Linear optimal filtering for discrete-time systems with random jump delays

This paper is concerned with the dynamic Markov jump filters for discrete-time system with random delays in the observations. It is assumed that the delay process is modeled as a finite state Markov chain. To overcome the difficulty of estimation caused by the random delays, the single random delayed measurement system is firstly rewritten as the multiplicative noise constant-delay system. Then, by applying the measurement reorganization approach, the system is further transformed into the delay-free one with Markov jump parameters. Finally, the estimator is derived by using the standard Markov jump filter theories. It is interesting to show that the presented filter for the system with random jump delays can be designed by performing two sets of standard Riccati equations with the same dimension as that of the original system. A simulation example is given to illustrate the effectiveness of the proposed result.