Timely Multi-Process Estimation with Erasures

TL;DR

This paper develops an optimal sampling and scheduling strategy for multiple Ornstein-Uhlenbeck processes over a constrained system with delays and erasures, minimizing long-term estimation error.

Contribution

It introduces a threshold-based sampling policy for multi-process estimation under delays and erasures, with explicit characterization of optimal thresholds and errors.

Findings

Optimal threshold policy derived for sampling schedules.

Explicit formulas for minimum long-term average sum MSE.

Analysis of effects of erasure probability and sampling constraints.

Abstract

We consider a multi-process remote estimation system observing $K$ independent Ornstein-Uhlenbeck processes. In this system, a shared sensor samples the $K$ processes in such a way that the long-term average sum mean square error (MSE) is minimized. The sensor operates under a total sampling frequency constraint $f_{\max}$ and samples the processes according to a Maximum-Age-First (MAF) schedule. The samples from all processes consume random processing delays, and then are transmitted over an erasure channel with probability $\epsilon$. Aided by optimal structural results, we show that the optimal sampling policy, under some conditions, is a \emph{threshold policy}. We characterize the optimal threshold and the corresponding optimal long-term average sum MSE as a function of $K$, $f_{\max}$, $\epsilon$, and the statistical properties of the observed processes.