Measure-of-disagreement of consensus and adaptive-consensus filters for spatially distributed systems

A measure of disagreement of the consensus and adaptive-consensus filters for spatially distributed systems is examined and defined in a similar way as in the finite dimensional case. Such a a measure of disagreement essentially examines the deviation of the state of each spatial filter from the average estimate of all filters. Convergence of each spatially consensus filter to the average implies that the proposed consensus filter agree with each other. However, the interesting observation is that the speed of convergence of the measure of disagreement to zero is linked to the speed of convergence of the state estimation errors to zero. As a consequence one must appropriately design filters so that convergence of the associated state errors to zero enhances the agreement of all consensus filters. The proposed theoretical results are demonstrated by extensive simulations for representative spatially distributed systems.