Convergence analysis of consensus based distributed filtering algorithm in sensor networks

This paper studies the distributed filtering problem of sensor networks, where a set of heterogeneous sensing nodes is required to estimate the state of a linear discrete-time dynamic system in a collaborative manner. Due to limited sensing range and communication constraints, just part of sensors can get observations of the process and a consensus based sub-optimal filtering algorithm is designed. The convergence properties of the estimation error covariance is further studied, and a necessary and sufficient convergence condition is provided based on LMIs. This condition shows that the convergence of the algorithm requires the target node in the extended topology of network is globally reachable and each sensing node is observable to the process. Simulation examples are given to illustrate the results.