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We consider the problem of transmission scheduling for the remote estimationof a discrete-time autoregressive Markov process that is driven by whiteGaussian noise. A sensor observes this process, and then decides to eitherencode the current state of this process into a data packet and attempts totransmit it to the estimator over an unreliable wireless channel modeled as aGilbert-Elliott channel, or does not send any update. Each transmission attemptconsumes $\lambda$ units of transmission power, and the remote estimator isassumed to be linear. The channel state is revealed only via the feedback(ACK\slash NACK) of a transmission, and hence the channel state is not revealedif no transmission occurs. The goal of the scheduler is to minimize theexpected value of an infinite-horizon cumulative discounted cost, in which theinstantaneous cost is composed of the following two quantities: (i)~squaredestimation error, (ii) transmission power. We show that this problem canequivalently be posed as a partially observable Markov decision process(POMDP), in which the scheduler maintains a belief about the current state ofthe channel, and makes decisions on the basis of the current value of theestimation error, and the belief state.~We then show that the optimal policy isof threshold-type, i.e. for each value of the estimation error $e$, there is athreshold $b\ust(e)$ such that when the error is equal to $e$, then it isoptimal to transmit only when the current belief state is greater than$b\ust(e)$.

Optimal Scheduling Policies for Remote Estimation of Autoregressive Markov Processes over Time-Correlated Fading Channel