Stability Analysis of Covariance Intersection-Based Kalman Consensus Filtering for Time-Varying Systems

The phenomena of unknown correlations are ubiquitously existing in general distributed filtering problems over sensor networks. And the covariance intersection (CI) fusion rule is an effective tool to tackle with this phenomena. During the recent years, the related CI-based Kalman consensus filters (CIKCFs) have been adopted to deal with unknown correlations in sensor networks. However, a systematic stability analysis result for the general CIKCF in the time-varying system setting remains to be established. This paper is written for this purpose. First, a general CIKCF with full features of CI is presented. Accordingly, the conditions for CIKCF to reach consensus with varying weights are investigated. Furthermore, a novel detectability condition, i.e., collectively uniform detectability, is proposed to ensure the error covariances of the CIKCF are uniformly bounded. Based on this condition, the estimation errors are further proven to be exponentially bounded in mean square with the aid of the stochastic stability lemma. Finally, an example is given to validate the effectiveness of the theoretical results.