Linear estimation for discrete-time systems with Markov jump delays

This paper is concerned with the linear minimum mean square error (MMSE) estimation for discrete-time systems with random delays in the observations. It is assumed that the delay process is modeled as a finite state Markov chain and only its transition probability matrix is known. To overcome the difficulty of estimation caused by random delays, the random delay system is firstly rewritten as a constant delay system with multiplicative noises. By applying the measurement reorganization approach, the system is further transformed into the delay-free one with Markov jump parameters. Then the estimator is derived by using the innovation analysis method in the Hilbert space, and the solution is given in terms of Riccati difference equations.