# Poisson multi-Bernoulli mixture filter: direct derivation and implementation

arXiv: https://arxiv.org/abs/1703.04264 · HTML: https://mlsanity.com/paper/1703.04264/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2017.

## Built on by (most cited first, 29 of 29)

- [GNN-PMB: A Simple but Effective Online 3D Multi-Object Tracker without Bells and Whistles](https://mlsanity.com/paper/2206.10255/) (2022)
- [Deep Learning Serves Traffic Safety Analysis: A Forward-looking Review](https://mlsanity.com/paper/2203.10939/) (2022)
- [Neural Enhanced Belief Propagation for Multiobject Tracking](https://mlsanity.com/paper/2212.08340/) (2022)
- [Neural Enhanced Belief Propagation for Data Association in Multiobject Tracking](https://mlsanity.com/paper/2203.09948/) (2022)
- [Radar and Camera Fusion for Object Detection and Tracking: A Comprehensive Survey](https://mlsanity.com/paper/2410.19872/) (2024)
- [Multi-Object Tracking using Poisson Multi-Bernoulli Mixture Filtering for Autonomous Vehicles](https://mlsanity.com/paper/2103.07783/) (2021)
- [Next Generation Multitarget Trackers: Random Finite Set Methods vs Transformer-based Deep Learning](https://mlsanity.com/paper/2104.00734/) (2021)
- [Can Deep Learning be Applied to Model-Based Multi-Object Tracking?](https://mlsanity.com/paper/2202.07909/) (2022)
- [A two-stage data association approach for 3D Multi-object Tracking](https://mlsanity.com/paper/2101.08684/) (2021)
- [Object Detection as Probabilistic Set Prediction](https://mlsanity.com/paper/2203.07980/) (2022)
- [SRCN3D: Sparse R-CNN 3D for Compact Convolutional Multi-View 3D Object Detection and Tracking](https://mlsanity.com/paper/2206.14451/) (2022)
- [A New Architecture for Neural Enhanced Multiobject Tracking](https://mlsanity.com/paper/2410.06294/) (2024)
- [Bayesian Multiobject Tracking With Neural-Enhanced Motion and Measurement Models](https://mlsanity.com/paper/2506.18124/) (2025)
- [Consistency issues in Gaussian Mixture Models reduction algorithms](https://mlsanity.com/paper/2104.12586/) (2021)
- [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)
- [Heterogeneous Graph Transformer for Multiple Tiny Object Tracking in RGB-T Videos](https://mlsanity.com/paper/2412.10861/) (2024)
- [OptiPMB: Enhancing 3D Multi-Object Tracking with Optimized Poisson Multi-Bernoulli Filtering](https://mlsanity.com/paper/2503.12968/) (2025)
- [A comparison between PMBM Bayesian track initiation and labelled RFS adaptive birth](https://mlsanity.com/paper/2207.06156/) (2022)
- [Set-Type Belief Propagation with Applications to Poisson Multi-Bernoulli SLAM](https://mlsanity.com/paper/2305.04797/) (2023)
- [Multi-Base Station Cooperative Sensing with AI-Aided Tracking](https://mlsanity.com/paper/2310.20403/) (2023)
- [Gaussian multi-target filtering with target dynamics driven by a stochastic differential equation](https://mlsanity.com/paper/2411.19814/) (2024)
- [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)
- [Model-based Multi-object Visual Tracking: Identification and Standard Model Limitations](https://mlsanity.com/paper/2508.13647/) (2025)
- [Integrated Detection and Tracking Based on Radar Range-Doppler Feature](https://mlsanity.com/paper/2509.06569/) (2025)
- [Causal neural set filtering for online multi-target tracking](https://mlsanity.com/paper/2609.16054/) (2026)
- [A Review Of Robotic World Models For Dynamic Environments Based On Factor And Scene Graphs](https://mlsanity.com/paper/2610.08800/) (2026)

## Abstract (arXiv)

We provide a derivation of the Poisson multi-Bernoulli mixture (PMBM) filter for multi-target tracking with the standard point target measurements without using probability generating functionals or functional derivatives. We also establish the connection with the δ-generalised labelled multi-Bernoulli (δ-GLMB) filter, showing that a δ-GLMB density represents a multi-Bernoulli mixture with labelled targets so it can be seen as a special case of PMBM. In addition, we propose an implementation for linear/Gaussian dynamic and measurement models and how to efficiently obtain typical estimators in the literature from the PMBM. The PMBM filter is shown to outperform other filters in the literature in a challenging scenario.