Distributed recursive filtering under random access protocols: A multirate strategy

Abstract This article addresses the distributed recursive filtering problem for a class of time‐varying multirate systems in sensor networks with randomly occurring nonlinearities and the communication protocol. A multirate model is considered where the sampling period of the sensors is slower than the updating period of the system state. Accordingly, the lifting technique is proposed to transform the multirate system into a single‐rate system. In order to avoid data collisions, the random access protocol (RAP) scheduling is applied to determine which signal/packet selected by RAP scheduling can access the shared network for each sensor. Attention is focused on the design of a distributed recursive filter such that, in the simultaneous presence of randomly occurring nonlinearities, the multirate strategy and the RAP scheduling, an upper bound for the filtering error covariance is obtained with the help of the mathematical induction method. Furthermore, by utilizing a novel matrix simplification technique, the filter parameters are recursively calculated by minimizing the obtained upper bound. Finally, the effectiveness of the proposed distributed recursive filtering scheme is demonstrated via a numerical example.