Distributed Kalman Filtering With Finite-Time Max-Consensus Protocol

This paper investigates the distributed state estimation problem for an unstable dynamic plant in a sparsely strongly connected sensors network. The dynamics of the plant are collectively observable for all sensors, but not necessarily locally observable for each sensor. We propose a finite-time consensus-based distributed estimator to cope with the local unobservability. This algorithm is based on the max-consensus technique, and the number of consensus iterations is precisely provided. We prove that this estimator is stable and the mean-squared error is equal to that obtained by the centralized estimator. Furthermore, we extend this finite-time consensus Kalman filtering algorithm to networks with nonuniform time-varying communication delays. By introducing the virtual nodes, which act as the relay nodes, we prove the stability of the algorithm. Finally, the effectiveness of the proposed distributed finite-time consensus filters is evaluated by simulation experiments.