Coding & Statistical Characterization of Radar Signal Fluctuation for Lie Group Machine Learning

Abstract

This paper describes new geometrical approaches to define the statistics of spatio-temporal measurements of the states of an electromagnetic wave, by using the notion of "average" state of this digital measurement as a Fréchet barycenter in a metric space to define and calculate a maximum entropy density (extension of the notion of Gaussian) to describe the fluctuations of the electromagnetic wave. The article will illustrate these new tools with examples of application in radar for the Doppler and spatio-temporal measurement of the electromagnetic wave by introducing a distance on the covariance matrices of the electromagnetic digital signal, based on the Koszul-Souriau-Fisher metric from Koszul Information Geometry and by applying Mean-Shift on this metric space or Lie Group Mean Shift considering data as elements of an homogeneous Manifold that could be represented by a Lie group .