Variational PMB filter via coordinate descent Kullback-Leibler divergence minimisation

2026-05-08

AI Summary

This work addresses the challenge of efficiently approximating the complex Poisson multi-Bernoulli mixture (PMBM) posterior in multi-object tracking. To this end, the authors propose a variational Poisson multi-Bernoulli (V-PMB) filtering method that operates in an augmented space encompassing object states, trajectory labels, and global association hypotheses. By minimizing the Kullback–Leibler divergence via coordinate descent, the method projects the full PMBM posterior onto the closest PMB density, thereby preserving essential posterior structure while enabling scalable inference. Compared to existing PMB implementations based on Murty’s algorithm, belief propagation, or nearest-neighbor heuristics, V-PMB demonstrates significantly improved tracking accuracy and robustness, particularly in scenarios involving dense target interactions and subsequent separations.

Abstract

This paper presents a new derivation of the variational Poisson multi-Bernoulli (V-PMB) filter for multi-target estimation proposed in [#Williams15]. The proposed derivation is based on considering an augmented space that includes the set of target states with their track indices and the global hypothesis variable. Then, we show that the V-PMB projection performs a coordinate descent Kullback-Leibler divergence (KLD) minimisation on this augmented space to fit the best possible PMB density to the Poisson multi-Bernoulli mixture (PMBM) posterior. We also show that this V-PMB projection keeps the probability hypothesis density of the posterior. The paper also includes a comparison with the PMBM filter and other PMB filter variants, including a track-oriented Murty-based implementation, a track-oriented loopy belief propagation implementation and a global nearest neighbour implementation, showing the benefits of the V-PMB filter compared to the other PMB filters when targets get in close proximity and then separate.

Problem

• multi-target tracking
• Poisson multi-Bernoulli mixture
• Kullback-Leibler divergence
• track coalescence
• variational approximation

Innovation

• variational PMB filter
• coordinate descent
• Kullback-Leibler divergence minimisation
• PMBM posterior
• multi-target tracking