LAUSR

This article studies a distributed Kalman filtering (DKF) algorithm with a fast convergence rate, based on a networked system with multiplicative noise. Each node involved in the distributed estimation can independently compute the optimal state estimate using its local measurements and by exchanging information with neighboring nodes. First, a DKF algorithm is proposed based on the idea of a message‐passing algorithm. Subsequently, the convergence of this DKF algorithm in a finite number of steps for acyclic graphs is given. Moreover, the equivalence between cyclic and acyclic graphs is demonstrated using the depth‐first search algorithm, thereby illustrating its convergence for general topological graphs. Finally, three examples are provided to demonstrate that this distributed algorithm can converge to the central Kalman filter estimate. Compared to other distributed algorithms, it exhibits faster convergence.