Optimal estimation for systems with time-varying delay

In this paper, the optimal estimation problem for discrete-time systems with time-varying delay in the measurement channel is studied. First, under the assumption that the time-varying delay is of a known upper bound, the single delayed measurement can be rewritten as multiple channel measurements that contain the same state information as the original measurement and each channel has single constant delay. We then derive the optimal estimator by adopting a re-organized innovation analysis approach. The estimator is given in terms of a Riccati difference equation with singular innovation covariance matrix whose solvability is established.