Dirichlet-process-mixture-based Bayesian nonparametric method for Markov switching process estimation

Dirichlet process (DP) mixtures were recently introduced to deal with switching linear dynamical models (SLDM). They assume the system can switch between an a priori infinite number of state-space representations (SSR) whose parameters are on-line inferred. The estimation problem can thus be of high dimension when the SSR matrices are unknown. Nevertheless, in many applications, the SSRs can be categorized in different classes. In each class, the SSRs are characterized by a known functional form but differ by a reduced set of unknown hyperparameters. To use this information, we thus propose a new hierarchical model for the SLDM wherein a discrete variable indicates the SSR class. Conditionally to this class, the distributions of the hyperparameters are modeled by DPs. The estimation problem is solved by using a Rao-Blackwellized particle filter. Simulation results show that our model outperforms existing methods in the field of target tracking.