Asymptotically Optimal Distributed Filtering of Continuous-Time Linear Systems
In this paper we prove the following new and unexpected result: it is possible
to design a continuous-time distributed filter for linear systems that asymptotically tends at
each node to the optimal centralized filter. The result concerns distributed estimation over a
connected undirected graph and it only requires to exchange the estimates among adjacent
nodes. We exhibit an algorithm containing a consensus term with a parametrized gain and show
that when the parameter becomes arbitrarily large the error covariance at each node becomes