Dirichlet process-based component detection in state-space models

An extension of the switching-state models (SSSM) that allows arbitrary number of components is presented. We introduce a Dirichlet process prior over the mixture components of the linear models. This prior allows the inference on the number of linear models to be put into the mixture. We develop a distance measure in the space of linear Kalman filters with the use of the Kullback-Leibler divergence over the conditional probabilities induced by the individual Kalman filters. The introduced distance measure allows to remove components that are no longer relevant, making the algorithm more effective. We test the proposed algorithm on both artificial and real-world data.