# Multi-Scan Implementation of the Trajectory Poisson Multi-Bernoulli Mixture Filter

arXiv: https://arxiv.org/abs/1912.01748 · HTML: https://mlsanity.com/paper/1912.01748/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2019.

## Built on by (most cited first, 4 of 4)

- [Transformer-Based Multi-Object Smoothing with Decoupled Data Association and Smoothing](https://mlsanity.com/paper/2312.17261/) (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)
- [Poisson multi-Bernoulli mixture filter for trajectory measurements](https://mlsanity.com/paper/2504.08421/) (2025)

## Abstract (arXiv)

The Poisson multi-Bernoulli mixture (PMBM) and the multi-Bernoulli mixture (MBM) are two multi-target distributions for which closed-form filtering recursions exist. The PMBM has a Poisson birth process, whereas the MBM has a multi-Bernoulli birth process. This paper considers a recently developed formulation of the multi-target tracking problem using a random finite set of trajectories, through which the track continuity is explicitly established. A multi-scan trajectory PMBM filter and a multi-scan trajectory MBM filter, with the ability to correct past data association decisions to improve current decisions, are presented. In addition, a multi-scan trajectory MBM01 filter, in which the existence probabilities of all Bernoulli components are either 0 or 1, is presented. This paper proposes an efficient implementation that performs track-oriented N-scan pruning to limit computational complexity, and uses dual decomposition to solve the involved multi-frame assignment problem. The performance of the presented multi-target trackers, applied with an efficient fixed-lag smoothing method, are evaluated in a simulation study.