Linear estimation for random delay systems

This paper is concerned with the linear estimation problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time-stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal linear filter is presented based on Kalman filtering technique. However, the optimal filter is time-varying, stochastic, and does not converge to a steady state in general. Then an alternative suboptimal filter with deterministic gains is developed under a new criteria. The estimator performance in terms of their error covariances is provided, and its mean square stability is established. Note that both filters have the same dimension as the original systems.