# A Poisson multi-Bernoulli mixture filter for coexisting point and extended targets

arXiv: https://arxiv.org/abs/2011.04464 · HTML: https://mlsanity.com/paper/2011.04464/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [Neural Enhanced Belief Propagation for Data Association in Multiobject Tracking](https://mlsanity.com/paper/2203.09948/) (2022)
- [Poisson multi-Bernoulli mixture filter for trajectory measurements](https://mlsanity.com/paper/2504.08421/) (2025)
- [Distributed Poisson multi-Bernoulli filtering via generalised covariance intersection](https://mlsanity.com/paper/2506.18397/) (2025)

## Abstract (arXiv)

This paper proposes a Poisson multi-Bernoulli mixture (PMBM) filter for coexisting point and extended targets, i.e., for scenarios where there may be simultaneous point and extended targets. The PMBM filter provides a recursion to compute the multi-target filtering posterior based on probabilistic information on data associations, and single-target predictions and updates. In this paper, we first derive the PMBM filter update for a generalised measurement model, which can include measurements originated from point and extended targets. Second, we propose a single-target space that accommodates both point and extended targets and derive the filtering recursion that propagates Gaussian densities for point targets and gamma Gaussian inverse Wishart densities for extended targets. As a computationally efficient approximation of the PMBM filter, we also develop a Poisson multi-Bernoulli (PMB) filter for coexisting point and extended targets. The resulting filters are analysed via numerical simulations.