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Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Generalizations of the auxiliary particle filter for
multiple target tracking
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal
Dpto. Se˜nales, Sistemas y Radiocomunicaciones, Universidad Polit´ecnica de Madrid,
Spain
†Dept. of Electrical and Computer Engineering, Curtin University, Australia
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Outline
1 Particle filters for Multiple target tracking
2 State partition particle filters
3 Generalizations of auxiliary particle filtering for MTT
APP
TRAPP
4 Simulations and results
Target dynamics and sensor modeling
Results
5 Conclusions
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Outline
1 Particle filters for Multiple target tracking
2 State partition particle filters
3 Generalizations of auxiliary particle filtering for MTT
APP
TRAPP
4 Simulations and results
Target dynamics and sensor modeling
Results
5 Conclusions
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Multiple target tracking.
Multiple target tracking
MTT is usually formulated in the Bayesian framework. The
information of interest about the targets is contained in the
multitarget posterior PDF.
Multitarget state
Xk
= (xk
1)T
, (xk
2)T
, ..., (xk
t )T
T
∈ Rn·t
Posterior PDF
p(Xk
|z1:k
)
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Particle filters.
PFs sample the state-space to build an approximation to the
posterior PDF.
The dimension of the state-space linearly grows with the
number of targets.
Sampling high-dimension state-spaces is very inefficient, giving
rise to the curse of dimensionality.
Some modifications are needed if PFs are to be successfully
applied to MTT.
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Outline
1 Particle filters for Multiple target tracking
2 State partition particle filters
3 Generalizations of auxiliary particle filtering for MTT
APP
TRAPP
4 Simulations and results
Target dynamics and sensor modeling
Results
5 Conclusions
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
State partition.
State partition
To appease the curse of dimensionality some algorithms assume posterior
independence between targets. This allows for the partition of the state-space to
individually sample the state of each target.
p(X
k+1
|z
1:k+1
) =
t
j=1
pj (x
k+1
j |z
1: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 multitarget
tracking 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 particle
filters,” IEEE Transactions on Signal Processing, 2002.
[3] A. F. Garc´ıa-Fern´andez, M. Morelande, and J. Grajal, “Two-layer particle filter for multiple target detection and
tracking,” IEEE Transactions on Aerospace and Electronic Systems, 2013.
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
Outline
1 Particle filters for Multiple target tracking
2 State partition particle filters
3 Generalizations of auxiliary particle filtering for MTT
APP
TRAPP
4 Simulations and results
Target dynamics and sensor modeling
Results
5 Conclusions
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
Auxiliary PFs for MTT.
When there is only one target present, both IP and PP come
down to the sequential-importance-resampling PF, which is
usually outperformed by the auxiliary particle filter.
Two particle filters, APP and TRAPP, are presented inspired
by the APF and the state-partition strategy of PP, resulting
on generalizations of the APF for multiple target tracking.
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
Auxiliary parallel partition.
APP
APP makes use of auxiliary particle filtering for each target,
selecting those subparticles at time k that are prone to generate
subparticles with higher target-likelihood at time k + 1 according
to zk+1 .
q(Xk+1
, a|z1:k+1
) =
t
j=1
qj (xk+1
j , aj |z1:k+1
)
qj (xk+1
j , aj |z1:k+1
) ∝ bj (µk+1
j,aj
)ωk
aj
p(xk+1
j |xk
j,aj
)
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
Auxiliary parallel partition. Example
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
Auxiliary parallel partition. Example
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
Auxiliary parallel partition. Example
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
Auxiliary parallel partition. Example
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
Auxiliary parallel partition. Example
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
Auxiliary parallel partition. Example
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
Auxiliary parallel partition. Example
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
Auxiliary parallel partition. Example
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
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 state
space. TRAPP makes use of auxiliary filtering followed by
target-resampling.
q(Xk+1
, a|z1:k+1
) =
t
j=1
qj (xk+1
j , aj |z1:k+1
)
qj (xk+1
j , aj |z1:k+1
) ∝ bj (xk+1
j )ωk
aj
p(xk+1
j |xk
j,aj
)
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
TRAPP. Example
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
TRAPP. Example
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
TRAPP. Example
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
APP
TRAPP
IP, PP, APP and TRAPP
auxiliary
filtering in
target sampling
target resampling accounts
for nearby
targets
avoids
particle
resampling
IP × × ×
PP × ×
APP ×
TRAPP
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Target dynamics and sensor modeling
Results
Outline
1 Particle filters for Multiple target tracking
2 State partition particle filters
3 Generalizations of auxiliary particle filtering for MTT
APP
TRAPP
4 Simulations and results
Target dynamics and sensor modeling
Results
5 Conclusions
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Target dynamics and sensor modeling
Results
Target dynamics.
The trajectories of the targets are generated according to an
independent nearly-constant velocity model.
0 20 40 60 80 100 120
0
20
40
60
80
100
120
1
2
3
4
5
6
7
8
x position [m]
yposition[m]
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Target dynamics and sensor modeling
Results
Sensor model.
A nonlinear measurement model is considered.
zk+1
i = hi (Xk+1
) + vk+1
i
hi (Xk+1
) =
t
j=1
SNR(dk+1
j,i )
SNR(dk+1
j,i ) =



SNR0 dk+1
j,i ≤ d0
SNR0
d2
0
(dk+1
j,i )2
dk+1
j,i > d0
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Target dynamics and sensor modeling
Results
Compared filters
PP
APP
TRAPP
Jointly Auxiliary PF (JA)
Adaptive Auxiliary PF (AA)
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Target dynamics and sensor modeling
Results
Tracking 1 target.
50 100 150 200 250 300 350 400 450 500
0
0.5
1
1.5
2
2.5
3
3.5
Number of particles
RMSOSPApositionerror[m]
TRAPP
APP
PP
AA
JA
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Target dynamics and sensor modeling
Results
Tracking 8 targets.
50 100 150 200 250 300 350 400 450 500
0
2
4
6
8
10
12
14
16
Number of particles
RMSOSPApositionerror[m]
TRAPP
APP
PP
AA
JA
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Target dynamics and sensor modeling
Results
Tracking 1 to 8 targets, 100 particles.
1 2 3 4 5 6 7 8
0
2
4
6
8
10
12
14
16
Number of targets
RMSOSPApositionerror[m]
TRAPP
APP
PP
AA
JA
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Target dynamics and sensor modeling
Results
Tracking 1 to 8 targets, 100 particles. Narrow likelihood.
1 2 3 4 5 6 7 8
0
2
4
6
8
10
12
Number of targets
RMSOSPApositionerror[m]
TRAPP
APP
PP
AA
JA
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Outline
1 Particle filters for Multiple target tracking
2 State partition particle filters
3 Generalizations of auxiliary particle filtering for MTT
APP
TRAPP
4 Simulations and results
Target dynamics and sensor modeling
Results
5 Conclusions
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Conclusions
Two particle filters, APP and TRAPP, have been developed
that generalize the auxiliary particle filtering for multiple
target tracking, making use of the state-partition strategy
based on posterior independence.
Both APP and TRAPP outperform similar filters for MTT and
are generally applicable algorithms.
APP generally outperforms TRAPP, however, TRAPP can
outperform APP when dealing with some measurement and
dynamic models and a high number of targets.
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
Particle filters for Multiple target tracking
State partition particle filters
Generalizations of auxiliary particle filtering for MTT
Simulations and results
Conclusions
Thank you
Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez†
, Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr

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Generalizations of the auxiliary particle filter for multiple target tracking

  • 1. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Generalizations of the auxiliary particle filter for multiple target tracking Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Dpto. Se˜nales, Sistemas y Radiocomunicaciones, Universidad Polit´ecnica de Madrid, Spain †Dept. of Electrical and Computer Engineering, Curtin University, Australia Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 2. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Outline 1 Particle filters for Multiple target tracking 2 State partition particle filters 3 Generalizations of auxiliary particle filtering for MTT APP TRAPP 4 Simulations and results Target dynamics and sensor modeling Results 5 Conclusions Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 3. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Outline 1 Particle filters for Multiple target tracking 2 State partition particle filters 3 Generalizations of auxiliary particle filtering for MTT APP TRAPP 4 Simulations and results Target dynamics and sensor modeling Results 5 Conclusions Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 4. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Multiple target tracking. Multiple target tracking MTT is usually formulated in the Bayesian framework. The information of interest about the targets is contained in the multitarget posterior PDF. Multitarget state Xk = (xk 1)T , (xk 2)T , ..., (xk t )T T ∈ Rn·t Posterior PDF p(Xk |z1:k ) Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 5. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Particle filters. PFs sample the state-space to build an approximation to the posterior PDF. The dimension of the state-space linearly grows with the number of targets. Sampling high-dimension state-spaces is very inefficient, giving rise to the curse of dimensionality. Some modifications are needed if PFs are to be successfully applied to MTT. Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 6. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Outline 1 Particle filters for Multiple target tracking 2 State partition particle filters 3 Generalizations of auxiliary particle filtering for MTT APP TRAPP 4 Simulations and results Target dynamics and sensor modeling Results 5 Conclusions Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 7. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions State partition. State partition To appease the curse of dimensionality some algorithms assume posterior independence between targets. This allows for the partition of the state-space to individually sample the state of each target. p(X k+1 |z 1:k+1 ) = t j=1 pj (x k+1 j |z 1: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 multitarget tracking 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 particle filters,” IEEE Transactions on Signal Processing, 2002. [3] A. F. Garc´ıa-Fern´andez, M. Morelande, and J. Grajal, “Two-layer particle filter for multiple target detection and tracking,” IEEE Transactions on Aerospace and Electronic Systems, 2013. Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 8. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP Outline 1 Particle filters for Multiple target tracking 2 State partition particle filters 3 Generalizations of auxiliary particle filtering for MTT APP TRAPP 4 Simulations and results Target dynamics and sensor modeling Results 5 Conclusions Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 9. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP Auxiliary PFs for MTT. When there is only one target present, both IP and PP come down to the sequential-importance-resampling PF, which is usually outperformed by the auxiliary particle filter. Two particle filters, APP and TRAPP, are presented inspired by the APF and the state-partition strategy of PP, resulting on generalizations of the APF for multiple target tracking. Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 10. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP Auxiliary parallel partition. APP APP makes use of auxiliary particle filtering for each target, selecting those subparticles at time k that are prone to generate subparticles with higher target-likelihood at time k + 1 according to zk+1 . q(Xk+1 , a|z1:k+1 ) = t j=1 qj (xk+1 j , aj |z1:k+1 ) qj (xk+1 j , aj |z1:k+1 ) ∝ bj (µk+1 j,aj )ωk aj p(xk+1 j |xk j,aj ) Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 11. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP Auxiliary parallel partition. Example Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 12. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP Auxiliary parallel partition. Example Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 13. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP Auxiliary parallel partition. Example Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 14. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP Auxiliary parallel partition. Example Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 15. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP Auxiliary parallel partition. Example Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 16. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP Auxiliary parallel partition. Example Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 17. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP Auxiliary parallel partition. Example Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 18. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP Auxiliary parallel partition. Example Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 19. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP 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 state space. TRAPP makes use of auxiliary filtering followed by target-resampling. q(Xk+1 , a|z1:k+1 ) = t j=1 qj (xk+1 j , aj |z1:k+1 ) qj (xk+1 j , aj |z1:k+1 ) ∝ bj (xk+1 j )ωk aj p(xk+1 j |xk j,aj ) Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 20. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP TRAPP. Example Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 21. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP TRAPP. Example Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 22. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP TRAPP. Example Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 23. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions APP TRAPP IP, PP, APP and TRAPP auxiliary filtering in target sampling target resampling accounts for nearby targets avoids particle resampling IP × × × PP × × APP × TRAPP Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 24. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Target dynamics and sensor modeling Results Outline 1 Particle filters for Multiple target tracking 2 State partition particle filters 3 Generalizations of auxiliary particle filtering for MTT APP TRAPP 4 Simulations and results Target dynamics and sensor modeling Results 5 Conclusions Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 25. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Target dynamics and sensor modeling Results Target dynamics. The trajectories of the targets are generated according to an independent nearly-constant velocity model. 0 20 40 60 80 100 120 0 20 40 60 80 100 120 1 2 3 4 5 6 7 8 x position [m] yposition[m] Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 26. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Target dynamics and sensor modeling Results Sensor model. A nonlinear measurement model is considered. zk+1 i = hi (Xk+1 ) + vk+1 i hi (Xk+1 ) = t j=1 SNR(dk+1 j,i ) SNR(dk+1 j,i ) =    SNR0 dk+1 j,i ≤ d0 SNR0 d2 0 (dk+1 j,i )2 dk+1 j,i > d0 Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 27. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Target dynamics and sensor modeling Results Compared filters PP APP TRAPP Jointly Auxiliary PF (JA) Adaptive Auxiliary PF (AA) Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 28. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Target dynamics and sensor modeling Results Tracking 1 target. 50 100 150 200 250 300 350 400 450 500 0 0.5 1 1.5 2 2.5 3 3.5 Number of particles RMSOSPApositionerror[m] TRAPP APP PP AA JA Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 29. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Target dynamics and sensor modeling Results Tracking 8 targets. 50 100 150 200 250 300 350 400 450 500 0 2 4 6 8 10 12 14 16 Number of particles RMSOSPApositionerror[m] TRAPP APP PP AA JA Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 30. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Target dynamics and sensor modeling Results Tracking 1 to 8 targets, 100 particles. 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 14 16 Number of targets RMSOSPApositionerror[m] TRAPP APP PP AA JA Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 31. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Target dynamics and sensor modeling Results Tracking 1 to 8 targets, 100 particles. Narrow likelihood. 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 Number of targets RMSOSPApositionerror[m] TRAPP APP PP AA JA Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 32. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Outline 1 Particle filters for Multiple target tracking 2 State partition particle filters 3 Generalizations of auxiliary particle filtering for MTT APP TRAPP 4 Simulations and results Target dynamics and sensor modeling Results 5 Conclusions Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 33. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Conclusions Two particle filters, APP and TRAPP, have been developed that generalize the auxiliary particle filtering for multiple target tracking, making use of the state-partition strategy based on posterior independence. Both APP and TRAPP outperform similar filters for MTT and are generally applicable algorithms. APP generally outperforms TRAPP, however, TRAPP can outperform APP when dealing with some measurement and dynamic models and a high number of targets. Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr
  • 34. Particle filters for Multiple target tracking State partition particle filters Generalizations of auxiliary particle filtering for MTT Simulations and results Conclusions Thank you Luis ´Ubeda-Medina , ´Angel F. Garc´ıa-Fern´andez† , Jes´us Grajal Generalizations of the auxiliary particle filter for multiple target tr