Dynamical filtering equations for Stochastic Hybrid System state estimation

This paper considers the topic of state estimation for the Stochastic Hybrid System (SHS). The SHS is a class of dynamical systems which can accurately describe many interacting continuous and discrete dynamics. State estimation for the SHS, also called hybrid estimation, is an important yet challenging problem. While most previous research has addressed the hybrid estimation for some special classes of the SHS, this paper solves this problem for the general SHS which is a class of continuous-time stochastic processes defined on a hybrid state space. The major contribution of this paper is the proposal of dynamical filtering equations for hybrid estimation. With a given sequence of noisy observations, the filtering equations describe the evolution of the probability distribution function (pdf) of the estimated hybrid state.