# Trajectory Poisson multi-Bernoulli filters

arXiv: https://arxiv.org/abs/2003.12767 · HTML: https://mlsanity.com/paper/2003.12767/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2020.

## Built on by (most cited first, 11 of 11)

- [Transformer-Based Multi-Object Smoothing with Decoupled Data Association and Smoothing](https://mlsanity.com/paper/2312.17261/) (2023)
- [Trajectory Poisson multi-Bernoulli mixture filter for traffic monitoring using a drone](https://mlsanity.com/paper/2306.16890/) (2023)
- [Continuous-discrete multiple target tracking with out-of-sequence measurements](https://mlsanity.com/paper/2106.04898/) (2021)
- [A comparison between PMBM Bayesian track initiation and labelled RFS adaptive birth](https://mlsanity.com/paper/2207.06156/) (2022)
- [Deep Fusion of Multi-Object Densities Using Transformer](https://mlsanity.com/paper/2209.08857/) (2022)
- [Set-Type Belief Propagation with Applications to Poisson Multi-Bernoulli SLAM](https://mlsanity.com/paper/2305.04797/) (2023)
- [Gaussian multi-target filtering with target dynamics driven by a stochastic differential equation](https://mlsanity.com/paper/2411.19814/) (2024)
- [Stone Soup Multi-Target Tracking Feature Extraction For Autonomous Search And Track In Deep Reinforcement Learning Environment](https://mlsanity.com/paper/2503.01293/) (2025)
- [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)
- [GOSPA and T-GOSPA quasi-metrics for evaluation of multi-object tracking algorithms](https://mlsanity.com/paper/2507.13706/) (2025)

## Abstract (arXiv)

This paper presents two trajectory Poisson multi-Bernoulli (TPMB) filters for multi-target tracking: one to estimate the set of alive trajectories at each time step and another to estimate the set of all trajectories, which includes alive and dead trajectories, at each time step. The filters are based on propagating a Poisson multi-Bernoulli (PMB) density on the corresponding set of trajectories through the filtering recursion. After the update step, the posterior is a PMB mixture (PMBM) so, in order to obtain a PMB density, a Kullback-Leibler divergence minimisation on an augmented space is performed. The developed filters are computationally lighter alternatives to the trajectory PMBM filters, which provide the closed-form recursion for sets of trajectories with Poisson birth model, and are shown to outperform previous multi-target tracking algorithms.