Distributed recursive filtering for multi-rate nonlinear systems under the Round-Robin scheduling

This paper is concerned with the distributed recursive filtering problem for a class of time-varying multi-rate systems in sensor networks with stochastic nonlinearities and the Round-Robin (RR) protocol. For the purpose of alleviating data collisions, the RR protocol is utilized to schedule the order of the data transmission, under which each sensor node only broadcasts partial information to both the corresponding local filter and its neighboring nodes. Due to different sampling rates of the plant and the sensors, the lifting technique is proposed by which the multi-rate sampled-data system under consideration is transformed into a single-rate system. The main purpose of this paper is to design a distributed recursive filter for each sensor such that, in the simultaneous presence of stochastic nonlinearities, the RR communication protocol and the multi-rate mechanism, an upper bound for the filtering error covariance is guaranteed and subsequently minimized by properly designing the filter parameters. Furthermore, by utilizing the mathematical induction method, a sufficient condition is established to ensure the uniform boundedness of the filtering error covariance. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed design scheme of distributed filters.