Multi-sensor Kalman filtering over packet-dropping networks subject to Round-Robin protocol scheduling

Abstract

This paper considers the filtering problem for a class of linear cyber-physical systems (CPSs) subject to the Round-Robin protocol (RRP) scheduling, where the RRP is adopted to efficiently avoid data collisions in multi-sensor application scenarios. Unlike most of the existing results concerning the scheduling effects of the RRP under reliable communication channels, the filtering problem over packet-dropping networks is investigated. In such a framework, an optimal Kalman-type recursive filter is derived in the minimum mean square error (MMSE) sense, which is different from the suboptimal filters with bounded error covariances proposed in the previous results. Due to the protocol-induced behaviors and the unreliability of the channels, the estimator may be unstable. Thus, the stability problem of the filter is mainly discussed. It can be proved that the filter is stable when the arrival rate of the measurements exceeds a certain threshold, where the threshold can be obtained by solving a quasi-convex optimization problem. Furthermore, a sufficient condition for the existence of the steady-state error covariance is presented and can be transferred into the feasibility of a certain linear matrix inequality (LMI). Finally, a simulation example is provided to demonstrate the developed results.