Stability of Kalman Filtering with a Random Measurement Equation: Application to Sensor Scheduling with Intermittent Observations

Abstract: Studying the stability of the Kalman filter whose measurements are randomly lost has been an active research topic for over a decade. In this paper we extend the existing results to a far more general setting in which the measurement equation, i.e., the measurement matrix and the measurement error covariance, are random. Our result also generalizes existing ones in the sense that it does not require the system matrix to be diagonalizable. For this general setting, we state a necessary and a sufficient condition for stability, and address its numerical computation. An important application of our generalization is a networking setting with multiple sensors which transmit their measurement to the estimator using a sensor scheduling protocol over a lossy network. We demonstrate how our result is used for assessing the stability of a Kalman filter in this multi-sensor setting.