Optimal Transport Between Gaussian Stationary Processes

• 成果类型: Article
• 署名作者: Zorzi, Mattia
• 署名单位: University of Padua
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3046567
• 发表日期: 2021
• 页码: 4939-4944
• 关键词: Transportation; estimation; Density measurement; Weight measurement; Gaussian Processes; Covariance matrices; Symmetric matrices; Convex Optimization; generalized covariance extension problem; Optimal Transport; Spectral Analysis

摘要

We consider the optimal transport problem between multivariate Gaussian stationary stochastic processes. The transportation effort is the variance of the filtered discrepancy process. The main contribution of this article is to show that the corresponding solution leads to a weighted Hellinger distance between multivariate power spectral densities. Then, we propose a spectral estimation approach in the case of indirect measurements, which is based on this distance.