Kalman Filtering With Intermittent Observations: On the Boundedness of the Expected Error Covariance

This paper addresses the stability of a Kalman filter when measurements are intermittently available due to constraints in the communication channel between the sensor and the estimator. We give a necessary condition and a sufficient condition, with a trivial gap between them, for the boundedness of the expected value of the estimation error covariance. These conditions are more general than the existing ones in the sense that they only require the state matrix of the system to be diagonalizable and the sequence of packet losses to be a stationary finite order Markov process. Hence, we extend the class of systems for which these conditions are known in two directions, namely, by including degenerate systems, and by considering network models more general than i.i.d. and Gilbert-Elliott. We show that these conditions recover known results from the literature when evaluated for non-degenerate systems under the assumption of i.i.d. or Gilbert-Elliott packet loss models.