Peak covariance stability of Kalman filter with bounded Markovian packet losses

This paper investigates the peak covariance stability of Kalman filter with possible packet losses in transmitting measurement outputs to the filter via an unreliable network. The packet losses are assumed to be bounded and driven by a finite state Markov process. It is shown that if the observability index of the discrete-time linear time-invariant (LTI) system under investigation is one, the Kalman filter is peak covariance stable under no additional condition. For discrete LTI systems with observability index greater than one, a sufficient condition for peak covariance stability is obtained in terms of the system dynamics and the probability transition matrix of the Markov chain. Finally, the validity of these results is demonstrated by numerical simulations.