Bayesian Smoothing for the Extended Object Random Matrix Model

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 the literature, one where the state density is modeled by a conditional density, and one where the state density is modeled by a factorized density. In this paper, we present closed-form Bayesian smoothing expressions for both the conditional and the factorized model. In a simulation study, we compare the performance of different versions of the smoother. Code is published on GitHub.