Optimal Remote Estimation Over Use-Dependent Packet-Drop Channels - Extended Version

TL;DR

This paper develops optimal transmission and estimation strategies for remote systems over channels with state-dependent packet drops, using threshold policies for Gaussian processes and applying to energy harvesting and human-in-the-loop systems.

Contribution

It introduces structural results for optimal policies in channels with finite state machine governed drop probabilities, including threshold-based policies for Gaussian processes.

Findings

Optimal threshold-based transmission policies for Gaussian processes.

Characterization of symmetric policies for linear time-invariant systems.

Application to energy harvesting and human visual search tasks.

Abstract

Consider a discrete-time remote estimation system formed by an encoder, a transmission policy, a channel, and a remote estimator. The encoder assesses a random process that the remote estimator seeks to estimate based on information sent to it by the encoder via the channel. The channel is affected by Bernoulli drops. The instantaneous probability of a drop is governed by a finite state machine (FSM). The state of the FSM is denoted as the channel state. At each time step, the encoder decides whether to attempt a transmission through the packet-drop link. The sequence of encoder decisions is the input to the FSM. This paper seeks to design an encoder, transmission policy and remote estimator that minimize a finite-horizon mean squared error cost. We present two structural results. The first result in which we assume that the process to be estimated is white and Gaussian, we show that there is an optimal transmission policy governed by a threshold on the estimation error. The second result characterizes optimal symmetric transmission policies for the case when the measured process is the state of a scalar linear time-invariant plant driven by white Gaussian noise. Use-dependent packet-drop channels can be used to quantify the effect of transmission on channel quality when the encoder is powered by energy harvesting. An application to a mixed initiative system in which a human operator performs visual search tasks is also presented.