Kalman Filtering with Correlated Noises over Unreliable Communication Network

Abstract

Abstract: In this paper, we study the Kalman filtering problem with correlated noises one time apart, when part or all
of the observation measurements are lost in a random way due to unreliable link between controller and estimator. By
"one time apart" we mean that the process noise at time step ???? does not contribute to the system measurement at time
step ????. Rather, it is the process noise at time step ???? − 1 that contributes to the system measurement at time step ????.
Observation losses can occur in a distributed control system where measurements are taken at different sensors in different physical locations, or one sensor needs to send its data in multiple packets. We formulate the Kalman filtering problem with correlated noises at one time apart and derived the Kalman filter update equations with random observation measurements. Then, we showed that the estimation error covariance (performance index) became a random quantity when the system measurements were collected at different intervals with different probability arrival rate. As a result, we investigated the statistical convergence properties of the performance index and found the stable and unstable regions so that this criterion could be bounded in a stable region and unbounded in an unstable one. The results are illustrated with some simple numerical examples.