Distributed parameter estimation under unreliable directed networks

Recent research on distributed parameter estimation often focuses on undirected or strongly connected and balanced networks. In this paper, we study the distributed parameter estimation problem for sensor networks under unreliable directed networks. A “consensus+innovation” type algorithm is proposed for each sensor or agent. We prove both mean square and almost sure convergence of the algorithm. We also derive a new general condition for directed networks. In the special case where the networks are undirected or strongly connected and balanced, the condition boils down to the global observability condition considered in the existing results.