Distributed detectability and filter design in homogeneous sensor networks

This paper studies distributed filtering problem of homogeneous sensor networks. Just part of sensors can get observations of the process and consensus based filters are applied. Both the distributed detectability and the suboptimal filter design are investigated. By converting the stability problem of estimation errors of sensors under time-varying topologies to the robust stability problem of some uncertain system, two sufficient distributed detectability conditions are provided. One is LMI-based and the other is given by the eigenvalues of the process matrix and Laplacian matrices. A suboptimal algorithm to design the consensus based filter gains is proposed and the convergence of the algorithm is discussed. Simulation examples are given to illustrate the results.