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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
Particle filters for Multiple target trackingState partition particle filters
Generalizations of auxiliary particle filtering for MTTSimulations and results
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
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
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
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
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)
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
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.
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
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
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
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.
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
APPTRAPP
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
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
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.
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
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 )
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
APPTRAPP
Auxiliary parallel partition. Example
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
APPTRAPP
Auxiliary parallel partition. Example
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
APPTRAPP
Auxiliary parallel partition. Example
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
APPTRAPP
Auxiliary parallel partition. Example
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
APPTRAPP
Auxiliary parallel partition. Example
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
APPTRAPP
Auxiliary parallel partition. Example
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
APPTRAPP
Auxiliary parallel partition. Example
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
APPTRAPP
Auxiliary parallel partition. Example
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
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 )
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
APPTRAPP
TRAPP. Example
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
APPTRAPP
TRAPP. Example
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
APPTRAPP
TRAPP. Example
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
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
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
Target dynamics and sensor modelingResults
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
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
Target dynamics and sensor modelingResults
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
]
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
Target dynamics and sensor modelingResults
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
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
Target dynamics and sensor modelingResults
Compared filters
PP
APP
TRAPP
Jointly Auxiliary PF (JA)
Adaptive Auxiliary PF (AA)
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
Target dynamics and sensor modelingResults
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
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
Target dynamics and sensor modelingResults
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
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
Target dynamics and sensor modelingResults
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
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
Target dynamics and sensor modelingResults
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
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
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
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
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.
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? 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
Thank you
Luis Ubeda-Medina?, Angel F. Garcıa-Fernandez†, Jesus Grajal? Generalizations of the auxiliary particle filter for multiple target tracking