Communication scheduling and remote estimation with energy harvesting sensor

We consider a remote estimation problem with an energy-harvesting sensor and a remote estimator. The sensor harvests energy from its environment (say, for example, through a solar cell) and uses this energy for the purpose of communicating with the estimator. Due to the randomness of energy available for communication, we need to find a communication scheduling strategy for the sensor. The estimator relies on messages communicated by the sensor to produce real-time estimates of the sensor's observations. We consider the problem of finding a communication scheduling strategy for the sensor and an estimation strategy for the estimator that jointly minimize an expected sum of communication and distortion costs over a finite time horizon. We find a dynamic programming characterization of optimal strategies. Under some symmetry assumptions on source statistics and the distortion metric, we show that an optimal communication strategy is a threshold based one and that the optimal estimate is always the most recently received sensor observation.