On distributed optimal Kalman-Bucy filtering by averaging dynamics of heterogeneous agents

Abstract

This paper studies a design and analysis of distributed Kalman-Bucy filter in sensor networks. When observability of the target system from each sensor is lost, boundedness of the covariance matrices for the individual Riccati equations are not guaranteed. In order to overcome this difficulty and to recover the optimality of the centralized Kalman-Bucy filter, we introduce exchange of covariance matrices with other agents. Then, since those Riccati equations and estimators are heterogenous, achieving consensus among them becomes the question. We employ the recently introduced notion of averaged dynamics, which is the average of all distributed Kalman-Bucy filters' dynamics, and show that sufficiently strong coupling gains guarantee arbitrarily precise recovery of optimality and the estimation error converges to zero when there is no noise. Numerical simulations show the performance of the proposed scheme.