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arXiv 2007.00428eess.SPcs.ITcs.LGmath.DGmath.IT
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电磁数字信息的基本几何结构:雷达电磁波的空间多普勒和极化波动数字测量的统计特性

The Basic Geometric Structures of Electromagnetic Digital Information: Statistical characterization of the digital measurement of spatio-Doppler and polarimetric fluctuations of the radar electromagnetic wave

Thales Land & Air Systems(泰雷斯陆空系统公司);Institut de Mathématiques de Bordeaux(波尔多数学研究所)

Frédéric Barbaresco, Yann Cabanes

摘要:

目的是描述新的几何方法来定义电磁波状态的时空和偏振测量的统计,使用Maurice Fr é chet,Jean-Louis Koszul和Jean-Marie Souriau的作品,特别是该数字测量的“平均”状态的概念作为Fr{é} Chet重心在度量空间中,以及从统计力学中推导出的模型,用于定义和计算熵的最大密度(高斯概念的扩展),以描述电磁波的波动。本文将说明这些新的工具与雷达应用的电磁波的多普勒,时空和极化测量的例子,通过引入距离的电磁数字信号的协方差矩阵的基础上,从信息几何的费舍尔度量。

英文摘要:

The aim is to describe new geometric approaches to define the statistics of spatio-temporal and polarimetric measurements of the states of an electromagnetic wave, using the works of Maurice Fr{é}chet, Jean-Louis Koszul and Jean-Marie Souriau, with in particular the notion of 'average' state of this digital measurement as a Fr{é}chet barycentre in a metric space and a model derived from statistical mechanics to define and calculate a maximum density of entropy (extension of the notion of Gaussian) to describe the fluctuations of the electromagnetic wave. The article will illustrate these new tools with examples of radar application for Doppler, spatio-temporal and polarimetric measurement of the electromagnetic wave by introducing a distance on the covariance matrices of the electromagnetic digital signal, based on Fisher's metric from Information Geometry.

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