发表机构
Linköping University; University of Maryland（林雪平大学; 马里兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于创新的连续随机过程采样，仅当出现足够新信息时采样，并刻画维纳过程的创新特性，证明创新稀疏化，且创新缺失携带信息，可显著降低远程估计的均方误差。
AI 中文摘要
本文提出了连续随机过程的基于创新的采样方法，其中仅当过程相对于所有先前样本展现出“足够新”的信息时才生成一个样本。由此产生的创新过程具有格结构以及三维状态表示。对于维纳过程，我们刻画了创新的方向、时机和频率。我们证明方向反转变得越来越罕见，并为其数量建立了极限定理。创新也变得越来越稀疏：创新的期望数量仅随时间的平方根增长，因此采样率渐近地趋于零。然后，我们研究了从稀疏接收的创新中进行远程估计。值得注意的是，创新的缺失本身携带信息：最小均方误差（MMSE）估计随信息年龄（AoI）演化，并且相较于传统的忽略静默的零阶保持（ZOH）估计器，实现了显著的均方误差（MSE）降低。最后，我们开发了易于处理的仿射年龄和指数年龄近似以供实际使用。总体而言，信息不仅通过创新的内容来传达，还通过其方向和时机来传达。
英文摘要
This work introduces innovation-based sampling of continuous stochastic processes, in which a sample is generated only when the process reveals ``sufficiently new'' information relative to all previous samples. The resulting innovation process admits a lattice structure and a three-dimensional state representation. For a Wiener process, we characterize the direction, timing, and frequency of innovations. We show that direction reversals become increasingly rare and establish limit theorems for their number. Innovations also become progressively sparser: the expected number of innovations grows only as the square root of time, and hence the sampling rate vanishes asymptotically. We then study remote estimation from sparsely received innovations. Notably, the absence of an innovation carries information: the minimum mean-square error (MMSE) estimate evolves with the age of information (AoI) and achieves a substantial MSE reduction over the conventional silence-ignorant zero-order hold (ZOH) estimator. Finally, we develop tractable affine-age and exponential-age approximations for practical use. Overall, information is conveyed not only by the content of innovations, but also by their direction and timing.
