Poisson Multi-Bernoulli Mixture Filter for Trajectory Measurements

Fontana, Marco ORCID: 0000-0003-0703-6535, Garcia-Fernandez, Angel F ORCID: 0000-0002-6471-8455 and Maskell, Simon ORCID: 0000-0003-1917-2913 (2025) Poisson Multi-Bernoulli Mixture Filter for Trajectory Measurements IEEE TRANSACTIONS ON SIGNAL PROCESSING, 73 (99). pp. 4301-4314. ISSN 1053-587X, 1941-0476

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Abstract

This paper presents a Poisson multi-Bernoulli mixture (PMBM) filter for multi-target filtering based on sensor measurements that are sets of trajectories in the last two-time step window. The proposed filter, the trajectory measurement PMBM (TM-PMBM) filter, propagates a PMBM density on the set of target states. In prediction, the filter obtains the PMBM density on the set of trajectories over the last two time steps. This density is then updated with the set of trajectory measurements. After the update step, the PMBM posterior on the set of two-step trajectories is marginalised to obtain a PMBM density on the set of target states. The filter provides a closed-form solution for multi-target filtering based on sets of trajectory measurements, estimating the set of target states at the end of each time window. Additionally, the paper proposes computationally lighter alternatives to the TM-PMBM filter by deriving a Poisson multi-Bernoulli (PMB) density through Kullback-Leibler divergence minimisation in an augmented space with auxiliary variables. The performance of the proposed filters are evaluated in a simulation study.

Item Type:	Article
Uncontrolled Keywords:	Trajectory, Time measurement, Target tracking, Information filters, Filtering theory, Filtering algorithms, Extraterrestrial measurements, Density measurement, Standards, Radar tracking, Bayesian estimation, multi-target filtering, Poisson multi-Bernoulli mixture filter, trajectory measurements
Divisions:	Faculty of Science & Engineering Faculty of Science & Engineering > School of Engineering Faculty of Science & Engineering > School of Engineering > Electrical Engineering and Electronics
Depositing User:	Symplectic Admin
Date Deposited:	22 Oct 2025 07:22
Last Modified:	23 May 2026 10:39
DOI:	10.1109/TSP.2025.3623496
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3194947
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