Trajectory PMB Filters for Extended Object Tracking Using Belief Propagation
Journal article, 2023

In this paper, we propose a Poisson multi-Bernoulli (PMB) filter for extended object tracking (EOT), which directly estimates the set of object trajectories, using belief propagation (BP). The proposed filter propagates a PMB density on the posterior of sets of trajectories through the filtering recursions over time, where the PMB mixture (PMBM) posterior after the update step is approximated as a PMB. The efficient PMB approximation relies on several important theoretical contributions. First, we present a PMBM conjugate prior on the posterior of sets of trajectories for a generalized measurement model, in which each object generates an independent set of measurements. The PMBM density is a conjugate prior in the sense that both the prediction and the update steps preserve the PMBM form of the density. Second, we present a factor graph representation of the joint posterior of the PMBM set of trajectories and association variables for the Poisson spatial measurement model. Importantly, leveraging the PMBM conjugacy and the factor graph formulation enables an elegant treatment on undetected objects via a Poisson point process and efficient inference on sets of trajectories using BP, where the approximate marginal densities in the PMB approximation can be obtained without enumeration of different data association hypotheses. To achieve this, we present a particle-based implementation of the proposed filter, where smoothed trajectory estimates, if desired, can be obtained via single-object particle smoothing methods, and its performance for EOT with ellipsoidal shapes is evaluated in a simulation study.

Belief propagation

Mathematical models

multi-object tracking

Radar tracking

particle belief propagation

factor graph

random finite sets


Sea measurements

Time measurement

Extended object tracking

Object tracking

sets of trajectories


Yuxuan Xia

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering

Angel Garcia

University of Liverpool

Florian Meyer

University of California at San Diego (UCSD)

Jason L. Williams

Commonwealth Scientific and Industrial Research Organisation (CSIRO)

Karl Granström


Lennart Svensson

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering

IEEE Transactions on Aerospace and Electronic Systems

0018-9251 (ISSN) 15579603 (eISSN)

Vol. 59 6 9312-9331 3317233

Subject Categories

Probability Theory and Statistics

Control Engineering

Signal Processing



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