Optimal Estimators for Systems With Finite Consecutive Packet Dropouts

This paper is concerned with the optimal estimation problem for discrete-time stochastic linear systems with finite consecutive packet dropouts. By introducing a set of new variables, a state augmented system with a lower order is obtained. Based on the new model, the optimal estimators including filter, predictor and smoother are readily solved in the least-mean-square sense via the innovation analysis approach. The solutions depend on the recursion of a Riccati equation and a Lyapunov equation. The steady-state estimators have also been investigated. A sufficient condition for the convergence of the optimal estimators has been given. A simulation shows the effectiveness of the proposed algorithms.