Local Design of Distributed State Estimators for Linear Discrete Time-Varying Systems Over Binary Sensor Networks: A Set-Membership Approach

This article is concerned with the distributed set-membership estimation problem for a class of discrete time-varying systems over binary sensor networks. For the binary sensors, the cases of fixed and time-varying thresholds are considered. In both the cases, the information useful for state estimation purposes is extracted by utilizing the crossings of binary measurements at two adjacent time instants, and then distributed estimators are constructed for each sensor node with the aid of the available measurements, where a set of vector saturation functions is introduced to resist the adverse effect of outliers during signal transmission. A novel distributed set-membership performance index is provided by averaging over the ellipsoidal constraints of all the sensor nodes, and the local performance analysis method is employed to establish sufficient criteria that guarantee the existence of desired estimators whose parameters are then derived for every node by recursively optimizing certain ellipsoids in the sense of matrix trace. The applicability and feasibility of the distributed set-membership schemes developed in this article are verified by two illustrative examples.