# Poisson multi-Bernoulli mixture trackers: continuity through random finite sets of trajectories

arXiv: https://arxiv.org/abs/1812.05131 · HTML: https://mlsanity.com/paper/1812.05131/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2018.

## Built on by (most cited first, 10 of 10)

- [GNN-PMB: A Simple but Effective Online 3D Multi-Object Tracker without Bells and Whistles](https://mlsanity.com/paper/2206.10255/) (2022)
- [A time-weighted metric for sets of trajectories to assess multi-object tracking algorithms](https://mlsanity.com/paper/2110.13444/) (2021)
- [Transformer-Based Multi-Object Smoothing with Decoupled Data Association and Smoothing](https://mlsanity.com/paper/2312.17261/) (2023)
- [Cell Tracking according to Biological Needs -- Strong Mitosis-aware Multi-Hypothesis Tracker with Aleatoric Uncertainty](https://mlsanity.com/paper/2403.15011/) (2024)
- [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)
- [Poisson multi-Bernoulli mixture filter for trajectory measurements](https://mlsanity.com/paper/2504.08421/) (2025)
- [Integrated Gaussian Processes for Robust and Adaptive Multi-Object Tracking](https://mlsanity.com/paper/2507.04116/) (2025)

## Abstract (arXiv)

The Poisson multi-Bernoulli mixture (PMBM) is an unlabelled multi-target distribution for which the prediction and update are closed. It has a Poisson birth process, and new Bernoulli components are generated on each new measurement as a part of the Bayesian measurement update. The PMBM filter is similar to the multiple hypothesis tracker (MHT), but seemingly does not provide explicit continuity between time steps. This paper considers a recently developed formulation of the multi-target tracking problem as a random finite set (RFS) of trajectories, and derives two trajectory RFS filters, called PMBM trackers. The PMBM trackers efficiently estimate the set of trajectories, and share hypothesis structure with the PMBM filter. By showing that the prediction and update in the PMBM filter can be viewed as an efficient method for calculating the time marginals of the RFS of trajectories, continuity in the same sense as MHT is established for the PMBM filter.