Measure of disagreement of spatially distributed filters for distributed parameter systems

This work establishes a metric for comparing the disagreement among local filters as designed for spatially distributed processes. It is assumed that a sensor network consists of groups of sensors, each of which provides a number of state measurements from sensing devices that are not necessarily identical and which only transmit their information to their own sensor group. The first type of filter considers spatially distributed filters that do not share information with each other (i.e. non-interacting). The second type of filter considers spatially distributed consensus filters which penalize the disagreement between them in a dynamic manner. A metric for examining the disagreement of the local filters, as extended from the finite dimensional case, essentially yields a deterministic analog of the standard deviation of the spatially local filter errors. Extensive simulation results serve to demonstrate the effectiveness of the consensus filters and the faster convergence of the disagreement of these filters when consensus terms are included in each of the local filters.