A Note on Optimal Distributed State Estimation for Linear Time-Varying Systems

In this technical note, we prove that the ODEFTC algorithm constitutes the first optimal distributed state estimator for continuous-time linear time-varying systems subject to stochastic disturbances. Particularly, we formally show that it is able to asymptotically recover the performance, in terms of error covariance of the estimates at each node, of the centralized Kalman-Bucy filter, which is known to be the optimal filter for the considered class of systems. Moreover, we provide a simple sufficient value for the consensus gain to guarantee the stability of the distributed estimator.