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The age of information, as a metric for evaluating information freshness, hasreceived a lot of attention. Recently, an interesting connection between theage of information and remote estimation error was found in a sampling problemof Wiener processes: If the sampler has no knowledge of the signal beingsampled, the optimal sampling strategy is to minimize the age of information;however, by exploiting causal knowledge of the signal values, it is possible toachieve a smaller estimation error. In this paper, we extend a previous studyby investigating a problem of sampling a stationary Gauss-Markov process,namely the Ornstein-Uhlenbeck (OU) process. The optimal sampling problem isformulated as a constrained continuous-time Markov decision process (MDP) withan uncountable state space. We provide an exact solution to this MDP: Theoptimal sampling policy is a threshold policy on instantaneous estimation errorand the threshold is found. Further, if the sampler has no knowledge of the OUprocess, the optimal sampling problem reduces to an MDP for minimizing anonlinear age of information metric. The age-optimal sampling policy is athreshold policy on expected estimation error and the threshold is found. Theseresults hold for (i) general service time distributions of the queueing serverand (ii) sampling problems both with and without a sampling rate constraint.Numerical results are provided to compare different sampling policies.

Sampling and Remote Estimation for the Ornstein-Uhlenbeck Process through Queues: Age of Information and Beyond