A numerical method for state estimation of continuous time Markov jump linear systems

This paper introduces an approximation procedure for implementing the Kalman-Bucy filter (KBF) for continuous-time Markov jump linear systems with perfect observation of the jump variable. The procedure involves the discretization of the jump times, which is performed using a quantization approach. It allows for a pre computation of the gain matrices of the KBF. We develop an error analysis indicating that error covariance of the proposed filter approaches the error covariance of the KBF, which is the optimal one for the considered estimation problem. A numerical example is included to illustrate the implementation and the performance of the approximating filter.