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In this paper, we consider sampling an Ornstein-Uhlenbeck (OU) processthrough a channel for remote estimation. The goal is to minimize the meansquare error (MSE) at the estimator under a sampling frequency constraint whenthe channel delay statistics is unknown. Sampling for MSE minimization isreformulated into an optimal stopping problem. By revisiting the thresholdstructure of the optimal stopping policy when the delay statistics is known, wepropose an online sampling algorithm to learn the optimum threshold usingstochastic approximation algorithm and the virtual queue method. We prove thatwith probability 1, the MSE of the proposed online algorithm converges to theminimum MSE that is achieved when the channel delay statistics is known. Thecumulative MSE gap of our proposed algorithm compared with the minimum MSE upto the $(k+1)$-th sample grows with rate at most $\mathcal{O}(\ln k)$. Ourproposed online algorithm can satisfy the sampling frequency constrainttheoretically. Finally, simulation results are provided to demonstrate theperformance of the proposed algorithm.

Sampling for Remote Estimation of an Ornstein-Uhlenbeck Process through Channel with Unknown Delay Statistics