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arXiv · 2209.11213

Timely Multi-Process Estimation with Erasures

Karim Banawan·Ahmed Arafa·Karim G. Seddik
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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.

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Karim Banawan, Ahmed Arafa, Karim G. Seddik. 2022-09-22. Timely Multi-Process Estimation with Erasures. https://arxiv.org/abs/2209.11213

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