Stability of the Kalman filtering with two periodically switching sensors over lossy networks

This paper considers the stability of Kalman filtering of a discrete-time stochastic system using two periodically switching sensors over a network subject to random packet losses, which is modeled by an independent and identically distributed Bernoulli process. It is proved that this problem can be converted into the stability of Kalman filtering using two sensors at each time instant, where the measurements of each sensor are transmitted via an independent lossy channel. Some necessary and sufficient conditions for stability of the estimation error covariance matrices are respectively established, and the effect of the periodic switching on the stability is revealed. Their implications and relationships with related results in the literature are discussed.