it is necessaryto continue to carry out energy accumulation For 119868119879(y119896)and 119868119873(y119896) respectively update state transition sets Γ119879(y119896+1)

0

01

02

03

04

05

06

07

08

09

1Fa

lse al

arm

pro

babi

lity

1309 121 11Detection threshold coefficient

Figure 6 False alarm probability versus detection threshold coeffi-cient

and Γ119873(y119896+1) according to (27) by utilizing the obtainedprecession feature parameter vectors PA119891y119896119879 and PA119891y119896119873

After 24 scans for 119868119873(y119896) we can obtain the consistency119862119904y119896 119873 = 392 and fitting error 119864119891y119896119873 = 026 which doesnot satisfy 119862119904y119896 lt 119879119862 and 119864119891y119896 lt 119879119864 On the contrary for119868119879(y119896) the consistency119862119904y119896119879 = 008 andfitting error119864119891y119896119879 =005 which satisfies 119862119904y119896 lt 119879119862 and 119864119891y119896 lt 119879119864 Thereforewe declare the presence of a target and the micromotionfeature parameter vector PA119891y119896119879 can be obtained as shownin Table 1 And the update process of the consistency fittingerror and the size of searching range gate are shown inFigure 9

From Figure 8 we can see that the consistency of theextractedmicromotion feature parameter vector is increasing(ie119862119904y119896 is decreasing)with energy accumulation and119862119904y119896119879can reduce to the value smaller than 119879119862 = 01 while119862119904y119896 119873 is always higher than 119879119862 = 01 Similarly the size


Trajectory 1Trajectory 2Trajectory 3

0

100

200

300

400

500

600

700

800

900

1000Ra

nge (

m)

6 8 104 12 142Scan number

(a)


0

100

200

300

400

500

600

700

800

900

1000

Rang

e (m

)

6 8 10 12 142 4Scan number

(b)

Figure 7 Backtracked range trajectories (a) induced by target (b) induced by noise


minus1

0

1

2

3

4

5

6

Rang

e (m

)

4 6 8 10 12 142Scan number

(a)


minus25

minus20

minus15

minus10

minus5

0

5

Rang

e (m

)


(b)

Figure 8 Backtracked range trajectories with coarse slope compensation (a) induced by target (b) induced by noise

of searching range gate has the same change trend with theconsistency At the same time the fitting error increaseswith energy accumulation and 119864119891y119896119879 can stabilize at thevalue which is smaller than 119879119864 while 119864119891y119896119873 will be higherthan 119879119864 Therefore the state sequence corresponding to the

target can be selected out and the other state sequencesinduced from noise can be eliminated Furthermore theobtained micromotion feature parameter vector shown inTable 1 is closed to the theoretical value which illustrates theeffectiveness of the proposed method


TargetNoise

2018 19 2316 2217 2421Scan number

0

5

10

15

20

25

30

Con

siste

ncy

(a)

TargetNoise

0

005

01

015

02

025

03

Fitti

ng er

ror (

m)

16 2018 19 2315 2217 2421Scan number

(b)

TargetNoise

6

8

10

12

14

16

18

20

22

Size

of s

earc

hing

rang

e gat

e

16 2018 19 2315 2217 2421Scan number

(c)

Figure 9 Update process (a) Consistency of the extracted micromotion feature parameters (b) Fitting error (c) Size of searching range gate

Table 1 Extracted micromotion feature parameter vector

Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106Estimatedvalue 2892 0319 0911 0028 2625 0252 26013 492114 1000023 times 106Error () 360 633 890 967 375 345 352 158 000


Table 2 Extracted micromotion feature parameter vector in with extended Hough transform method

Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106

Estimatedvalue 6200 0500 0600 0100 1700 0100 13800 653000 1000043 times 106Error () 10667 6667 4000 22258 3281 6169 4509 3060 000

Next the detection performance and micromotion fea-ture extraction performance of the proposed method arecomparedwith the traditional TBDmethod and the extendedHough transform method respectively With the proposedmethod the false alarm probability and the detection proba-bility are 119875FA = 00052 and 119875119863 = 08823 With the traditionalTBD method fixing the false alarm probability as 00052the detection probability is 04827 Obviously the detectionperformance of the proposed method is better than thatof the traditional TBD method Further the micromotionfeature extraction performance is defined as the estimatederror of each micromotion feature parameter With theextendedHough transformmethod themicromotion featureparameter vector is obtained shown in Table 2 Due to thelow SNR the micromotion feature parameter vector can notbe extracted effectively with the extended Hough transformmethod while the high micromotion feature extractionperformance can be obtained with the proposed methodshown as Table 1

Finally the detection performance and micromotionfeature extraction performance with different SNRs are con-sidered Fixing the false alarm probability as 00052 thedetection probability of the proposed method is better thanthat of the traditional TBD method shown in Figure 10Without loss of generality we think the micromotion featureextraction is successful when the estimated error of eachmicromotion feature parameter is less than 10 The successof micromotion feature extraction with different SNRs isshown in Figure 11 We can see that the success of micromo-tion feature extraction with the proposed method is muchhigher than that with the extendedHough transformmethodwhen SNR is lower than 11 dB What is more important isthat the micromotion feature parameters can be extractedwithout transmitting additional pulses which can save theradar resources and provide real-time information for targetrecognition

5 Conclusions

A micromotion feature extraction method for space targetbased on TBD is proposed in this paper This methodestablishes a feedback loop between micromotion featureextraction and TBD of target As a result the micromotionfeature can be extracted concurrent with target detecting andtracking and the detection performance can be improvedThe steps of the method are described in detail and somesimulations are given to illustrate its effectiveness It isnoted that the cone-shaped target is taken as an example

Proposed methodTraditional TBD

0

01

02

03

04

05

06

07

08

09

1

Det

ectio

n pr

obab

ility

1510 200 5SNR (dB)

Figure 10 Detection probability versus SNR

Proposed methodExtended Hough transform

0

01

02

03

04

05

06

07

08

09

1

Succ

ess o

f mic

rom

otio

n fe

atur

e par

amet

er ex

trac

tion

0 10 15 205SNR (dB)

Figure 11 Success of micromotion feature extraction versus SNR


for describing and verifying the proposed feature extractingmethod In fact the proposedmethod is not influenced by theshape of the target The proposed feature extracting methodis suitable for the fixed scatterer model slide scatterer modeland any other kinds of micromotion forms by using thecorresponding fitting curves

However the radar resource is limited the resourcesaturationwill be an important problemwhen there aremanytargets coexisting in the radar monitoring area Thus thereasonable and effective resources scheduling algorithms areimportant for exploiting the benefits of the proposedmethodThe related study will be presented in another independentmanuscript

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported in part by the National Natural Sci-ence Foundation of China under Grants 61631019 61471386and 61571457 and in part byMinistry of Education Singaporeunder Grant MOE2016-T2-1-070

References

[1] Y Luo Q Zhang N Yuan F Zhu and F Gu ldquoThree-dimen-sional precession feature extraction of space targetsrdquo IEEETransactions on Aerospace and Electronic Systems vol 50 no2 pp 1313ndash1329 2014

[2] P Suresh T Thayaparan T Obulesu and K VenkataramaniahldquoExtracting micro-doppler radar signatures from rotating tar-gets using fourier-bessel transform and time-frequency analy-sisrdquo IEEE Transactions on Geoscience and Remote Sensing vol52 no 6 pp 3204ndash3210 2014

[3] B Peng Z Liu X Wei and X Li ldquoSinusoidal Frequency Mod-ulation Sparse Recovery for Precession Rate Estimation UsingLow-Frequency Long-Range Radarrdquo IEEE Sensors Journal vol15 no 12 pp 7329ndash7340 2015

[4] V C Chen F Li S-S Ho and H Wechsler ldquoMicro-dopplereffect in radar Phenomenon model and simulation studyrdquoIEEE Transactions on Aerospace and Electronic Systems vol 42no 1 pp 2ndash21 2006

[5] X Chen J Guan X Li and Y He ldquoEffective coherent inte-gration method for marine target with micromotion via phasedifferentiation and radon-Lvrsquos distributionrdquo IET Radar Sonarand Navigation vol 9 no 9 pp 1284ndash1295 2015

[6] J-B Zhuang Z-M Deng Y-S Ye Y-X Zhang and Y-YChen ldquoMicro-doppler ambiguity resolution based on short-time compressed sensingrdquo Journal of Electrical and ComputerEngineering vol 2015 Article ID 864508 2015

[7] Y-X Liu X Li and Z-W Zhuang ldquoEstimation of micro-motion parameters based on micro-Dopplerrdquo IET Signal Pro-cessing vol 4 no 3 pp 213ndash217 2010

[8] J Niu K Li W Jiang X Li G Kuang and H Zhu ldquoA newmethod ofmicro-motion parameters estimation based on cyclicautocorrelation functionrdquo Science China Information Sciencesvol 56 no 10 pp 1ndash11 2013

[9] C Cai W Liu J S Fu and L Lu ldquoEmpirical mode decompo-sition of micro-Doppler signaturerdquo in Proceedings of the 2005IEEE International Radar Conference Record RADAR 2005 pp895ndash899 usa May 2005

[10] Y Luo Q Zhang CW Qiu S Li et al ldquoMicro-Doppler featureextraction for wideband imaging radar based on complex imageorthogonalmatching pursuit decompositionrdquo IETRadar Sonarand Navigation vol 7 no 8 pp 914ndash924 2013

[11] M Li and Y Jiang ldquoBistatic occlusion effect of missile warheadbased on micro-Doppler effectrdquo Optik-International Journal forLight and Electron Optics vol 125 no 19 pp 5630ndash5634 2014

[12] L Ma J Liu T Wang Y Li and X Wang ldquoMicro-Dopplercharacteristics of sliding-type scattering center on rotationallysymmetric targetrdquo Science China Information Sciences vol 54no 9 pp 1957ndash1967 2011

[13] X Bai and Z Bao ldquoHigh-resolution 3D imaging of precessioncone-shaped targetsrdquo IEEE Transactions on Antennas and Prop-agation vol 62 no 8 pp 4209ndash4219 2014

[14] X Bai and Z Bao ldquoImaging of rotation-symmetric space targetsbased on electromagnetic modelingrdquo IEEE Transactions onAerospace and Electronic Systems vol 50 no 3 pp 1680ndash16892014

[15] X PanWWang J Liu D Feng Y Liu and GWang ldquoFeaturesextraction of rotationally symmetric ballistic targets based onmicro-Dopplerrdquo Progress in Electromagnetics Research vol 137pp 727ndash740 2013

[16] J Yan H Liu B Jiu Z Liu and Z Bao ldquoJoint Detection andTracking Processing Algorithm for Target Tracking in MultipleRadar Systemrdquo IEEE Sensors Journal vol 15 no 11 pp 6534ndash6541 2015

[17] S M Tonissen and R J Evans ldquoPerformance of dynamicprogramming techniques for track-before-detectrdquo IEEE Trans-actions on Aerospace and Electronic Systems vol 32 no 4 pp1440ndash1451 1996

[18] F Papi V Kyovtorov R Giuliani F Oliveri and D TarchildquoBernoulli filter for track-before-detect using MIMO radarrdquoIEEE Signal Processing Letters vol 21 no 9 pp 1145ndash1149 2014

[19] Y-J Chen Q Zhang H Jiang Y Luo and Y-A Chen ldquoA cogni-tive feature extracting method for space targetrdquo in Proceedingsof the 36th IEEE International Geoscience and Remote SensingSymposium IGARSS 2016 pp 3148ndash3151 chn July 2016

[20] S Buzzi M Lops L Venturino and M Ferri ldquoTrack-before-detect procedures in a multi-target environmentrdquo IEEE Trans-actions on Aerospace and Electronic Systems vol 44 no 3 pp1135ndash1150 2008

[21] H Jiang W Yi G Cui L Kong and X Yang ldquoTrack-before-detect strategies for range distributed target detectionin compound-Gaussian clutterrdquo Signal Processing vol 120 pp462ndash467 2016

[22] M Zhao Q Zhang Y Luo and L Sun ldquoMicromotion FeatureExtraction and Distinguishing of Space Group Targetsrdquo IEEEGeoscience and Remote Sensing Letters vol 14 no 2 pp 174ndash178 2017

[23] G Dartmann E Zandi andG Ascheid ldquoAmodified levenberg-marquardt method for the bidirectional relay channelrdquo IEEETransactions on Vehicular Technology vol 63 no 8 pp 4096ndash4101 2014

[24] X Bai M Xing F Zhou G Lu and Z Bao ldquoImaging ofmicromotion targets with rotating parts based on empirical-mode decompositionrdquo IEEE Transactions on Geoscience andRemote Sensing vol 46 no 11 pp 3514ndash3523 2008

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



micromotion feature extraction methods for the slide scat-terermodel Unfortunately most of the existingmicromotionfeature extraction methods for the fixed scatterer modelwill not function properly because the micro-Doppler curveof a slide scatterer is much different from that of a fixedscatterer Although some methods based on the complexgeneralizedRadon transform and extendedHough transformare proposed for micromotion feature extraction based onthe slide scatterer model [14 15] the computation load ofthese methods is heavy and the methods need high pulserepetition frequency (PRF) to avoid the frequency domainaliasing phenomenon In this case a lot of radar resourcesneeds to be allocated for micromotion feature extraction

In fact the existingmicromotion feature extractionmeth-ods of space target are implemented after target detection andtracking It is necessary to allocate the limited radar resourcesfor target detecting tracking and feature extraction succes-sively In the case of multitarget monitoring the allocationcontradiction of radar resources will be serious To overcomethis problem we intend to seek a novel approach whichcan implement target detecting and tracking simultaneouslywhen extracting the micromotion features of a space targetwhich can be available for both the fixed scatterer model andthe slide scatterer model

In recent years the track-before-detect (TBD) technol-ogy has shown good performance in weak target detectingand tracking Unlike traditional techniques that declare thepresence of a target at each scan the TBD technology pro-cesses more consecutive scans jointly and then it declaresthe presence of a target and its track [16ndash18] Through theinterscan accumulation the TBD technology can improvethe probability of target detection The idea of establishing afeedback loop between feature extraction and TBD of targethas been provided in our previous preliminary work [19] Inthis paper a micromotion feature extractionmethod of spacetarget based on TBD technology is further proposed In themethod the tracks of target scatterers can be obtained duringthe TBD of target and the tracks are the range-slow-timecurves of target scatterers indeed We call the range-slow-time curve as ldquorange trajectoryrdquo in this paper On this basiswe attempt to add the micromotion feature extraction intothe process of target detecting and tracking by establishing afeedback loop namely that the micromotion feature param-eters are extracted via fitting the obtained range trajectoryaccording to the mathematical expression of m-D effect andin turn the extracted micromotion feature parameters areutilized to update the parameters of TBD adaptively As aresult the micromotion feature extraction detecting andtracking of space target can be implemented simultaneouslywith the information feedback which can provide real-timeand effective information for target recognition By changingthe mathematical expressions of different kinds of m-Deffects for range trajectory fitting the fixed scatterer modelthe slide scatterer model and any kinds of micromotionforms can be processed with the proposed method

This paper is organized as follows Taking the conicaltarget contains a fixed scatterer and two slide scatterers as anexample the micromotion feature of the target precession isanalyzed in Section 2 Combining with the TBD technology

z

an

O y

c

bd

x

r0

Υ

Figure 1 The geometry of conical target with precession

the micromotion feature extraction method is presented indetail in Section 3 Simulations are presented in Section 4 andsome conclusions are made in the last section

2 Micromotion Feature of ConicalTarget with Precession

When the space target is flying outside the atmosphere itneeds to spin around its own axis of symmetry to main-tain stability Meanwhile it needs to cone around a spatialdirectional axis due to the lateral force caused by projectileseparation and bait release These two types of rotationformed the precession of target For a conical target itusually consists of three dominant scatterers (ie one tip-cone scatterer and two cone-base scatterers) where the tip-cone scatterer can be treated as a fixed tip-cone scattererand the cone-base scatterers are slide cone-base scatterersThe geometry of conical target with precession is shownin Figure 1 where 119874 is the target center and the target isrotating around 119911-axis with precession angle 120599 and precessionfrequency 120596 rads The distance between the radar and thetarget center is denoted as 119877119888 The radar LOS is denoted as997888n 119910-axis is in the plane determined by 997888n and 119911-axis and119909-axis is established according to the right-hand rule TheLOS can be represented as 997888n = sin120573997888rarry + cos120573997888rarrz where120573 is the angle between LOS and 119911-axis The target consistsof three scatterers denoted as 119886 119888 and 119889 respectively Theradius of the base circle is 1199030 the distance between the targetcentroid and scatterer 119886 is denoted as |119900119886| and the verticaldistance between the target centroid and the bottom circle isrepresented as |119900119887| According to the rigid body dynamicsthe velocity of target should be along 119911-axis and the velocityis given as V

Assume that the angle between 119909-axis and the projectionof vector997888rarroa on the119909119900119910 plane is1206010 at time 119905 = 0 then the angle








(3)


(4)












Scatterer a

Scatterer d

Scatterer c

minus6

minus4

minus2

0

2

4

6

Rang

e (m

)

0 0402 06 08Slow-time (t)




119872 =






isin [minus1198791199012 1198791199012 ] 119898 isin (1 119872 + 1)

(6)




(7)


119885119896 (x119896) = 119872+1sum119898=1


119894119896 = 1 119873119903 119895119896 = 1 119873120579

(8)



(119868 (x119896minus1)) (9)



(119868 (x119896minus1)) (10)



119877 (119896) = 119903119886 (119896 sdot Δ119905) (11)





119885119896 (y119896) = 119875sum119901=1

119885119896 ((119894119896119901 119895119896)) (12)




119879120572 = 120574119870119875 (13)





119862 (1198771199011 (119896) = 1198771199012 (119896)) lt 120589119870 forall1199011 = 1199012 (14)





(15)


minPA




(16)






11986811198771 (119896) = 119861119886 + 11986211988611989611986821198771 (119896) = 119860119886 sin (120596119886119896 + 1206010119886)

119860119886 = minus |119900119886| sin120573 sin 120599 + 120585


(17)





1198681119877+ (119896) = 119861119888119889 + 1198621198881198891198961198682119877+ (119896) = 119860119888119889 sin (120596119888119889119896 + 1206010119888119889)

119860119888119889 = 2 |119900119887| sin120573 sin 120599 + 120585119861119888119889 = 2 |119900119887| cos120573 cos 120599 + 2119877119888 + 120585

119862119888119889 = minus2 cos120573 sdot V + 120585120596119888119889 = 120596 + 1205851206010119888119889 = 1206010 + 120585

(19)





1206010ini

=



(20)



1003817100381710038171003817100381710038171003817+ 10038171003817100381710038171003817100381710038171198773 (119896) + 1199030 (119904119899)radic1198652 (119904119899) minus |119900119887| (119904119899) 1198651 (119904119899)



(21)


PA ≜ PA (argmin119904119899119864 (119904119899)) (22)


119864 ≜ min119904119899119864 (119904119899) (23)



PA119891 ≜ PA (arg min11987711198772 1198773

119864) (24)


119864119891 ≜ min11987711198772 1198773

119864 (25)






PA119891y119896

= [|119900119886|y119896 1206010y119896 120573y119896 120599y119896 120596y119896 Vy119896 |119900119887|y119896 1199030y119896 119877119888y119896] (26)









(27)

where



(28)



1003816100381610038161003816100381610038161003816100381610038161003816PA119891y119896minus110038161003816100381610038161003816 ) (29)




119891119877 (119862119904y119896) = 119903119898 + 120582 sdot 119862119904y119896 (30)













4 Simulations











k = k + 1

k = k + 1


k ge KN

Csy lt TC

Efy lt TE

Csy gt TC

orEfy gt TE



lt T2 k = KM

lt T1 k lt KM




I(y (k


z

O(0 0 1000)km

= 500 ms





0

01

02

03

04

05

06

07

08

09

1Fa

lse al

arm

pro

babi

lity








0

100

200

300

400

500

600

700

800

900

1000Ra

nge (

m)


(a)


0

100

200

300

400

500

600

700

800

900

1000

Rang

e (m

)

6 8 10 12 142 4Scan number

(b)



minus1

0

1

2

3

4

5

6

Rang

e (m

)

4 6 8 10 12 142Scan number

(a)


minus25

minus20

minus15

minus10

minus5

0

5

Rang

e (m

)


(b)





TargetNoise

2018 19 2316 2217 2421Scan number

0

5

10

15

20

25

30

Con

siste

ncy

(a)

TargetNoise

0

005

01

015

02

025

03

Fitti

ng er

ror (

m)

16 2018 19 2315 2217 2421Scan number

(b)

TargetNoise

6

8

10

12

14

16

18

20

22

Size

of s

earc

hing

rang

e gat

e

16 2018 19 2315 2217 2421Scan number

(c)



Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)




Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106




5 Conclusions



0

01

02

03

04

05

06

07

08

09

1

Det

ectio

n pr

obab

ility

1510 200 5SNR (dB)



0

01

02

03

04

05

06

07

08

09

1

Succ

ess o

f mic

rom

otio

n fe

atur

e par

amet

er ex

trac

tion

0 10 15 205SNR (dB)







Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















(3)


(4)












Scatterer a

Scatterer d

Scatterer c

minus6

minus4

minus2

0

2

4

6

Rang

e (m

)

0 0402 06 08Slow-time (t)




119872 =






isin [minus1198791199012 1198791199012 ] 119898 isin (1 119872 + 1)

(6)




(7)


119885119896 (x119896) = 119872+1sum119898=1


119894119896 = 1 119873119903 119895119896 = 1 119873120579

(8)



(119868 (x119896minus1)) (9)



(119868 (x119896minus1)) (10)



119877 (119896) = 119903119886 (119896 sdot Δ119905) (11)





119885119896 (y119896) = 119875sum119901=1

119885119896 ((119894119896119901 119895119896)) (12)




119879120572 = 120574119870119875 (13)





119862 (1198771199011 (119896) = 1198771199012 (119896)) lt 120589119870 forall1199011 = 1199012 (14)





(15)


minPA




(16)






11986811198771 (119896) = 119861119886 + 11986211988611989611986821198771 (119896) = 119860119886 sin (120596119886119896 + 1206010119886)

119860119886 = minus |119900119886| sin120573 sin 120599 + 120585


(17)





1198681119877+ (119896) = 119861119888119889 + 1198621198881198891198961198682119877+ (119896) = 119860119888119889 sin (120596119888119889119896 + 1206010119888119889)

119860119888119889 = 2 |119900119887| sin120573 sin 120599 + 120585119861119888119889 = 2 |119900119887| cos120573 cos 120599 + 2119877119888 + 120585

119862119888119889 = minus2 cos120573 sdot V + 120585120596119888119889 = 120596 + 1205851206010119888119889 = 1206010 + 120585

(19)





1206010ini

=



(20)



1003817100381710038171003817100381710038171003817+ 10038171003817100381710038171003817100381710038171198773 (119896) + 1199030 (119904119899)radic1198652 (119904119899) minus |119900119887| (119904119899) 1198651 (119904119899)



(21)


PA ≜ PA (argmin119904119899119864 (119904119899)) (22)


119864 ≜ min119904119899119864 (119904119899) (23)



PA119891 ≜ PA (arg min11987711198772 1198773

119864) (24)


119864119891 ≜ min11987711198772 1198773

119864 (25)






PA119891y119896

= [|119900119886|y119896 1206010y119896 120573y119896 120599y119896 120596y119896 Vy119896 |119900119887|y119896 1199030y119896 119877119888y119896] (26)









(27)

where



(28)



1003816100381610038161003816100381610038161003816100381610038161003816PA119891y119896minus110038161003816100381610038161003816 ) (29)




119891119877 (119862119904y119896) = 119903119898 + 120582 sdot 119862119904y119896 (30)













4 Simulations











k = k + 1

k = k + 1


k ge KN

Csy lt TC

Efy lt TE

Csy gt TC

orEfy gt TE



lt T2 k = KM

lt T1 k lt KM




I(y (k


z

O(0 0 1000)km

= 500 ms





0

01

02

03

04

05

06

07

08

09

1Fa

lse al

arm

pro

babi

lity








0

100

200

300

400

500

600

700

800

900

1000Ra

nge (

m)


(a)


0

100

200

300

400

500

600

700

800

900

1000

Rang

e (m

)

6 8 10 12 142 4Scan number

(b)



minus1

0

1

2

3

4

5

6

Rang

e (m

)

4 6 8 10 12 142Scan number

(a)


minus25

minus20

minus15

minus10

minus5

0

5

Rang

e (m

)


(b)





TargetNoise

2018 19 2316 2217 2421Scan number

0

5

10

15

20

25

30

Con

siste

ncy

(a)

TargetNoise

0

005

01

015

02

025

03

Fitti

ng er

ror (

m)

16 2018 19 2315 2217 2421Scan number

(b)

TargetNoise

6

8

10

12

14

16

18

20

22

Size

of s

earc

hing

rang

e gat

e

16 2018 19 2315 2217 2421Scan number

(c)



Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)




Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106




5 Conclusions



0

01

02

03

04

05

06

07

08

09

1

Det

ectio

n pr

obab

ility

1510 200 5SNR (dB)



0

01

02

03

04

05

06

07

08

09

1

Succ

ess o

f mic

rom

otio

n fe

atur

e par

amet

er ex

trac

tion

0 10 15 205SNR (dB)







Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Scatterer a

Scatterer d

Scatterer c

minus6

minus4

minus2

0

2

4

6

Rang

e (m

)

0 0402 06 08Slow-time (t)




119872 =






isin [minus1198791199012 1198791199012 ] 119898 isin (1 119872 + 1)

(6)




(7)


119885119896 (x119896) = 119872+1sum119898=1


119894119896 = 1 119873119903 119895119896 = 1 119873120579

(8)



(119868 (x119896minus1)) (9)



(119868 (x119896minus1)) (10)



119877 (119896) = 119903119886 (119896 sdot Δ119905) (11)





119885119896 (y119896) = 119875sum119901=1

119885119896 ((119894119896119901 119895119896)) (12)




119879120572 = 120574119870119875 (13)





119862 (1198771199011 (119896) = 1198771199012 (119896)) lt 120589119870 forall1199011 = 1199012 (14)





(15)


minPA




(16)






11986811198771 (119896) = 119861119886 + 11986211988611989611986821198771 (119896) = 119860119886 sin (120596119886119896 + 1206010119886)

119860119886 = minus |119900119886| sin120573 sin 120599 + 120585


(17)





1198681119877+ (119896) = 119861119888119889 + 1198621198881198891198961198682119877+ (119896) = 119860119888119889 sin (120596119888119889119896 + 1206010119888119889)

119860119888119889 = 2 |119900119887| sin120573 sin 120599 + 120585119861119888119889 = 2 |119900119887| cos120573 cos 120599 + 2119877119888 + 120585

119862119888119889 = minus2 cos120573 sdot V + 120585120596119888119889 = 120596 + 1205851206010119888119889 = 1206010 + 120585

(19)





1206010ini

=



(20)



1003817100381710038171003817100381710038171003817+ 10038171003817100381710038171003817100381710038171198773 (119896) + 1199030 (119904119899)radic1198652 (119904119899) minus |119900119887| (119904119899) 1198651 (119904119899)



(21)


PA ≜ PA (argmin119904119899119864 (119904119899)) (22)


119864 ≜ min119904119899119864 (119904119899) (23)



PA119891 ≜ PA (arg min11987711198772 1198773

119864) (24)


119864119891 ≜ min11987711198772 1198773

119864 (25)






PA119891y119896

= [|119900119886|y119896 1206010y119896 120573y119896 120599y119896 120596y119896 Vy119896 |119900119887|y119896 1199030y119896 119877119888y119896] (26)









(27)

where



(28)



1003816100381610038161003816100381610038161003816100381610038161003816PA119891y119896minus110038161003816100381610038161003816 ) (29)




119891119877 (119862119904y119896) = 119903119898 + 120582 sdot 119862119904y119896 (30)













4 Simulations











k = k + 1

k = k + 1


k ge KN

Csy lt TC

Efy lt TE

Csy gt TC

orEfy gt TE



lt T2 k = KM

lt T1 k lt KM




I(y (k


z

O(0 0 1000)km

= 500 ms





0

01

02

03

04

05

06

07

08

09

1Fa

lse al

arm

pro

babi

lity








0

100

200

300

400

500

600

700

800

900

1000Ra

nge (

m)


(a)


0

100

200

300

400

500

600

700

800

900

1000

Rang

e (m

)

6 8 10 12 142 4Scan number

(b)



minus1

0

1

2

3

4

5

6

Rang

e (m

)

4 6 8 10 12 142Scan number

(a)


minus25

minus20

minus15

minus10

minus5

0

5

Rang

e (m

)


(b)





TargetNoise

2018 19 2316 2217 2421Scan number

0

5

10

15

20

25

30

Con

siste

ncy

(a)

TargetNoise

0

005

01

015

02

025

03

Fitti

ng er

ror (

m)

16 2018 19 2315 2217 2421Scan number

(b)

TargetNoise

6

8

10

12

14

16

18

20

22

Size

of s

earc

hing

rang

e gat

e

16 2018 19 2315 2217 2421Scan number

(c)



Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)




Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106




5 Conclusions



0

01

02

03

04

05

06

07

08

09

1

Det

ectio

n pr

obab

ility

1510 200 5SNR (dB)



0

01

02

03

04

05

06

07

08

09

1

Succ

ess o

f mic

rom

otio

n fe

atur

e par

amet

er ex

trac

tion

0 10 15 205SNR (dB)







Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119885119896 (y119896) = 119875sum119901=1

119885119896 ((119894119896119901 119895119896)) (12)




119879120572 = 120574119870119875 (13)





119862 (1198771199011 (119896) = 1198771199012 (119896)) lt 120589119870 forall1199011 = 1199012 (14)





(15)


minPA




(16)






11986811198771 (119896) = 119861119886 + 11986211988611989611986821198771 (119896) = 119860119886 sin (120596119886119896 + 1206010119886)

119860119886 = minus |119900119886| sin120573 sin 120599 + 120585


(17)





1198681119877+ (119896) = 119861119888119889 + 1198621198881198891198961198682119877+ (119896) = 119860119888119889 sin (120596119888119889119896 + 1206010119888119889)

119860119888119889 = 2 |119900119887| sin120573 sin 120599 + 120585119861119888119889 = 2 |119900119887| cos120573 cos 120599 + 2119877119888 + 120585

119862119888119889 = minus2 cos120573 sdot V + 120585120596119888119889 = 120596 + 1205851206010119888119889 = 1206010 + 120585

(19)





1206010ini

=



(20)



1003817100381710038171003817100381710038171003817+ 10038171003817100381710038171003817100381710038171198773 (119896) + 1199030 (119904119899)radic1198652 (119904119899) minus |119900119887| (119904119899) 1198651 (119904119899)



(21)


PA ≜ PA (argmin119904119899119864 (119904119899)) (22)


119864 ≜ min119904119899119864 (119904119899) (23)



PA119891 ≜ PA (arg min11987711198772 1198773

119864) (24)


119864119891 ≜ min11987711198772 1198773

119864 (25)






PA119891y119896

= [|119900119886|y119896 1206010y119896 120573y119896 120599y119896 120596y119896 Vy119896 |119900119887|y119896 1199030y119896 119877119888y119896] (26)









(27)

where



(28)



1003816100381610038161003816100381610038161003816100381610038161003816PA119891y119896minus110038161003816100381610038161003816 ) (29)




119891119877 (119862119904y119896) = 119903119898 + 120582 sdot 119862119904y119896 (30)













4 Simulations











k = k + 1

k = k + 1


k ge KN

Csy lt TC

Efy lt TE

Csy gt TC

orEfy gt TE



lt T2 k = KM

lt T1 k lt KM




I(y (k


z

O(0 0 1000)km

= 500 ms





0

01

02

03

04

05

06

07

08

09

1Fa

lse al

arm

pro

babi

lity








0

100

200

300

400

500

600

700

800

900

1000Ra

nge (

m)


(a)


0

100

200

300

400

500

600

700

800

900

1000

Rang

e (m

)

6 8 10 12 142 4Scan number

(b)



minus1

0

1

2

3

4

5

6

Rang

e (m

)

4 6 8 10 12 142Scan number

(a)


minus25

minus20

minus15

minus10

minus5

0

5

Rang

e (m

)


(b)





TargetNoise

2018 19 2316 2217 2421Scan number

0

5

10

15

20

25

30

Con

siste

ncy

(a)

TargetNoise

0

005

01

015

02

025

03

Fitti

ng er

ror (

m)

16 2018 19 2315 2217 2421Scan number

(b)

TargetNoise

6

8

10

12

14

16

18

20

22

Size

of s

earc

hing

rang

e gat

e

16 2018 19 2315 2217 2421Scan number

(c)



Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)




Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106




5 Conclusions



0

01

02

03

04

05

06

07

08

09

1

Det

ectio

n pr

obab

ility

1510 200 5SNR (dB)



0

01

02

03

04

05

06

07

08

09

1

Succ

ess o

f mic

rom

otio

n fe

atur

e par

amet

er ex

trac

tion

0 10 15 205SNR (dB)







Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












11986811198771 (119896) = 119861119886 + 11986211988611989611986821198771 (119896) = 119860119886 sin (120596119886119896 + 1206010119886)

119860119886 = minus |119900119886| sin120573 sin 120599 + 120585


(17)





1198681119877+ (119896) = 119861119888119889 + 1198621198881198891198961198682119877+ (119896) = 119860119888119889 sin (120596119888119889119896 + 1206010119888119889)

119860119888119889 = 2 |119900119887| sin120573 sin 120599 + 120585119861119888119889 = 2 |119900119887| cos120573 cos 120599 + 2119877119888 + 120585

119862119888119889 = minus2 cos120573 sdot V + 120585120596119888119889 = 120596 + 1205851206010119888119889 = 1206010 + 120585

(19)





1206010ini

=



(20)



1003817100381710038171003817100381710038171003817+ 10038171003817100381710038171003817100381710038171198773 (119896) + 1199030 (119904119899)radic1198652 (119904119899) minus |119900119887| (119904119899) 1198651 (119904119899)



(21)


PA ≜ PA (argmin119904119899119864 (119904119899)) (22)


119864 ≜ min119904119899119864 (119904119899) (23)



PA119891 ≜ PA (arg min11987711198772 1198773

119864) (24)


119864119891 ≜ min11987711198772 1198773

119864 (25)






PA119891y119896

= [|119900119886|y119896 1206010y119896 120573y119896 120599y119896 120596y119896 Vy119896 |119900119887|y119896 1199030y119896 119877119888y119896] (26)









(27)

where



(28)



1003816100381610038161003816100381610038161003816100381610038161003816PA119891y119896minus110038161003816100381610038161003816 ) (29)




119891119877 (119862119904y119896) = 119903119898 + 120582 sdot 119862119904y119896 (30)













4 Simulations











k = k + 1

k = k + 1


k ge KN

Csy lt TC

Efy lt TE

Csy gt TC

orEfy gt TE



lt T2 k = KM

lt T1 k lt KM




I(y (k


z

O(0 0 1000)km

= 500 ms





0

01

02

03

04

05

06

07

08

09

1Fa

lse al

arm

pro

babi

lity








0

100

200

300

400

500

600

700

800

900

1000Ra

nge (

m)


(a)


0

100

200

300

400

500

600

700

800

900

1000

Rang

e (m

)

6 8 10 12 142 4Scan number

(b)



minus1

0

1

2

3

4

5

6

Rang

e (m

)

4 6 8 10 12 142Scan number

(a)


minus25

minus20

minus15

minus10

minus5

0

5

Rang

e (m

)


(b)





TargetNoise

2018 19 2316 2217 2421Scan number

0

5

10

15

20

25

30

Con

siste

ncy

(a)

TargetNoise

0

005

01

015

02

025

03

Fitti

ng er

ror (

m)

16 2018 19 2315 2217 2421Scan number

(b)

TargetNoise

6

8

10

12

14

16

18

20

22

Size

of s

earc

hing

rang

e gat

e

16 2018 19 2315 2217 2421Scan number

(c)



Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)




Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106




5 Conclusions



0

01

02

03

04

05

06

07

08

09

1

Det

ectio

n pr

obab

ility

1510 200 5SNR (dB)



0

01

02

03

04

05

06

07

08

09

1

Succ

ess o

f mic

rom

otio

n fe

atur

e par

amet

er ex

trac

tion

0 10 15 205SNR (dB)







Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1206010ini

=



(20)



1003817100381710038171003817100381710038171003817+ 10038171003817100381710038171003817100381710038171198773 (119896) + 1199030 (119904119899)radic1198652 (119904119899) minus |119900119887| (119904119899) 1198651 (119904119899)



(21)


PA ≜ PA (argmin119904119899119864 (119904119899)) (22)


119864 ≜ min119904119899119864 (119904119899) (23)



PA119891 ≜ PA (arg min11987711198772 1198773

119864) (24)


119864119891 ≜ min11987711198772 1198773

119864 (25)






PA119891y119896

= [|119900119886|y119896 1206010y119896 120573y119896 120599y119896 120596y119896 Vy119896 |119900119887|y119896 1199030y119896 119877119888y119896] (26)









(27)

where



(28)



1003816100381610038161003816100381610038161003816100381610038161003816PA119891y119896minus110038161003816100381610038161003816 ) (29)




119891119877 (119862119904y119896) = 119903119898 + 120582 sdot 119862119904y119896 (30)













4 Simulations











k = k + 1

k = k + 1


k ge KN

Csy lt TC

Efy lt TE

Csy gt TC

orEfy gt TE



lt T2 k = KM

lt T1 k lt KM




I(y (k


z

O(0 0 1000)km

= 500 ms





0

01

02

03

04

05

06

07

08

09

1Fa

lse al

arm

pro

babi

lity








0

100

200

300

400

500

600

700

800

900

1000Ra

nge (

m)


(a)


0

100

200

300

400

500

600

700

800

900

1000

Rang

e (m

)

6 8 10 12 142 4Scan number

(b)



minus1

0

1

2

3

4

5

6

Rang

e (m

)

4 6 8 10 12 142Scan number

(a)


minus25

minus20

minus15

minus10

minus5

0

5

Rang

e (m

)


(b)





TargetNoise

2018 19 2316 2217 2421Scan number

0

5

10

15

20

25

30

Con

siste

ncy

(a)

TargetNoise

0

005

01

015

02

025

03

Fitti

ng er

ror (

m)

16 2018 19 2315 2217 2421Scan number

(b)

TargetNoise

6

8

10

12

14

16

18

20

22

Size

of s

earc

hing

rang

e gat

e

16 2018 19 2315 2217 2421Scan number

(c)



Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)




Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106




5 Conclusions



0

01

02

03

04

05

06

07

08

09

1

Det

ectio

n pr

obab

ility

1510 200 5SNR (dB)



0

01

02

03

04

05

06

07

08

09

1

Succ

ess o

f mic

rom

otio

n fe

atur

e par

amet

er ex

trac

tion

0 10 15 205SNR (dB)







Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












PA119891y119896

= [|119900119886|y119896 1206010y119896 120573y119896 120599y119896 120596y119896 Vy119896 |119900119887|y119896 1199030y119896 119877119888y119896] (26)









(27)

where



(28)



1003816100381610038161003816100381610038161003816100381610038161003816PA119891y119896minus110038161003816100381610038161003816 ) (29)




119891119877 (119862119904y119896) = 119903119898 + 120582 sdot 119862119904y119896 (30)













4 Simulations











k = k + 1

k = k + 1


k ge KN

Csy lt TC

Efy lt TE

Csy gt TC

orEfy gt TE



lt T2 k = KM

lt T1 k lt KM




I(y (k


z

O(0 0 1000)km

= 500 ms





0

01

02

03

04

05

06

07

08

09

1Fa

lse al

arm

pro

babi

lity








0

100

200

300

400

500

600

700

800

900

1000Ra

nge (

m)


(a)


0

100

200

300

400

500

600

700

800

900

1000

Rang

e (m

)

6 8 10 12 142 4Scan number

(b)



minus1

0

1

2

3

4

5

6

Rang

e (m

)

4 6 8 10 12 142Scan number

(a)


minus25

minus20

minus15

minus10

minus5

0

5

Rang

e (m

)


(b)





TargetNoise

2018 19 2316 2217 2421Scan number

0

5

10

15

20

25

30

Con

siste

ncy

(a)

TargetNoise

0

005

01

015

02

025

03

Fitti

ng er

ror (

m)

16 2018 19 2315 2217 2421Scan number

(b)

TargetNoise

6

8

10

12

14

16

18

20

22

Size

of s

earc

hing

rang

e gat

e

16 2018 19 2315 2217 2421Scan number

(c)



Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)




Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106




5 Conclusions



0

01

02

03

04

05

06

07

08

09

1

Det

ectio

n pr

obab

ility

1510 200 5SNR (dB)



0

01

02

03

04

05

06

07

08

09

1

Succ

ess o

f mic

rom

otio

n fe

atur

e par

amet

er ex

trac

tion

0 10 15 205SNR (dB)







Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















4 Simulations











k = k + 1

k = k + 1


k ge KN

Csy lt TC

Efy lt TE

Csy gt TC

orEfy gt TE



lt T2 k = KM

lt T1 k lt KM




I(y (k


z

O(0 0 1000)km

= 500 ms





0

01

02

03

04

05

06

07

08

09

1Fa

lse al

arm

pro

babi

lity








0

100

200

300

400

500

600

700

800

900

1000Ra

nge (

m)


(a)


0

100

200

300

400

500

600

700

800

900

1000

Rang

e (m

)

6 8 10 12 142 4Scan number

(b)



minus1

0

1

2

3

4

5

6

Rang

e (m

)

4 6 8 10 12 142Scan number

(a)


minus25

minus20

minus15

minus10

minus5

0

5

Rang

e (m

)


(b)





TargetNoise

2018 19 2316 2217 2421Scan number

0

5

10

15

20

25

30

Con

siste

ncy

(a)

TargetNoise

0

005

01

015

02

025

03

Fitti

ng er

ror (

m)

16 2018 19 2315 2217 2421Scan number

(b)

TargetNoise

6

8

10

12

14

16

18

20

22

Size

of s

earc

hing

rang

e gat

e

16 2018 19 2315 2217 2421Scan number

(c)



Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)




Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106




5 Conclusions



0

01

02

03

04

05

06

07

08

09

1

Det

ectio

n pr

obab

ility

1510 200 5SNR (dB)



0

01

02

03

04

05

06

07

08

09

1

Succ

ess o

f mic

rom

otio

n fe

atur

e par

amet

er ex

trac

tion

0 10 15 205SNR (dB)







Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














k = k + 1

k = k + 1


k ge KN

Csy lt TC

Efy lt TE

Csy gt TC

orEfy gt TE



lt T2 k = KM

lt T1 k lt KM




I(y (k


z

O(0 0 1000)km

= 500 ms





0

01

02

03

04

05

06

07

08

09

1Fa

lse al

arm

pro

babi

lity








0

100

200

300

400

500

600

700

800

900

1000Ra

nge (

m)


(a)


0

100

200

300

400

500

600

700

800

900

1000

Rang

e (m

)

6 8 10 12 142 4Scan number

(b)



minus1

0

1

2

3

4

5

6

Rang

e (m

)

4 6 8 10 12 142Scan number

(a)


minus25

minus20

minus15

minus10

minus5

0

5

Rang

e (m

)


(b)





TargetNoise

2018 19 2316 2217 2421Scan number

0

5

10

15

20

25

30

Con

siste

ncy

(a)

TargetNoise

0

005

01

015

02

025

03

Fitti

ng er

ror (

m)

16 2018 19 2315 2217 2421Scan number

(b)

TargetNoise

6

8

10

12

14

16

18

20

22

Size

of s

earc

hing

rang

e gat

e

16 2018 19 2315 2217 2421Scan number

(c)



Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)




Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106




5 Conclusions



0

01

02

03

04

05

06

07

08

09

1

Det

ectio

n pr

obab

ility

1510 200 5SNR (dB)



0

01

02

03

04

05

06

07

08

09

1

Succ

ess o

f mic

rom

otio

n fe

atur

e par

amet

er ex

trac

tion

0 10 15 205SNR (dB)







Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

100

200

300

400

500

600

700

800

900

1000Ra

nge (

m)


(a)


0

100

200

300

400

500

600

700

800

900

1000

Rang

e (m

)

6 8 10 12 142 4Scan number

(b)



minus1

0

1

2

3

4

5

6

Rang

e (m

)

4 6 8 10 12 142Scan number

(a)


minus25

minus20

minus15

minus10

minus5

0

5

Rang

e (m

)


(b)





TargetNoise

2018 19 2316 2217 2421Scan number

0

5

10

15

20

25

30

Con

siste

ncy

(a)

TargetNoise

0

005

01

015

02

025

03

Fitti

ng er

ror (

m)

16 2018 19 2315 2217 2421Scan number

(b)

TargetNoise

6

8

10

12

14

16

18

20

22

Size

of s

earc

hing

rang

e gat

e

16 2018 19 2315 2217 2421Scan number

(c)



Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)




Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106




5 Conclusions



0

01

02

03

04

05

06

07

08

09

1

Det

ectio

n pr

obab

ility

1510 200 5SNR (dB)



0

01

02

03

04

05

06

07

08

09

1

Succ

ess o

f mic

rom

otio

n fe

atur

e par

amet

er ex

trac

tion

0 10 15 205SNR (dB)







Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










TargetNoise

2018 19 2316 2217 2421Scan number

0

5

10

15

20

25

30

Con

siste

ncy

(a)

TargetNoise

0

005

01

015

02

025

03

Fitti

ng er

ror (

m)

16 2018 19 2315 2217 2421Scan number

(b)

TargetNoise

6

8

10

12

14

16

18

20

22

Size

of s

earc

hing

rang

e gat

e

16 2018 19 2315 2217 2421Scan number

(c)



Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)




Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106




5 Conclusions



0

01

02

03

04

05

06

07

08

09

1

Det

ectio

n pr

obab

ility

1510 200 5SNR (dB)



0

01

02

03

04

05

06

07

08

09

1

Succ

ess o

f mic

rom

otio

n fe

atur

e par

amet

er ex

trac

tion

0 10 15 205SNR (dB)







Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Parameter |119900119886|(m)

|119900119887|(m)

1199030(m)

1206010(rad)

120573(∘)

120599(∘)

120596(rads)

V(ms)

119877119888(m)

Ture value 3000 0300 1000 0031 2530 0261 25132 500000 106




5 Conclusions



0

01

02

03

04

05

06

07

08

09

1

Det

ectio

n pr

obab

ility

1510 200 5SNR (dB)



0

01

02

03

04

05

06

07

08

09

1

Succ

ess o

f mic

rom

otio

n fe

atur

e par

amet

er ex

trac

tion

0 10 15 205SNR (dB)







Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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