Optimal filtering of discrete-time hybrid systems

This paper is concerned with discrete-time hybrid filtering of linear non-Gaussian systems coupled by a hidden switching process. An optimal control approach is used to derive a finite-dimensional recursive filter which is optimal in the sense of the most probable trajectory estimate. Models with unknown switching distributions are considered. Extensions to nonlinear hybrid systems are given. Numerical examples are considered and computational experiments are reported. These examples demonstrate that our filtering scheme outperforms popular filtering schemes available in the literature.