MCMC-based posterior independence approximation for RFS multitarget particle filters

The objective of this paper is to approximate the unlabelled posterior random finite set (RFS) density in multitarget tracking (MTT) using particle filters (PFs). The unlabelled posterior can be equivalently represented by any labelled density that belongs to the posterior RFS family. For the limited number of particles used in practice, PFs that assume posterior independence among target states outperform those without it. Consequently, we can improve the PF approximation by aiming at the labelled density within the posterior RFS family whose target states are as independent as possible. In this paper, we focus on the case of fixed and known number of targets and propose an algorithm based on Markov chain Monte Carlo (MCMC) that pursues this aim. This algorithm can be added to any PF with posterior independence assumption.