Generalizations of the auxiliary particle filter for multiple target tracking

Particle filters for Multiple target trackingState partition particle filters

Generalizations of auxiliary particle filtering for MTTSimulations and results

Conclusions

Generalizations of the auxiliary particle filter formultiple target tracking

Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal?

?Dpto. Senales, Sistemas y Radiocomunicaciones, Universidad Politecnica de Madrid,Spain

†Dept. of Electrical and Computer Engineering, Curtin University, Australia

Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? Generalizations of the auxiliary particle filter for multiple target tracking



Conclusions

Outline

1 Particle filters for Multiple target tracking

2 State partition particle filters

3 Generalizations of auxiliary particle filtering for MTTAPPTRAPP

4 Simulations and resultsTarget dynamics and sensor modelingResults

5 Conclusions




Conclusions

Outline





5 Conclusions




Conclusions

Multiple target tracking.

Multiple target tracking

MTT is usually formulated in the Bayesian framework. Theinformation of interest about the targets is contained in themultitarget posterior PDF.

Multitarget state

Xk =[(xk1)T , (xk2)T , ..., (xkt )T

]T∈ Rn·t

Posterior PDF

p(Xk |z1:k)




Conclusions

Particle filters.

PFs sample the state-space to build an approximation to theposterior PDF.

The dimension of the state-space linearly grows with thenumber of targets.

Sampling high-dimension state-spaces is very inefficient, givingrise to the curse of dimensionality.Some modifications are needed if PFs are to be successfullyapplied to MTT.




Conclusions

Outline





5 Conclusions




Conclusions

State partition.

State partition

To appease the curse of dimensionality some algorithms assume posteriorindependence between targets. This allows for the partition of the state-space toindividually sample the state of each target.

p(Xk+1|z1:k+1) =t∏

j=1

pj (xk+1j |z1:k+1)

Some algorithms that work under the independence assumption are:

Independent Joint Optimal Importance Density PF (IJOID) [1].Independent Partition PF (IP) [2].Parallel Partition PF (PP) [3].

[1] W. Yi, M. R. Morelande, L. Kong, and J. Yang, “A computationally efficient particle filter for multitargettracking using an independence approximation,” IEEE Transactions on Signal Processing, Feb. 2013.[2] M. Orton and W. Fitzgerald, “A Bayesian approach to tracking multiple targets using sensor arrays and particlefilters,” IEEE Transactions on Signal Processing, 2002.[3] A. F. Garcıa-Fernandez, M. Morelande, and J. Grajal, “Two-layer particle filter for multiple target detection andtracking,” IEEE Transactions on Aerospace and Electronic Systems, 2013.




Conclusions

APPTRAPP

Outline





5 Conclusions




Conclusions

APPTRAPP

Auxiliary PFs for MTT.

When there is only one target present, both IP and PP comedown to the sequential-importance-resampling PF, which isusually outperformed by the auxiliary particle filter.

Two particle filters, APP and TRAPP, are presented inspiredby the APF and the state-partition strategy of PP, resultingon generalizations of the APF for multiple target tracking.




Conclusions

APPTRAPP

Auxiliary parallel partition.

APP

APP makes use of auxiliary particle filtering for each target,selecting those subparticles at time k that are prone to generatesubparticles with higher target-likelihood at time k + 1 accordingto zk+1 .

q(Xk+1, a|z1:k+1) =t∏

j=1

qj(xk+1j , aj |z1:k+1)

qj(xk+1j , aj |z1:k+1) ∝ bj(µ

k+1j ,aj

)ωkajp(xk+1

j |xkj ,aj )




Conclusions

APPTRAPP

Auxiliary parallel partition. Example




Conclusions

APPTRAPP





Conclusions

APPTRAPP





Conclusions

APPTRAPP





Conclusions

APPTRAPP





Conclusions

APPTRAPP





Conclusions

APPTRAPP





Conclusions

APPTRAPP





Conclusions

APPTRAPP

Target-resampling auxiliary parallel partition.

TRAPP PF

Target-resampling (as in IP and PP) is not always undesirable,depending on the sensor model and the dimension of the statespace. TRAPP makes use of auxiliary filtering followed bytarget-resampling.

q(Xk+1, a|z1:k+1) =t∏

j=1

qj(xk+1j , aj |z1:k+1)

qj(xk+1j , aj |z1:k+1) ∝ bj(x

k+1j )ωk

ajp(xk+1

j |xkj ,aj )




Conclusions

APPTRAPP

TRAPP. Example




Conclusions

APPTRAPP

TRAPP. Example




Conclusions

APPTRAPP

TRAPP. Example




Conclusions

APPTRAPP

IP, PP, APP and TRAPP

auxiliaryfiltering in

target sampling

target resampling accountsfor nearby

targets

avoidsparticle

resampling

IP × X × ×

PP × X X ×

APP X × X X

TRAPP X X X X




Conclusions

Target dynamics and sensor modelingResults

Outline





5 Conclusions




Conclusions


Target dynamics.

The trajectories of the targets are generated according to anindependent nearly-constant velocity model.

0 20 40 60 80 100 1200

20

40

60

80

100

120

1

2

3

4

5

6

7

8

x position [m]

y p

ositio

n [m

]




Conclusions


Sensor model.

A nonlinear measurement model is considered.

zk+1i = hi (X

k+1) + vk+1i

hi (Xk+1) =

√√√√ t∑j=1

SNR(dk+1j ,i )

SNR(dk+1j ,i ) =

SNR0 dk+1j ,i ≤ d0

SNR0d2

0

(dk+1j,i )2

dk+1j ,i > d0




Conclusions


Compared filters

PP

APP

TRAPP

Jointly Auxiliary PF (JA)

Adaptive Auxiliary PF (AA)




Conclusions


Tracking 1 target.

50 100 150 200 250 300 350 400 450 5000

0.5

1

1.5

2

2.5

3

3.5

Number of particles

RM

S O

SP

A p

ositio

n e

rror

[m]

TRAPP

APP

PP

AA

JA




Conclusions


Tracking 8 targets.

50 100 150 200 250 300 350 400 450 5000

2

4

6

8

10

12

14

16

Number of particles

RM

S O

SP

A p

ositio

n e

rror

[m]

TRAPP

APP

PP

AA

JA




Conclusions


Tracking 1 to 8 targets, 100 particles.

1 2 3 4 5 6 7 80

2

4

6

8

10

12

14

16

Number of targets

RM

S O

SP

A p

ositio

n e

rror

[m]

TRAPP

APP

PP

AA

JA




Conclusions


Tracking 1 to 8 targets, 100 particles. Narrow likelihood.

1 2 3 4 5 6 7 80

2

4

6

8

10

12

Number of targets

RM

S O

SP

A p

ositio

n e

rror

[m]

TRAPP

APP

PP

AA

JA




Conclusions

Outline





5 Conclusions




Conclusions

Conclusions

Two particle filters, APP and TRAPP, have been developedthat generalize the auxiliary particle filtering for multipletarget tracking, making use of the state-partition strategybased on posterior independence.

Both APP and TRAPP outperform similar filters for MTT andare generally applicable algorithms.

APP generally outperforms TRAPP, however, TRAPP canoutperform APP when dealing with some measurement anddynamic models and a high number of targets.




Conclusions

Thank you


Date post:	06-Aug-2015
Category:	Engineering
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