Design of consensus and adaptive consensus filters for distributed parameter systems

This work establishes an abstract framework that considers the distributed filtering of spatially varying processes using a sensor network. It is assumed that the 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. A modification to the local spatially distributed filters provides the non-adaptive case of spatially distributed consensus filters which penalize the disagreement amongst themselves in a dynamic manner. A subsequent modification to this scheme incorporates the adaptation of the consensus gains in the disagreement terms of all local filters. Both the well-posedness of these two consensus spatially distributed filters and the convergence of the associated observation errors to zero in appropriate norms are presented. Their performance is demonstrated on three different examples of a diffusion partial differential equation with point measurements.