Kalman Filtering over Networks in Presence of Multi-Channel Correlated Packet Drops

Abstract

In this paper, we study a modified Kalman filter (MKF) over networks admitted multi-channel packet drops and investigate the existence of a stabilizing solution to the corresponding modified algebraic Riccati equation (MARE). Random multi-channel packet drops, compared with other previous formulations, are allowed to be correlated in spatial in this contribution. We first derive two different necessary and sufficient conditions to ensure mean-square detectability of the considered system in operator- and time-domain respectively. Then, including the necessity of the mean-square detectability, an explicit necessary and sufficient condition to the existence of a stabilizing solution to the MARE is derived, which can perfectly reduce to the existence condition to standard algebraic Riccati equation (ARE) whenever the absent of packet drops. Meanwhile, the stabilizing solution can be obtained by solving a set of linear matrix inequalities (LMIs).