Covariance-Intersection-based Distributed Kalman Filtering: Stability Problems Revisited

Abstract: This paper studies the stability of covariance-intersection (CI)-based distributed Kalman filtering in time-varying systems. For the general time-varying case, a relationship between the error covariance and the observability Gramian is established. Utilizing this relationship, we demonstrate an intuition that the stability of a node is only related to the observability of those nodes that can reach it uniformly. For the periodic time-varying case, it is proved by a monotonicity analysis method that CI-based distributed Kalman filtering converges periodically for any initial condition. The convergent point is shown to be the unique positive definite solution to a Riccati-like equation. Additionally, by constructing an intermediate difference equation, the closed-loop transition matrix of the estimation error system is proved to be Schur stable. Notably, all theoretical results are obtained without requiring network connectivity assumptions. Finally, simulations verify the effectiveness of the stability results.