Recursive Filtering for Nonlinear Systems with Relay Communication, Energy Harvesting and Correlated Noises

In this paper, the recursive filtering problem is investigated for stochastic nonlinear systems with relay communication, energy harvesting and correlated noises. The relay node receives signals transmitted from the sensor, then amplifies and forwards these signals to the filter. The transmission power of the sensor and the relay node is characterized by random variables obeying certain probability distribution. The energy harvesting technique is also employed to sustain the operation of both the sensor and the relay node, where the corresponding energy harvesting models are established to describe evolution of their energy levels. The process and the measurement noises are one-step autocorrelated and two-step cross-correlated, respectively. Furthermore, the channel noises are considered as one-step autocorrelated due to influence of the communication environment. The objective of this paper is to establish a recursive filter to address the state estimation problem in the presence of relay communication, energy harvesting, and correlated noises within a unified framework. By means of recursive computation and stochastic analysis, a certain upper bound is guaranteed on the second moment matrix of the filtering error, and then minimized by appropriately designed filter gain at each time step. In addition, the boundedness issue is also discussed to assess the filtering performance. Finally, two examples are presented to illustrate the effectiveness and practicability of the designed filtering strategy.