Optimal scheduling strategy for networked estimation with energy harvesting

Joint optimization of scheduling and estimation policies is considered for a system with two sensors and two noncollocated estimators. Each sensor produces an independent and identically distributed sequence of random variables, and each estimator forms estimates of the corresponding sequence with respect to the mean-squared error sense. The data generated by the sensors are transmitted to the corresponding estimators over a bandwidth-constrained wireless network that can support a single packet per time slot. The access to the limited communication resources is determined by a scheduler that decides which sensor measurement to transmit based on both observations. The scheduler has an energy-harvesting battery of limited capacity, which couples the decision-making problem in time. Despite the overall lack of convexity of this problem, it is shown that this system admits a globally optimal scheduling and estimation strategy pair under the assumption that the distributions of the random variables at the sensors are symmetric and unimodal. Additionally, the optimal scheduling policy has a structure characterized by a threshold function that depends on the time index and energy level. A recursive algorithm for threshold computation is provided.