Control-Theoretical and Topological Analysis of Covariance Intersection Based Distributed Kalman Filter

Abstract

Covariance intersection (CI) extends Kalman filter (KF) in distributed estimation, since it can fuse Gaussian estimates in the absence of the estimates' correlations. However, even with the preliminary success on the integration of CI and KF, existing discussion limited in global behavior is unable to directly deal with a system with a mixture of unbounded-covariance and bounded-covariance agents. In other words, until this letter there has been no explicit investigation on the analytic relationship between effective observability in each agent and system topology, to the best of our knowledge. To formalize these problems, we establish CI-based KF with explicit CI topology, on top of the conventional KF with observation exchanges. Consequently, the effect of CI on KF can be characterized by the impact of individual CI links on each agents. In particular, we systematically show that CI links can diminish the effective unobservable space, which relaxes the boundedness criterion. In addition, as a conservative fusion scheme, there may exist CI links that provide no improvement on estimation performance but generate additional uncertainty. A method is proposed to identify and then to suppress such redundant CI links for enhanced estimation performance. Finally, the pros and cons of CI on distributed estimation algorithms are comprehensively characterized and substantiated by a numerical example.