Hybrid optimal filtering for linear continuous-time Markovian jump systems with non-Gaussian noises by MPT approach

Abstract

In this paper, we study the optimal filtering problems for a class of linear continuoustime Markovian jump systems with non-Gaussian noises by most probable trajectory (MPT) approach based on principle of hybrid optimality. The systems are described by the switching systems with Markovian mode transitions. In this paper we consider both cases (A) the modes are accessible and (B) the modes are inaccessible. The necessary and sufficient conditions for the solvability of the optimal filtering problems are given by coupled Riccati differential equations with initial conditions. Finally, we give numerical examples.