Moving horizon estimation over relay channels: Dealing with packet losses

Abstract

This paper is concerned with the moving horizon estimation problem for networked systems over relay channels. The relay channel under consideration is a wireless communication channel with a so-called relay node. Under the effects of relay node, the signal transmission between the plant and estimator is determined by a combination of three communication processes, namely the sensor-to-estimator, the sensor-to-relay and the relay-to-estimator communication processes. In order to characterize the impact of such kind of relay-channel-based communication, a three-terminal relay model is employed to describe the signal transmission behaviors between the plant and the estimator. Three Bernoulli-distributed white sequences are adopted to model the packet losses occurring in the communication processes. A full information estimation strategy is firstly developed in the sense of maximum a posteriori according to the system dynamics and transmission behaviors. Then, a moving horizon estimator is designed based on the derived full information estimation strategy. Furthermore, the solution of the proposed moving horizon estimation strategy is achieved by using the completing-the-square approach and, subsequently, sufficient conditions are derived to guarantee the mean-square ultimate boundedness of the resultant error dynamics of the state estimation. Two simulation examples are given to demonstrate the effectiveness of our developed estimation scheme.