Power Allocation for Remote Estimation Over Known and Unknown Gilbert-Elliott Channels

In this paper, we consider the problem of power scheduling of a sensor that transmits over a (possibly) unknown Gilbert-Elliott (GE) channel for remote state estimation. The sensor supports two power modes, namely low power, and high power. The scheduling policy determines when to use low power or high power for data transmission over a fading channel with temporal correlation while satisfying the energy constraints. Although error-free acknowledgement/negative-acknowledgement (ACK/NACK) signals are provided by the remote estimator, they only provide meaningful information about the underlying channel state when low power is utilized. This leads to a partially observable Markov decision process (POMDP) problem and we derive conditions that preserve the optimality of a stationary schedule derived for its fully observable counterpart. However, implementing this schedule requires knowledge of the parameters of the GE model which are not available in practice. To address this, we adopt a Bayesian framework to learn these parameters online and propose an algorithm that is shown to satisfy the energy constraint while achieving near-optimal performance via simulation.