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Power Allocation of Sensor Transmission for Remote Estimation Over an Unknown Gilbert-Elliott Channel

In this paper, we consider the problem of scheduling the power of a sensor when transmitting over an unknown Gilbert-Elliott (GE) channel for remote state estimation. The sensor supports two power modes, namely low power and high power, which are to be selected for transmission over the channel in order to minimize a cost on the error covariance, while satisfying the energy constraints. The remote estimator provides error-free acknowledgement/negative-acknowledgement (ACK/NACK) messages to the sensor only when low power is utilized. We first consider the Partially Observable Markov Decision Process (POMDP) problem for the case of known GE channels and derive conditions for optimality of a stationary schedule. Next, a Bayesian inference approach is used through which the channels statistics are approximately learned when they are initially unknown. An algorithm is proposed in which the sensor adjusts its scheduling policy based on the energy constraint.