This paper presents the formulation of distributed Kalman-Bucy filter algorithm for a network of autonomous sensors, which is modeled as a connected undirected graph. Development of the distributed Kalman-Bucy filter is formulated as two average consensus problems in terms of weighted inverse of measurement noise covariance matrices and weighted measurements. The proposed algorithm utilizes the static average consensus protocol to solve the first consensus problem and the proportional-integral based dynamic average consensus protocol to solve the latter. The distributed Kalman-Bucy filter algorithm is optimal in the sense that the performance of the proposed algorithm asymptotically approaches that of a centralized filter. Numerical simulations are presented to demonstrate the performance of the proposed scheme.
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