Poisson Multi-Bernoulli Mixtures for Sets of Trajectories

Granstrom, Karl, Svensson, Lennart, Xia, Yuxuan, Williams, Jason and Garcia-Fernandez, Angel F ORCID: 0000-0002-6471-8455 (2025) Poisson Multi-Bernoulli Mixtures for Sets of Trajectories IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, 61 (2). pp. 5178-5194. ISSN 0018-9251, 1557-9603

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Abstract

The Poisson multi-Bernoulli mixture (PMBM) density is a conjugate multitarget density for the standard point target model with Poisson point process birth. This means that both the filtering and predicted densities for the set of targets are PMBM. In this article, we first show that the PMBM density is also conjugate for sets of trajectories with the standard point target measurement model. Second, based on this theoretical foundation, we develop two trajectory PMBM filters that provide recursions to calculate the posterior density for the set of all trajectories that have ever been present in the surveillance area, and the posterior density of the set of trajectories present at the current time step in the surveillance area. These two filters, therefore, provide complete probabilistic information on the considered trajectories enabling optimal trajectory estimation. Third, we establish that the density of the set of trajectories in any time window, given the measurements in a possibly different time window, is also a PMBM. Finally, the trajectory PMBM filters are evaluated via simulations, and are shown to yield State-of-the-Art performance compared to other multitarget tracking algorithms based on random finite sets and multiple hypothesis tracking.

Item Type:	Article
Uncontrolled Keywords:	Trajectory, Filters, Target tracking, Time measurement, Bayes methods, Standards, Radar tracking, Surveillance, Radio frequency, Density measurement, Conjugate priors, multiple target tracking, point targets, Poisson multi-Bernoulli mixtures (PMBMs), sets of trajectories
Divisions:	Faculty of Science & Engineering Faculty of Science & Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	16 Dec 2024 08:09
Last Modified:	16 Jun 2026 20:11
DOI:	10.1109/TAES.2024.3517576
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3189183
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