Optimal Sampling and Scheduling for Remote Fusion Estimation of Correlated Wiener Processes

2025-10-25

AI Summary

In distributed sensor networks, asynchronous and correlated observations degrade the accuracy of remote state estimation. Method: This paper proposes a joint sampling–scheduling–estimation framework for optimal remote fusion estimation of correlated Wiener processes. Leveraging the separation principle, we establish, for the first time, a structural equivalence between Age of Information (AoI) and minimum mean-square error (MMSE), proving AoI serves as a sufficient proxy for estimation performance. Based on this insight, we design an AoI-weighted fusion estimator and a Maximum-Age-First (MAF) scheduling policy, and derive the optimal sampling interval under an infinite-horizon average-cost criterion. Contribution/Results: Theoretical analysis and experiments demonstrate that the proposed method achieves simultaneous AoI optimality and MMSE optimality under pull-based communication, significantly improving fusion accuracy for asynchronous, correlated data.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

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.

Problem

• Fusing asynchronous correlated observations for remote estimation
• Jointly optimizing sampling scheduling and estimation policies
• Establishing equivalence between AoI and MSE optimization

Innovation

• Weighted-sum fusion estimator conditioned on AoI
• Maximum Age First scheduler for stale sources
• AoI-optimal sampler equivalent to MSE-optimal design