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

## TL;DR

This paper introduces Poisson multi-Bernoulli mixture (PMBM) trajectory filters that ensure continuity over time by modeling multi-target trajectories as random finite sets, bridging the gap between Bayesian filtering and hypothesis-based methods.

## Contribution

It derives two novel PMBM trajectory filters that maintain hypothesis structure and continuity, extending the PMBM framework to trajectory estimation.

## Key findings

- Efficiently estimates multi-target trajectories.
- Establishes continuity similar to multiple hypothesis tracking.
- Shares hypothesis structure with existing PMBM filter.

## Abstract

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.