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

Equivalent temporalseparation [s]at = 110 ktsV

Approach Take-Off

Temporalseparation [s]

120 / 180*

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

/800 6

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

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

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

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

measurement-updates

current uncertainty boundrelative large

fused uncertainty bounds couldbe extracted from filterscovariance

Applicationof fusion filters

forWake Vortex prediction

Model / Prediction

[www.cerfacs.fr]

[www.eurocontrol.be]

Measurement

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

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

measurements

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

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

Cannon Radar

Example with specific model

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

kkQPP +ΦΦ=

kkk uxx Γ+Φ= −−

1ˆˆ( )−− −+= kkkkk xHzKxx ˆˆˆ

( ) 1−−− += kT

kkRHPHHPK

( ) −−=kkk

x0, P0

Example for position estimation – propagation

• Simple 1st order example (constant velocity):

• yields:

new position = old position + old velocity * sample Time

TimeupdateMeasurement-Update

kkQPP +ΦΦ=

( ) 1−−− += kT

kkRHPHHPK

( ) −−=kkk

x0, P0

{ {xFx

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎞⎜⎜⎝

skkk Txxx Δ⋅+= +−

−11 &

Example for position estimation – propagation

• Simple Kalman Filter: Measurement update

Timeupdate

Measurement-Update

kkQPP +ΦΦ=

( ) 1−−− += kT

kkRHPHHPK

( ) −−=kkk

x0, P0

Example for position estimation – correction

• Correction through measurement

estimated Position corrected by difference model <> measurement

kkQPP +ΦΦ=

( ) 1−−− += kT

kkRHPHHPK

( ) −−=kkk

x0, P0

( )−−+ ⋅−+= kkkkk xHzKxx

Example for position estimation – uncertainty

• calculated uncertainty:

Timeupdate

Measurement-Update

kkQPP +ΦΦ=

( ) 1−−− += kT

kkRHPHHPK

( ) −−=kkk

x0, P0

Example for position estimation – uncertainty

kkQPP +ΦΦ=

( ) 1−−− += kT

kkRHPHHPK

( ) −−=kkk

x0, P0

WV fusion filters:General layout

anddefinitions

Possible future on-board system

NED-COSNED-COS

body-COS

AttitudeΘ

Model-Prediction

Transition to possible Wake Vortex estimationtechniques via Kalman Filters

Time-Update

Measurement-Update

kkQPP +ΦΦ=

( ) 1−−− += kT

kkRHPHHPK

( ) −−=kkk

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

processingLIDAR /

WV-model

Loose Coupled – open loop error state

Fusion Filter

error state

A/C data

MET data

zyx ,,,Γ

processingLIDAR /

WV-model

zyx ΔΔΔΔΓ

output

Loose coupled – closed loop error state

Fusion Filter

error state

A/C data

MET data

zyx ,,,Γ

processingLIDAR /

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 /

WV-model

zyx ΔΔΔΔΓ

output

Loose Coupled full state

Fusion Filter

full state

A/C data

MET data

zyx ,,,Γprocessing

LIDAR /

output

( )( )( )−

−−

,ˆˆ 11

adapted established models

Tight Coupled Full state

Fusion Filter

full state

A/C data

MET data

θ,, rΓprocessing

LIDAR /

output

( )( )( )−

−−

,ˆˆ 11

Deep Coupled full state

Fusion Filter

full state

A/C data

MET data

θ̂,ˆ,ˆ rfd

processingLIDAR /

output

( )( )( )−

−−

,ˆˆ 11

First implementation

First implementation with general PVA model

• First modelling WV traffic and strength as PVA

Timeupdate

Measurement-Update

kkQPP +ΦΦ=

( ) 1−−− += kT

kkRHPHHPK

( ) −−=kkk

x0, P0

[ ]Tzzzyyyx ******** ΓΓ= &&&&&&&

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

0000000010000000000000000010000000010000000000000000010000000010

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: s.schoenhals@tu-bs.de / m.steen@tu-bs.de

Thank you foryour attention!

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