A stability with optimality analysis of consensus-based distributed filters for discrete-time linear systems

In this paper we investigate how stability and optimality of consensus-based distributed filters depend on the number consensus steps in a discrete-time setting for both directed undirected graphs. By introducing two new algorithms, simpler one based dynamic averaging estimates more complex version where local error covariance matrices are exchanged as well, able to derive complete theoretical analysis. particular show that alone suffices approximate optimal centralized estimate if is large enough needed can be computed way. These results shed light advantages well fundamental limitations shared by all existing proposals class algorithms basic case linear time-invariant systems, relevant analysis situations.