# Trajectory PMB Filters for Extended Object Tracking Using Belief Propagation

arXiv: https://arxiv.org/abs/2207.10164 · HTML: https://mlsanity.com/paper/2207.10164/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2022.

## Built on by (most cited first, 2 of 2)

- [Set-Type Belief Propagation with Applications to Poisson Multi-Bernoulli SLAM](https://mlsanity.com/paper/2305.04797/) (2023)
- [PiVoT: A Variational Solution for Real-time Large-scale Multi-object Detection and Tracking under Heavy Clutter](https://mlsanity.com/paper/2607.13891/) (2026)

## Abstract (arXiv)

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.