Optimal full-order and reduced-order estimators for discrete-time systems with multiple packet dropouts

This paper is concerned with the estimation problem for discrete-time stochastic linear systems with multiple packet dropouts. Based on a recently developed model for multiple-packet dropouts, the original system is transferred to a stochastic parameter system by augmentation of the state and measurement. The optimal full-order linear filter of the form of employing the received outputs at the current and last time instants is investigated. The solution to the optimal linear filter is given in terms of a Riccati difference equation governed by packet arrival rate. The optimal filter is reduced to the standard Kalman filter when there are no packet dropouts. The steady-state filter is also studied. A sufficient condition for the existence of the steady-state filter is given and the asymptotic stability of the optimal filter is analyzed. At last, a reduced-order filter is investigated.