Distributed State Estimation for Continuous-Time Linear Systems With Correlated Measurement Noise

In this article, the problem of distributed state estimation for a continuous-time linear system with a sensor network is investigated, where each sensor can only communicate with its neighbors and contains time-correlated measurement noise. To solve this problem, a novel augmented leader-following information fusion strategy is first proposed to collect measurements and system matrices. Then, a class of distributed state estimators is developed with bounded estimation error covariances. Further, a closed-form relation between the designed distributed estimator and the centralized estimator is established. It is found that the estimation performance of the former converges to that of the latter when the consensus gain tends to infinity. The proposed estimator is further extended to the fully distributed case by introducing an adaptive law for the consensus gain without using any global information. Moreover, it is shown that the designed estimator is applicable for systems with deterministic noise. Finally, several comparative numerical simulations are provided to demonstrate the effectiveness and superiority of the theoretical results.