Sampling of the Wiener Process for Remote Estimation Over a Channel With Random Delay
Sampling of the Wiener Process for Remote Estimation Over a Channel With Random Delay
复制标题
DOI：
10.1109/tit.2019.2937336
复制
发表时间：
2020-02-01
影响因子：
2.5
通讯作者：
Uysal, Elif
中科院分区：
文献类型：
--
作者：
Sun, Yin;Polyanskiy, Yury;Uysal, Elif
在本文中，我们考虑对维纳过程进行采样的问题，样本通过一个被建模为队列的信道转发给远程估计器。估计器根据因果接收的样本重建实时信号值的估计。我们研究在采样率约束下使均方估计误差最小化的最优在线采样策略。我们证明最优采样策略是一种阈值策略，并找到了最优阈值。该阈值由维纳过程在随机服务时间内的变化量以及最大允许采样率决定。此外，如果采样时间与所观测的维纳过程相互独立，那么上述使估计误差最小化的采样问题就等同于使信息年龄最小化的采样问题。这揭示了信息年龄与远程估计误差之间一种有趣的联系。我们的比较表明，最优采样策略所实现的估计误差可能比信息年龄最优采样、零等待采样和周期性采样的估计误差小得多。
In this paper, we consider a problem of sampling a Wiener process, with samples forwarded to a remote estimator over a channel that is modeled as a queue. The estimator reconstructs an estimate of the real-time signal value from causally received samples. We study the optimal online sampling strategy that minimizes the mean square estimation error subject to a sampling rate constraint. We prove that the optimal sampling strategy is a threshold policy, and find the optimal threshold. This threshold is determined by how much the Wiener process varies during the random service time and the maximum allowed sampling rate. Further, if the sampling times are independent of the observed Wiener process, the above sampling problem for minimizing the estimation error is equivalent to a sampling problem for minimizing the age of information. This reveals an interesting connection between the age of information and remote estimation error. Our comparisons show that the estimation error achieved by the optimal sampling policy can be much smaller than those of age-optimal sampling, zero-wait sampling, and periodic sampling.