Asymptotically Optimal Distributed Filtering of Continuous-Time Linear Systems

In this paper we prove the following new and unexpected result: it is possibleto design a continuous-time distributed filter for linear systems that asymptotically tends ateach node to the optimal centralized filter. The result concerns distributed estimation over aconnected undirected graph and it only requires to exchange the estimates among adjacentnodes. We exhibit an algorithm containing a consensus term with a parametrized gain and showthat when the parameter becomes arbitrarily large the error covariance at each node becomesarbitrarily close to the error covariance of the optimal centralized Kalman filter.