A Recursive Matrix Inequality Approach to Distributed Filtering Over Binary Sensor Networks: Handling Amplify-and-Forward Relays

This article addresses the distributed filtering problem for a class of discrete time-varying systems over a binary sensor network (BSN) with amplify-and-forwarded (AF) relays, where the plant and binary measurements are subject to random noises that have known statistical information. The formulation of the topology of BSN with AF relays is first carried out. To reflect the dithering of the threshold of the binary sensor, a random variable with zero mean is utilized, and then useful information for estimation purposes is extracted by employing the joint distribution functions of measurement noises and the new random variable. Signal transmissions among neighbors are realized over fading channels, with a part of sensors communicating via relays. The desired distributed filter for each sensor is constructed using the available information from itself and its neighbors such that the resulting filtering error dynamics satisfies the desired exponential boundedness. To combat the fading effect, the relay matrix and the encoder matrix are designed in the sense of minimum mean square error so as to guarantee the effectiveness of the transmitted signal. The sufficient criterion for each sensor (with or without a relay) is established within the framework of the local performance analysis. The desired filter gains for each sensor are derived by solving a constrained optimization problem. Finally, an illustrative simulation example is used to demonstrate the applicability and effectiveness of the developed distributed filtering scheme.