On the Gersgorin Disc Theorem applied to Radar Polarimetry

Abstract

This contribution is concerned with the mathematical formulation and theoretical background of the discs in the context of Radar Polarimetry. We consider strict radar backscattering, the monostatic case, character-ised by the random Sinclair matrix S(t) in a common linear basis. Using the target feature vectors leads to the Hermitian positive semidefinite Covariance matrices, where the eigenvalues are obtained by unitarily diagonali-zation. A special region G(A), called the discs and the associated boundaries denoted by circles is considered to be of possible value in revealing information about the eigenvalues of a given Covariance matrices. We arrive at particular classes of easily computed regions in the plane that are guaranteed to include the eigenvalues of a given covariance matrix.