Hybrid filtering for linear systems with non-Gaussian disturbances

This paper is concerned with hybrid filtering of a non-Gaussian system coupled by a hidden switching process. An optimal control approach is used to derive a finite-dimensional recursive filter that is optimal in the sense of the most probable trajectory (MPT) estimate. An approximate scheme is obtained when the probability distribution of the switching process converges to a limiting distribution, which is often easier to obtain. Numerical examples are considered, and computational experiments are reported. In these examples, our schemes outperform popular filtering schemes available in the literature.