Generalizations of the auxiliary particle filter for multiple target tracking

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 Úbeda-Medina , Ángel F. Garc´ıa-Fernández†
, Jesús Grajal
Dpto. Señales, Sistemas y Radiocomunicaciones, Universidad Politécnica de Madrid,
Spain
†Dept. of Electrical and Computer Engineering, Curtin University, Australia
, Jesús Grajal Generalizations of the auxiliary particle filter for multiple target tr

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

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
)

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.

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-Fernández, M. Morelande, and J. Grajal, “Two-layer particle filter for multiple target detection and
tracking,” IEEE Transactions on Aerospace and Electronic Systems, 2013.

Conclusions
APP
TRAPP
Outline
APP
TRAPP
Results
5 Conclusions

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.

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
)

Conclusions
APP
TRAPP
Auxiliary parallel partition. Example

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
)

Conclusions
APP
TRAPP
TRAPP. Example

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

Conclusions
Results
Outline
APP
TRAPP
Results
5 Conclusions

Conclusions
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]

Conclusions
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

Conclusions
Results
Compared ﬁlters
PP
APP
TRAPP
Jointly Auxiliary PF (JA)
Adaptive Auxiliary PF (AA)

Conclusions
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

Conclusions
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
TRAPP
APP
PP
AA
JA

Conclusions
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
TRAPP
APP
PP
AA
JA

Conclusions
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
TRAPP
APP
PP
AA
JA

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.

Conclusions
Thank you

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