Consistent distributed state estimation with global observability over sensor network

TL;DR

This paper introduces a distributed Kalman filter for sensor networks that ensures consistent state estimation without requiring global information at each sensor, leveraging covariance intersection and global observability.

Contribution

It proposes a novel sub-optimal distributed Kalman filter with proven consistency, bounded error covariance, and convergence under network connectivity and observability conditions.

Findings

The proposed DKF is consistent and provides real-time error covariance bounds.

Adaptive CI weights improve filter accuracy.

Simulation results confirm effectiveness in practical scenarios.

Abstract

This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that a networked Kalman filter with optimal gain parameter is actually a centralized filter, since it requires each sensor to have global information which is usually forbidden in large networks. Then, a sub-optimal distributed Kalman filter (DKF) is proposed by employing the covariance intersection (CI) fusion strategy. It is proven that the proposed DKF is of consistency, that is, the upper bound of error covariance matrix can be provided by the filter in real time. The consistency also enables the design of adaptive CI weights for better filter precision. Furthermore, the boundedness of covariance matrix and the convergence of the proposed filter are proven based on the strong connectivity of directed network topology and the global observability which permits the sub-system with local sensor's measurements to be unobservable. Meanwhile, to keep the covariance of the estimation error bounded, the proposed DKF does not require the system matrix to be nonsingular at each moment, which seems to be a necessary condition in the main DKF designs under global observability. Finally, simulation results of two examples show the effectiveness of the algorithm in the considered scenarios.