Performance analysis of trace proximity based distributed Kalman filter

Abstract

This paper analyzes the performance of the distributed Kalman filter based on trace proximity criterion and neighboring-node measurements (TPCNM) proposed in Liu et al. (2022) where the performance analysis includes the boundness, convergence, mean square error and estimation error covariance. First, we prove that the boundness of the distributed Kalman filter based on TPCNM is ensured under proper conditions. Second, the convergence conditions for the distributed Kalman filter based on TPCNM with some constraints for the value of node are established using a novel matrix difference equation (MDE), two equalities in the distributed Kalman filter based on TPCNM and some results presented in this paper where one equality contains a term with both the measurement matrix and the measurement noise covariance matrix. In addition, the mean square error performance for the distributed Kalman filter based on TPCNM is analyzed, and it is proved that the matrix $P$ in the distributed Kalman filter based on TPCNM is the real estimation error covariance. A scalar dynamic system example and a radar tracking example are provided to illustrate the validity and correctness of the developed methods.