On Gibbs Sampling Architecture for Labeled Random Finite Sets Multi-Object Tracking

TL;DR

This paper enhances Gibbs sampling for labeled random finite sets in multi-object tracking by proposing a parallelizable sample generation method and efficient early termination criteria, improving computational efficiency.

Contribution

It introduces a short chain, multi-simulation sampling technique and heuristic early stopping rules tailored for labeled RFS filters, enabling faster and parallelizable Gibbs sampling.

Findings

Parallel processing implementation demonstrated.

Heuristic early termination reduces sample size.

Improved sampling efficiency shown in simulations.

Abstract

Gibbs sampling is one of the most popular Markov chain Monte Carlo algorithms because of its simplicity, scalability, and wide applicability within many fields of statistics, science, and engineering. In the labeled random finite sets literature, Gibbs sampling procedures have recently been applied to efficiently truncate the single-sensor and multi-sensor $\delta$-generalized labeled multi-Bernoulli posterior density as well as the multi-sensor adaptive labeled multi-Bernoulli birth distribution. However, only a limited discussion has been provided regarding key Gibbs sampler architecture details including the Markov chain Monte Carlo sample generation technique and early termination criteria. This paper begins with a brief background on Markov chain Monte Carlo methods and a review of the Gibbs sampler implementations proposed for labeled random finite sets filters. Next, we propose a short chain, multi-simulation sample generation technique that is well suited for these applications and enables a parallel processing implementation. Additionally, we present two heuristic early termination criteria that achieve similar sampling performance with substantially fewer Markov chain observations. Finally, the benefits of the proposed Gibbs samplers are demonstrated via two Monte Carlo simulations.