Kalman filtering with uncertain process and measurement noise covariances with application to state estimation in sensor networks

Distributed state estimation under uncertain process and measurement noise covariances is considered. An algorithm based on sensor fusion using Kalman filtering is investigated. It is shown that if the covariances are decomposed into a known nominal covariance plus an uncertainty term, then the uncertainty of the actual estimation error covariance for the Kalman filter grows linearly with the size of the uncertainty term. This result is extended to the sensor fusion scheme to give an upper bound on the actual error covariance for the fused state estimate. Examples are provided to illustrate how the theory can be applied in practice.