# Poisson Multi-Bernoulli Approximations for Multiple Extended Object Filtering

arXiv: https://arxiv.org/abs/1801.01353 · HTML: https://mlsanity.com/paper/1801.01353/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2018.

## Built on by (most cited first, 1 of 1)

- [Distributed Poisson multi-Bernoulli filtering via generalised covariance intersection](https://mlsanity.com/paper/2506.18397/) (2025)

## Abstract (arXiv)

The Poisson multi-Bernoulli mixture (PMBM) is a multi-object conjugate prior for the closed-form Bayes random finite sets filter. The extended object PMBM filter provides a closed-form solution for multiple extended object filtering with standard models. This paper considers computationally lighter alternatives to the extended object PMBM filter by propagating a Poisson multi-Bernoulli (PMB) density through the filtering recursion. A new local hypothesis representation is presented where each measurement creates a new Bernoulli component. This facilitates the developments of methods for efficiently approximating the PMBM posterior density after the update step as a PMB. Based on the new hypothesis representation, two approximation methods are presented: one is based on the track-oriented multi-Bernoulli (MB) approximation, and the other is based on the variational MB approximation via Kullback-Leibler divergence minimisation. The performance of the proposed PMB filters with gamma Gaussian inverse-Wishart implementations are evaluated in a simulation study.