# Poisson multi-Bernoulli mixture filter: direct derivation and implementation

## TL;DR

This paper derives the Poisson multi-Bernoulli mixture (PMBM) filter for multi-target tracking without using complex functional calculus, connects it with the elta-GLMB filter, and demonstrates its superior performance in challenging scenarios.

## Contribution

It provides a direct derivation of the PMBM filter, clarifies its relation to the elta-GLMB filter, and offers an efficient implementation for linear/Gaussian models.

## Key findings

- PMBM outperforms existing filters in challenging scenarios.
- Connection established between PMBM and elta-GLMB filters.
- Efficient implementation for linear/Gaussian models provided.

## Abstract

We provide a derivation of the Poisson multi-Bernoulli mixture (PMBM) filter for multi-target tracking with the standard point target measurements without using probability generating functionals or functional derivatives. We also establish the connection with the \delta-generalised labelled multi-Bernoulli (\delta-GLMB) filter, showing that a \delta-GLMB density represents a multi-Bernoulli mixture with labelled targets so it can be seen as a special case of PMBM. In addition, we propose an implementation for linear/Gaussian dynamic and measurement models and how to efficiently obtain typical estimators in the literature from the PMBM. The PMBM filter is shown to outperform other filters in the literature in a challenging scenario.