Exact Bayesian and particle filtering of stochastic hybrid systems

The standard way of applying particle filtering to stochastic hybrid systems is to make use of hybrid particles, where each particle consists of two components, one assuming Euclidean values, and the other assuming discrete mode values. This paper develops a novel particle filter (PF) for a discrete-time stochastic hybrid system. The novelty lies in the use of the exact Bayesian equations for the conditional mode probabilities given the observations. Therefore particles are needed for the Euclidean valued state component only. The novel particle filter is referred to as the interacting multiple model (IMM) particle filter (IMMPF) because it incorporates a filter step which is of the same form as the interaction step of the IMM algorithm. Through Monte Carlo simulations, it is shown that the IMMPF has significant advantage over the standard PF, in particular for situations where conditional switching rate or conditional mode probabilities have small values.