Timely Multi-Process Estimation with Erasures
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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 ϵ. Aided by optimal structural results, we show that the optimal sampling policy, under some conditions, is a threshold policy. We characterize the optimal threshold and the corresponding optimal long-term average sum MSE as a function of K, f_max, ϵ, and the statistical properties of the observed processes.
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