# Bayesian Smoothing for the Extended Object Random Matrix Model

## TL;DR

This paper develops closed-form Bayesian smoothing formulas for two variants of the extended object random matrix model, enhancing tracking accuracy in extended object tracking applications.

## Contribution

It introduces novel Bayesian smoothing expressions for both conditional and factorized models in the extended object random matrix framework.

## Key findings

- Bayesian smoothers improve tracking performance.
- Closed-form solutions are derived for both model types.
- Simulation results compare the effectiveness of different smoothers.

## Abstract

The random matrix model is popular in extended object tracking, due to its relative simplicity and versatility. In this model, the extended object state consists of a kinematic vector for the position and motion parameters (velocity, etc), and an extent matrix. Two versions of the model can be found in literature, one where the state density is modelled by a conditional density, and one where the state density is modelled by a factorized density. In this paper, we present closed form Bayesian smoothing expression for both the conditional and the factorised model. In a simulation study, we compare the performance of different versions of the smoother.