On the Gersgorin Disc Theorem applied to Radar Polarimetry

Conference: EUSAR 2006 - 6th European Conference on Synthetic Aperture Radar
05/16/2006 - 05/18/2006 at Dresden, Germany

Proceedings: EUSAR 2006

Pages: 4Language: englishTyp: PDF

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Danklmayer, A. (Microwaves and Radar Institute, DLR – German Aerospace Centre, Oberpfaffenhofen, Germany)
Boerner, W.-M. (University of Illinois at Chicago, Department of Electrical and Computer Engineering, Communications, Sensing & Imaging and Navigation Laboratory, Chicago IL/USA)
Chandra, M. (Chair for Microwave Engineering and Photonics, Chemnitz University of Technology, Germany)

This contribution is concerned with the mathematical formulation and theoretical background of the Gersgorin discs in the context of Radar Polarimetry. We consider strict radar backscattering, the monostatic case, characterised 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 diagonalization. A special region G(A), called the Gersgorin discs and the associated boundaries denoted by Gersgorin 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.