# Poisson multi-Bernoulli mixture filter for trajectory measurements

arXiv: https://arxiv.org/abs/2504.08421 · HTML: https://mlsanity.com/paper/2504.08421/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 45 references that are in the map.
- First posted on arXiv 11 Apr 2025.

## Builds on (most cited first, 12 of 12)

- [Generalized optimal sub-pattern assignment metric](https://mlsanity.com/paper/1601.05585/) (2016)
- [Poisson multi-Bernoulli mixture filter: direct derivation and implementation](https://mlsanity.com/paper/1703.04264/) (2017)
- [Extended Object Tracking: Introduction, Overview and Applications](https://mlsanity.com/paper/1604.00970/) (2016)
- [Multiple target tracking based on sets of trajectories](https://mlsanity.com/paper/1605.08163/) (2016)
- [Trajectory Poisson multi-Bernoulli filters](https://mlsanity.com/paper/2003.12767/) (2020)
- [Poisson multi-Bernoulli mixture trackers: continuity through random finite sets of trajectories](https://mlsanity.com/paper/1812.05131/) (2018)
- [Gaussian implementation of the multi-Bernoulli mixture filter](https://mlsanity.com/paper/1908.08819/) (2019)
- [Trajectory PHD and CPHD filters](https://mlsanity.com/paper/1811.08820/) (2018)
- [Multi-Scan Implementation of the Trajectory Poisson Multi-Bernoulli Mixture Filter](https://mlsanity.com/paper/1912.01748/) (2019)
- [Poisson Multi-Bernoulli Mixtures for Sets of Trajectories](https://mlsanity.com/paper/1912.08718/) (2019)
- [A Poisson multi-Bernoulli mixture filter for coexisting point and extended targets](https://mlsanity.com/paper/2011.04464/) (2020)
- [A second-order PHD filter with mean and variance in target number](https://mlsanity.com/paper/1704.02084/) (2017)

## Abstract (arXiv)

This paper presents a Poisson multi-Bernoulli mixture (PMBM) filter for multi-target filtering based on sensor measurements that are sets of trajectories in the last two-time step window. The proposed filter, the trajectory measurement PMBM (TM-PMBM) filter, propagates a PMBM density on the set of target states. In prediction, the filter obtains the PMBM density on the set of trajectories over the last two time steps. This density is then updated with the set of trajectory measurements. After the update step, the PMBM posterior on the set of two-step trajectories is marginalised to obtain a PMBM density on the set of target states. The filter provides a closed-form solution for multi-target filtering based on sets of trajectory measurements, estimating the set of target states at the end of each time window. Additionally, the paper proposes computationally lighter alternatives to the TM-PMBM filter by deriving a Poisson multi-Bernoulli (PMB) density through Kullback-Leibler divergence minimisation in an augmented space with auxiliary variables. The performance of the proposed filters are evaluated in a simulation study.