Minimum-Variance Recursive State Estimation for 2-D Systems: When Asynchronous Multi-Channel Delays meet Energy Harvesting Constraints

This paper is concerned with the state estimation problem for two-dimensional systems with asynchronous multichannel delays and energy harvesting constraints. In the system, each smart sensor has a certain probability of harvesting energy from the external environment, the authorized transmission between the sensor and the remote filter is contingent upon the current energy level of the sensor, which results in intermittent transmission of observation information. Addressing the issue of incomplete observation information due to asynchronous multi-channel delays, a novel approach for observation partition reconstruction is proposed to convert the delayed activated observation sequences into equivalent delay-free activated observation sequences. Through generating spatial equivalency validation, it is found that the reconstructed delay-free activated observation sequences contain the same information as the original delayed activated observation sequences. Based on the reconstructed activated observation sequence and activated probability, a novel unbiased h+1-step recursive estimator is constructed. Then, the evolution of the probability distribution of the energy level is discussed. The estimation gains are obtained by minimizing the filtering error covariance. Subsequently, through parameter assumptions, a uniform lower bound and a recursive upper bound for the filtering error covariance are presented. And the monotonicity analysis of activated probability on estimation performance is given. Finally, the effectiveness of the proposed estimation scheme is verified through a numerical simulation example.