Abstract: In this paper, the optimal energy scheduling problem is investigated in the sensor network with energy sharing and imperfect feedback information. Each sensor is equipped with an energy harvesting module and a transceiver device for the energy sharing between adjacent sensors. Sensors can transmit information and receive packet receipt acknowledgments from the remote estimator via erroneous feedback channels. The goal of this paper is to determine the energies used for data transmission and for sharing between sensors to ensure high-quality estimation performance. To address the challenges posed by imperfect feedback, a novel approach is first proposed for the synergistic estimation of the probability distribution of feedback information for each sensor. Subsequently, a joint error covariance estimation method based on the concept of information state is introduced. By this method, the impact of other sensors' transmission power on the overall transmission process is effectively accounted for. As a result, the proposed energy scheduling problem with uncertain feedback is converted into a Markov decision process (MDP) with perfect information, which becomes more amenable to analysis and solution. The Bellman dynamic programming (DP) equation is employed to obtain the optimal solution. In situations where feedback information may be missing, the relative value iteration algorithm is utilized to solve the Bellman equation, through which the optimal energy allocation strategy is derived. Ultimately, the structural results and a numerical simulation verify the performance of the proposed energy allocation policy.

Key words: energy harvesting, energy sharing, imperfect feedback information, Markov decision process, dynamic programming