Optimal transmit power allocation strategies are proposed for an energy harvesting estimation system, where energy can be harvested from the environment and buffered in a battery for future use. With the aim of minimizing the mean squared error at the receiver, two types of side information (SI) available to the transmitter are considered: causal SI (energy harvested in the past) and non-causal SI (energy harvested in the past, present and future). For the case where non-causal SI is available and battery storage is unlimited, it is shown that the optimal power allocation can be attained by a simple water-filling-like procedure, where the water level follows a non-decreasing staircase function. Dynamic programming is used to optimize the allocation policy when causal SI is available. The issue of unknown transmit power at the receiver is also addressed.
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