FIR Filtering for Discrete-Time Markov Jump Linear Systems

This paper is concerned with finite impulse response (FIR) filtering problem for discrete-time linear system which possesses stochastically jumping parameters described by a finite-state Markov process. An FIR filter processes the measured inputs and outputs on a finite receding horizon linearly and the filter gain is obtained by minimizing variance of the error between real state and estimated one. According to inverse computation, system matrix is always assumed to be non-singular. In terms of engineering application, we must have complete access to the current time jump mode. The FIR filter is presented in batch form and recursive form, respectively, and Kalman filter is also addressed for comparison. Finally, a numerical example is given to illustrate the design procedure and their effectiveness.