On the Convergence Conditions of Distributed Dynamic State Estimation Using Sensor Networks: A Unified Framework

In this paper, the problem of distributed state estimation using sensor networks is considered for a very general scenario, where: 1) the process model of the target and the sensing models of local agents are assumed to be linear and time varying; 2) the communication topology between agents is modeled as a general directed graph, and is subject to change with time; and 3) there might exist a time-varying set of agents not directly sensing the target. A distributed hybrid information fusion (DHIF) algorithm, which requires no global parameter and only one communication iteration per time instant, is proposed. The DHIF algorithm computes confident but consistent estimates. The convergence of the proposed algorithm is guaranteed with very mild sufficient conditions formulated in such a general scenario. Specifically, the directed switching graphs do not necessarily need to be (jointly) strongly connected nor balanced. Then the conditions are shown to be “almost” necessary. In the special case where the process/sensing models and the topology are both time invariant, the conditions are necessary after certain relaxation. Comparisons with existing algorithms are shown both analytically and numerically. The convergence results are illustrated in simulations. In the end, the proposed algorithm is also extended to the situation with nonlinearities involved, and illustrated in simulation.