Stability analysis for Kalman filters with random measurement matrices

This paper addresses the stability of a Kalman filter when measurements are intermittently available due to an unreliable communication channel between sensors and the estimator. This intermittent behaviour can be modelled as a random and time-varying measurement system. We consider a general discrete-time system with a random measurement matrix and study the stability condition for the associate Kalman filter. By deep dissecting the system structure, the necessary and sufficient stability condition for the Kalman filter is given. We also give methods to checking the stability condition for specific linear systems. Our results generalize previously known stability conditions where the system matrix structure is restricted.