Efficient particle filtering for jump Markov systems. Application to time-varying autoregressions

In this paper, we present an efficient particle filtering method to perform optimal estimation in jump Markov (nonlinear) systems (JMSs). Such processes consist of a mixture of heterogeneous models and possess a natural hierarchical structure. We take advantage of these specificities in order to develop a generic filtering methodology for these models. The method relies on an original and nontrivial combination of techniques that have been presented recently in the filtering literature, namely, the auxiliary particle filter and the unscented transform. This algorithm is applied to the complex problem of time-varying autoregressive estimation with an unknown time-varying model order. More precisely, we develop an attractive and original probabilistic model that relies on a flexible pole representation that easily lends itself to interpretations. We show that this problem can be formulated as a JMS and that the associated filtering problem can be efficiently addressed using the generic methodology developed in this paper. Simulations demonstrate the performance of our method compared to standard particle filtering techniques.