Recursive Distributed Filtering for Time-Varying Systems Over Sensor Network via Rayleigh Fading Channels: Tackling Binary Measurements

Abstract

This paper is concerned with the distributed filtering problem for a class of discrete time-varying stochastic systems over binary sensor networks with the Rayleigh fading channels. Both the system state and measurement are subject to random noises with known statistical information, where the distribution function of measurement noise is employed to extract the functional information for state estimation purposes. The communication between a sensor node and its neighboring ones is implemented over a Rayleigh fading channel. For each binary sensor, a distributed filter is constructed by virtue of the available information from itself and its neighboring nodes, and the overall filtering error dynamics is guaranteed to be exponentially ultimately bounded in the mean square sense. By resorting to a local performance analysis method, sufficient criteria are established for ensuring the existence of the desired distributed filter in terms of a set of recursive linear matrix inequalities. The desired filter parameters are recursively calculated on every node by solving an optimization problem at each time instant with the aim of improving the estimation accuracy. Finally, some comparative results are presented to demonstrate the applicability and effectiveness of the developed distributed filtering scheme.