Multi-Bernoulli Mixture Filter: Complete Derivation and Sequential Monte Carlo Implementation

TL;DR

This paper provides a complete derivation and a Sequential Monte Carlo implementation of the Multi-Bernoulli Mixture (MBM) filter, demonstrating its superior performance over classical PHD filters in nonlinear measurement scenarios.

Contribution

It offers a full derivation of the MBM filter without using probability generating functionals and introduces a Gibbs sampling-based truncation method for implementation.

Findings

MBM filter outperforms classical PHD filter in simulations.

Sequential Monte Carlo implementation with Gibbs sampling is effective.

Complete derivation enhances understanding of MBM filter's theoretical foundation.

Abstract

Multi-Bernoulli mixture (MBM) filter is one of the exact closed-form multi-target Bayes filters in the random finite sets (RFS) framework, which utilizes multi-Bernoulli mixture density as the multi-target conjugate prior. This filter is the variant of Poisson multi-Bernoulli mixture filter when the birth process is changed to a multi-Bernoulli RFS or a multi-Bernoulli mixture RFS from a Poisson RFS. On the other hand, labeled multi-Bernoulli mixture filter evolves to MBM filter when the label is discarded. In this letter, we provide a complete derivation of MBM filter where the derivation of update step does not use the probability generating functional. We also describe the sequential Monte Carlo implementation and adopt Gibbs sampling for truncating the MBM filtering density. Numerical simulation with a nonlinear measurement model shows that MBM filter outperforms the classical probability hypothesis density filter.