Asymptotically Optimal Consensus-based Distributed Filtering of Continuous-Time Linear Systems

We describe a consensus-based distributed filtering algorithm for linear systems with a parametrized gain and show that when the parameter becomes large the error covariance at each node becomes arbitrarily close to the error covariance of the optimal centralized Kalman filter. The result concerns distributed estimation over a connected un-directed or directed graph and for static configurations it only requires to exchange the estimates among adjacent nodes. A comparison with related approaches confirms the theoretical results and shows that the method can be applied to a wide range of distributed estimation problems.