Student’s t-Based Robust Poisson Multi-Bernoulli Mixture Filter under Heavy-Tailed Process and Measurement Noises

Abstract

A novel Student’s t-based robust Poisson multi-Bernoulli mixture (PMBM) filter is proposed to effectively perform multi-target tracking under heavy-tailed process and measurement noises. To cope with the common scenario where the process and measurement noises possess different heavy-tailed degrees, the proposed filter models this noise as two Student’s t-distributions with different degrees of freedom. Furthermore, this method considers that the scale matrix of the one-step predictive probability density function is unknown and models it as an inverse-Wishart distribution to mitigate the influence of heavy-tailed process noise. A closed-form recursion of the PMBM filter for propagating the approximated Gaussian-based PMBM posterior density is derived by introducing the variational Bayesian approach and a hierarchical Gaussian state-space model. The overall performance improvement is demonstrated through three simulations.