In distributed sensor networks, sensors often observe a dynamic process within overlapping regions. Due to random delays, these correlated observations arrive at the fusion center asynchronously, raising a central question: How can one fuse asynchronous yet correlated information for accurate remote fusion estimation? This paper addresses this challenge by studying the joint design of sampling, scheduling, and estimation policies for monitoring a correlated Wiener process. Though this problem is coupled, we establish a separation principle and identify the joint optimal policy: the optimal fusion estimator is a weighted-sum fusion estimator conditioned on Age of Information (AoI), the optimal scheduler is a Maximum Age First (MAF) scheduler that prioritizes the most stale source, and the optimal sampling can be designed given the optimal estimator and the MAF scheduler. To design the optimal sampling, we show that, under the infinite-horizon average-cost criterion, optimizing AoI is equivalent to optimizing MSE under pull-based communications, despite the presence of strong inter-sensor correlations. This structural equivalence allows us to identify the MSE-optimal sampler as one that is AoI-optimal. This result underscores an insight: information freshness can serve as a design surrogate for optimal estimation in correlated sensing environments.

翻译：在分布式传感器网络中，传感器常观测重叠区域内的动态过程。由于随机延迟，这些相关观测以异步方式到达融合中心，从而引出一个核心问题：如何融合异步但相关的信息以实现准确的远程融合估计？本文通过研究用于监测相关维纳过程的采样、调度与估计策略的联合设计来应对这一挑战。尽管该问题具有耦合性，我们建立了分离原理并确定了联合最优策略：最优融合估计器是基于信息年龄（AoI）的加权和融合估计器；最优调度器是优先处理最陈旧信源的最大年龄优先（MAF）调度器；在给定最优估计器与MAF调度器的前提下可设计最优采样策略。为设计最优采样，我们证明在无限时域平均代价准则下，尽管存在强烈的传感器间相关性，在基于拉取的通信方式中优化AoI等价于优化均方误差（MSE）。这一结构等价性使我们得以将MSE最优采样器识别为AoI最优采样器。该结果揭示了一个重要见解：在相关感知环境中，信息新鲜度可作为最优估计设计的替代指标。