Optimal Estimation in Spatially Distributed Systems: How Far to Share Measurements From?

• 成果类型: Article
• 署名作者: Arbelaiz, Juncal; Bamieh, Bassam; Hosoi, Anette E.; Jadbabaie, Ali
• 署名单位: Massachusetts Institute of Technology (MIT); Princeton University; University of California System; University of California Santa Barbara; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3504257
• 发表日期: 2025
• 页码: 3226-3239
• 关键词: Kalman filters; Spatiotemporal phenomena; Noise measurement; Filtering; Fourier transforms; kernel; Particle measurements; Location awareness; convolution; Atmospheric measurements; Distributed parameter systems; estimation; Kalman filtering; uncertain systems

摘要

In this article, we consider the centralized optimal estimation problem in spatially distributed systems. We use the setting of spatially invariant systems as an idealization for which concrete and detailed results are given. Such estimators are known to have a degree of spatial localization in the sense that the estimator gains decay in space, with the spatial decay rates serving as a proxy for how far measurements need to be shared in an optimal distributed estimator. In particular, we examine the dependence of spatial decay rates on problem specifications such as system dynamics, measurement, and process noise variances, as well as their spatial autocorrelations. We propose nondimensional parameters that characterize the decay rates as a function of problem specifications. In particular, we find an interesting matching condition between the characteristic lengthscale of the dynamics and the measurement noise correlation lengthscale for which the optimal centralized estimator is completely decentralized. A new graphical technique-termed the branch point locus-is introduced to quantify spatial decay rates in terms of analyticity regions in the complex spatial frequency plane. Our results are illustrated through two case studies of systems with dynamics modeled by diffusion and the Swift-Hohenberg equation, respectively.