Linear estimation for discrete-time systems with Markov jump delays

This paper investigates the linear minimum mean square error estimation for discrete-time linear systems with Markov jump delays. In order to solve the optimal estimation problem, the single Markov delayed measurement is firstly rewritten as an equivalent measurement with multiple constant delays, and then a delay-free Markov jump linear system is obtained via state augmentation. The estimator is derived on the basis of the geometric arguments in the Hilbert space, and a recursive equation of the filter is obtained by solving the Riccati equations.