Distributed Consensus-Based Extended Kalman Filtering: A Bayesian Perspective

In this paper, we study the distributed state estimation problem where a set of nodes cooperatively estimate the hidden state of a nonlinear dynamic system based on sequential observations. As a common approach to solve this problem, the extended Kalman filter (EKF) is considered from a Bayesian perspective. After linearizing the state-space model using the first-order Taylor series, we construct an equivalent maximum-a-posteriori (MAP) estimation problem under linear Gaussian assumptions coupled with a consensus constraint. The consensus-based MAP problem is solved distributedly by the alternating direction method of multiplier (ADMM). The resulting distributed algorithm ensures robust consensus-based state estimates among nodes and is able to converge to the central solution.