first approach to wake vortex predicting and detecting ... · pdf filefirst approach to wake...

First approach to wake vortex predicting and detecting integrated

fusion filters

EEC Scientific Seminar, 07.11.2008

EEC Scientific Seminar, 07.11.2008 2Institute of Flight GuidanceTU Braunschweig

Outline

• motivation/current situation• state-of-the-art approaches

– prediction models• characteristics, pros/cons

– measurement technologies• characteristics, pros/cons

• new fusion approach• excursus filter technologies• implementation for wake vortex detection and prediction• results of first approach


Wake Vortices-

General issues


Wake vortices as capacity limiting factors

• today: separation rules based on worst-case-scenario – (calm atmosphere, no lateral wind long wake vortex lifetime)

• unnecessarily limiting capacities in favorable conditions• but: separation reduction only possible while preserving safety level

Categories based on aircraft max. take-off weight

Leading aircraft Following aircraft

Spatialseparation

[nm]

Equivalent temporalseparation [s]at = 110 ktsV

HEA

VY

HEA

VY

MED

IUM

MED

IUM

LIG

HT

LIG

HT

4

5

6

5

131

164

196

164

Approach Take-Off

Temporalseparation [s]

n/a

120 / 180*

120 / 180*

120 / 180*

HEAVY: > 136t , MEDIUM: 7 - 136t , LIGHT: < 7t (*) if taking off from intermediate position

SUPE

R –

A380

/800 6

7

8


The Propagation


State-of-the-art approaches - prediction

• propagation of wake vortex behaviour• models: P2P (DLR), PVM (UCL), AVOSS-PA (NASA)

proven in several EU projects• prediction of:

– turbulence strength (circulation)– vortex trajectory in y and z– uncertainty bounds


Consideration of wake vortex characteristics

• two phase vortex decay

– 1. phase: turbulent diffusion

– 2. phase: rapid decay1. phase

2. phase


Consideration of influence parameters

• atmospheric influence

– vortex reascensionnear ground

– wind shear influence


The Measurement


State-of-the-art approaches: measurement

• wake vortex monitoring

– based on LIDAR (also RADAR coming into focus)

– research activities in several EU-projects

– principle: Doppler-effect measurement

– laser beam reflected by aerosols– aerosol LOS movement changes

phase of transmitted light = frequency shift

TXRX

LIDAR


State-of-the-art approaches: measurement

– ∆f ~ vaerosol

– circulation determination from velocity profile:

– core position determination from v(r)trajectory

rv(r)2 (r) π=Γ


Measurement applications

• ground based scan pattern

• airborne measurements

• in both cases, only line-of-sight velocity is measured

Lidar


Measurement display example

• example of Lidar measurements visualisation

[www.onera.fr]


Complementary attributes

updated information of vortex stateno information about real wake vortex state

reduced uncertainty on measurement update

increasing uncertainty bounds due to model and input uncertainties

low measurement update ratehigh prediction update rate

limited accuracyshort term stability

no information about vortex state between measurements/due to loss of track

forecast

measurementprediction

Taking advantage by using only the positivecharacteristics of each system

Typical example of two complementary systems


Example of complementary attributes

*t

*y

measurement-updates

current uncertainty boundrelative large

fused uncertainty bounds couldbe extracted from filterscovariance


Applicationof fusion filters

forWake Vortex prediction


Goal

Γ*

t*

z*

t*

y*

t*

Model / Prediction

[www.cerfacs.fr]

[www.eurocontrol.be]

Measurement


Goal

Model / Prediction Measurement


Simple discrete Kalman Filter Principle

Timeupdate

Measurement-Update

x0, P0


Someillustratingexamples


Example with general model

• constant position– measurements come in at low frequency– no information between measurements

t1 t2

t

Obs.



• constant velocity– measurements at low frequency– short time accurate information bewteen

measurements

t1 t2

t

Obs.



• constant acceleration– measurements at low frequency– more accurate between measurements

t

Obs.


Example with specific model

• Tracking object example: cannon-launched projectile tracking– model of movement exists (e.g. gravity, drag)

high frequent prediction– low frequent measurement updates model

x

y

Cannon Radar

g

drag

Θ


Example with specific model

g

drag

Θ

accuracy and coasting capability depends on modelling of system behaviour

better modelhigher accuracy and better coasting


Example for position estimation

• Simple Kalman Filter: Propagation

Timeupdate

Measurement-Update

kT

kkQPP +ΦΦ=

−

−

1

kkk uxx Γ+Φ= −−

1ˆˆ( )−− −+= kkkkk xHzKxx ˆˆˆ

( ) 1−−− += kT

kT

kkRHPHHPK

( ) −−=kkk

PHKIP

x0, P0


Example for position estimation – propagation

• Simple 1st order example (constant velocity):

• yields:

new position = old position + old velocity * sample Time

TimeupdateMeasurement-Update

kT

kkQPP +ΦΦ=

−

−

1



( ) 1−−− += kT

kT

kkRHPHHPK

( ) −−=kkk

PHKIP

x0, P0

{ {xFx

xx

xx

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛&

321&&

&

&

0010

skkk Txxx Δ⋅+= +−

+−

−11 &


Example for position estimation – propagation

• Simple Kalman Filter: Measurement update

Timeupdate

Measurement-Update

kT

kkQPP +ΦΦ=

−

−

1



( ) 1−−− += kT

kT

kkRHPHHPK

( ) −−=kkk

PHKIP

x0, P0


Example for position estimation – correction

• Correction through measurement

estimated Position corrected by difference model <> measurement


kT

kkQPP +ΦΦ=

−

−

1



( ) 1−−− += kT

kT

kkRHPHHPK

( ) −−=kkk

PHKIP

x0, P0

( )−−+ ⋅−+= kkkkk xHzKxx


Example for position estimation – uncertainty

• calculated uncertainty:

Timeupdate

Measurement-Update

kT

kkQPP +ΦΦ=

−

−

1



( ) 1−−− += kT

kT

kkRHPHHPK

( ) −−=kkk

PHKIP

x0, P0


Example for position estimation – uncertainty


kT

kkQPP +ΦΦ=

−

−

1



( ) 1−−− += kT

kT

kkRHPHHPK

( ) −−=kkk

PHKIP

x0, P0


WV fusion filters:General layout

anddefinitions


Possible future on-board system

NED-COSNED-COS

body-COS

AttitudeΘ

r

Model-Prediction


Transition to possible Wake Vortex estimationtechniques via Kalman Filters

Time-Update

Measurement-Update

kT

kkQPP +ΦΦ=

−

−

1



( ) 1−−− += kT

kT

kkRHPHHPK

( ) −−=kkk

PHKIP

x0, P0

state (WV traffic, MET, possiblyLIDAR-angles)

model statetransition(establishedprediction models)

error/uncertainty-feedback

measured quantities(position, strength, range, bearing, TBD)

Covariance (analogous to uncertainty boundin current models, but decreased bymeasurement)


Uncoupled

A/C data

MET data

zyx ,,,Γ

zyx ,,,Γ

processingLIDAR /

RADAR

WV-model


Loose Coupled – open loop error state

Fusion Filter

error state

A/C data

MET data

zyx ,,,Γ

zyx ,,,Γ

processingLIDAR /

RADAR

WV-model

zyx ΔΔΔΔΓ

,,

−

output


Loose coupled – closed loop error state

Fusion Filter

error state

A/C data

MET data

zyx ,,,Γ

zyx ,,,Γ

processingLIDAR /

RADAR

WV-model

zyx ΔΔΔΔΓ

,,

output


Tight coupled – closed loop error state

Fusion Filter

error state

A/C data

MET data

θ,, rΓ

zyx ,,,Γ

processingLIDAR /

RADAR

WV-model

zyx ΔΔΔΔΓ

,,

output


Loose Coupled full state

Fusion Filter

full state

A/C data

MET data

zyx ,,,Γprocessing

LIDAR /

RADAR

output

( )( )( )−

−−

−+

=

kkk

kkk

xhzK

uxfx

ˆ

,ˆˆ 11

adapted established models


Tight Coupled Full state

Fusion Filter

full state

A/C data

MET data

θ,, rΓprocessing

LIDAR /

RADAR

output

( )( )( )−

−−

−+

=

kkk

kkk

xhzK

uxfx

ˆ

,ˆˆ 11



Deep Coupled full state

Fusion Filter

full state

A/C data

MET data

θ̂,ˆ,ˆ rfd

processingLIDAR /

RADAR

output

( )( )( )−

−−

−+

=

kkk

kkk

xhzK

uxfx

ˆ

,ˆˆ 11



First implementation


First implementation with general PVA model

• First modelling WV traffic and strength as PVA

Timeupdate

Measurement-Update

kT

kkQPP +ΦΦ=

−

−

1



( ) 1−−− += kT

kT

kkRHPHHPK

( ) −−=kkk

PHKIP

x0, P0



[ ]Tzzzyyyx ******** ΓΓ= &&&&&&&

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

0000000010000000000000000010000000010000000000000000010000000010

F

xFx ⋅=&• basic system dynamic equation

• with

• and

here state-of-the-art predictionmodels will be implemented in near future



• results quite good for fusion filter w/o real modelling of dynamicsbehaviour stems only from self-learning capability of filter



• Simulated LIDAR outage between t* = 3.5 and t* = 4.9– filter continues delivering output– once established prediction models are inserted, the filter will

behave like those models taking into account self-estimated errors


Conclusions

• model predictions and measurement are complementary• taking advantages by fusion of both• general definitions and methods were defined• first implementation results show proof-of-concept

– keeping in mind, that the WV behaviour is not modelled within thefilters yet

results show that fusion approach is applicable for future WV prediction and detection systems

• further steps– deriving error state explanation for a chosen established prediction

model– implementing and testing the loose coupled error state filter– benchmarking against measurement and sole prediction model


Contact: Dipl.-Ing. Shanna Schönhals

Dipl.-Ing. Meiko Steen

Institute of Flight Guidance, TU Braunschweig

Fon: +49 531 391 9858 / +49 531 391 9837

Mail: [email protected] / [email protected]

Thank you foryour attention!

first approach to wake vortex predicting and detecting ... · pdf filefirst approach to wake...

Documents