Ornstein-Uhlenbeck过程的抽样和远距离估计：信息时代及以后
Sampling and Remote Estimation for the Ornstein-Uhlenbeck Process through Queues: Age of Information and Beyond
摘要：
信息时代作为评价信息新鲜度的一个指标，受到了广泛的关注。最近，在维纳过程的采样问题中发现了信息年龄和远程估计误差之间的有趣联系：如果采样器不知道被采样的信号，则最优采样策略是最小化信息年龄;然而，通过利用信号值的因果知识，可以实现较小的估计误差。在本文中，我们扩展了以前的研究，通过调查的问题，采样平稳高斯-马尔可夫过程，即Ornstein-Uhlenbeck过程。最优采样问题被表述为一个具有不可数状态空间的约束连续时间马尔可夫决策过程（MDP）。我们给出了这个MDP的精确解：最优抽样策略是一个关于瞬时估计误差的阈值策略，并且找到了阈值，而且，如果抽样者不知道随机过程，则最优抽样问题归结为一个最小化非线性信息度量年龄的MDP.年龄最优抽样策略是一个关于期望估计误差的阈值策略，并找到了阈值，这些结果对（i）服务器的一般服务时间分布和（ii）有和没有采样率约束的抽样问题都成立.数值结果比较不同的抽样政策。
英文摘要：
The age of information, as a metric for evaluating information freshness, has received a lot of attention. Recently, an interesting connection between the age of information and remote estimation error was found in a sampling problem of Wiener processes: If the sampler has no knowledge of the signal being sampled, the optimal sampling strategy is to minimize the age of information; however, by exploiting causal knowledge of the signal values, it is possible to achieve a smaller estimation error. In this paper, we extend a previous study by investigating a problem of sampling a stationary Gauss-Markov process, namely the Ornstein-Uhlenbeck (OU) process. The optimal sampling problem is formulated as a constrained continuous-time Markov decision process (MDP) with an uncountable state space. We provide an exact solution to this MDP: The optimal sampling policy is a threshold policy on instantaneous estimation error and the threshold is found. Further, if the sampler has no knowledge of the OU process, the optimal sampling problem reduces to an MDP for minimizing a nonlinear age of information metric. The age-optimal sampling policy is a threshold policy on expected estimation error and the threshold is found. These results hold for (i) general service time distributions of the queueing server and (ii) sampling problems both with and without a sampling rate constraint. Numerical results are provided to compare different sampling policies.
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