On consistency and stability of distributed Kalman filter under mismatched noise covariance and uncertain dynamics

This paper considers the state estimation problem for a class of discrete-time linear time-varying systems over a peer-to-peer sensor network under mismatched noise covariance and uncertain dynamics. To deal with the inconsistency and instability of distributed Kalman filter for the problem, we propose a general consistent distributed Kalman filter framework by considering compensation to the mismatched noise covariance and the uncertain dynamics. The estimated error covariance of the distributed filter is proven to be monotonic with respect to compensation parameters. Futhermore, we show the design methods of compensation matrices to ensure consistency of the proposed filter in each sensor. Then, stability of the proposed distributed Kalman filter is demonstrated. Simulation examples show the effectiveness of our methods.(c) 2023 Elsevier Ltd. All rights reserved.