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

arXiv: https://arxiv.org/abs/2303.16285 · HTML: https://mlsanity.com/paper/2303.16285/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2023.

## Built on by (most cited first, 1 of 1)

- [Policy Zooming: Adaptive Discretization-based Infinite-Horizon Average-Reward Reinforcement Learning](https://mlsanity.com/paper/2405.18793/) (2024)

## Abstract (arXiv)

We consider the problem of transmission scheduling for the remote estimation of a discrete-time autoregressive Markov process that is driven by white Gaussian noise. A sensor observes this process, and then decides to either encode the current state of this process into a data packet and attempts to transmit it to the estimator over an unreliable wireless channel modeled as a Gilbert-Elliott channel, or does not send any update. Each transmission attempt consumes λ units of transmission power, and the remote estimator is assumed to be linear. The channel state is revealed only via the feedback (ACKslash NACK) of a transmission, and hence the channel state is not revealed if no transmission occurs. The goal of the scheduler is to minimize the expected value of an infinite-horizon cumulative discounted cost, in which the instantaneous cost is composed of the following two quantities: (i)~squared estimation error, (ii) transmission power. We show that this problem can equivalently be posed as a partially observable Markov decision process (POMDP), in which the scheduler maintains a belief about the current state of the channel, and makes decisions on the basis of the current value of the estimation error, and the belief state.~We then show that the optimal policy is of threshold-type, i.e. for each value of the estimation error e, there is a threshold bust(e) such that when the error is equal to e, then it is optimal to transmit only when the current belief state is greater than bust(e).