Polarimetric Covariance Matrix Analysis of Random Radar Targets

Abstract : Two equivalent approaches for the description of mean polarimetric backscattering features or random radar targets exist, the so-called Mueller matrix and the covariance matrix approach. The covariance matrix contains measurable radar observables and is directly related to the statistics of the elements of the scattering matrix which determines the instantaneous backscattering features of a target. In this paper, a covariance matrix analysis for reciprocal random targets is performed by unitary similarity transformations preserving important polarimetric invariances. The derivatives of covariance matrix elements with respect to the transmitter polarization reveal interesting functional relations between characteristic polarization states and covariance matrix elements. Analytical and numerical algorithms to determine optimal polarizations for cross- and copolar power are presented. The connection of the covariance matrix approach with the Mueller matrix formulation is shown in detail. Polarimetric covariance matrix analysis is illustrated by polarimetric radar measurements of terrain, rain and manmade clutter and documented with according graphical evaluation.