Poisson multi-Bernoulli conjugate prior for multiple extended object filtering

TL;DR

This paper introduces a Poisson multi-Bernoulli mixture conjugate prior for multiple extended object filtering, providing a mathematically consistent framework that handles detection, data association, and tracking of multiple targets, including undetected ones.

Contribution

It develops a new conjugate prior model for extended object filtering that maintains its form through prediction and update steps, and proposes practical approximations for data association.

Findings

The extended target PMBM filter outperforms d-GLMB and LMB filters in simulations.

The method effectively tracks both detected and undetected targets using Lidar data.

The proposed approach offers a consistent Bayesian framework for multiple extended object tracking.

Abstract

This paper presents a Poisson multi-Bernoulli mixture (PMBM) conjugate prior for multiple extended object filtering. A Poisson point process is used to describe the existence of yet undetected targets, while a multi-Bernoulli mixture describes the distribution of the targets that have been detected. The prediction and update equations are presented for the standard transition density and measurement likelihood. Both the prediction and the update preserve the PMBM form of the density, and in this sense the PMBM density is a conjugate prior. However, the unknown data associations lead to an intractably large number of terms in the PMBM density, and approximations are necessary for tractability. A gamma Gaussian inverse Wishart implementation is presented, along with methods to handle the data association problem. A simulation study shows that the extended target PMBM filter performs well in comparison to the extended target d-GLMB and LMB filters. An experiment with Lidar data illustrates the benefit of tracking both detected and undetected targets.