Application of Manifold Separation to Polarimetric Capon Beamformer and Source Tracking

Two adaptive Capon methods that jointly estimate the azimuth-angle and polarization of the sources in a closed-form are proposed. It is shown that the azimuth-angles of the sources may be estimated from the roots of a complex-valued polynomial or by rooting a real-valued polynomial, instead. The latter method is particularly useful in tracking arbitrarily polarized sources in a sequential snapshot-by-snapshot manner using root-tracking techniques. The proposed polynomial rooting based methods are applicable to polarization sensitive arrays regardless of the array geometry including conformal arrays, and take into account array nonidealities. A large-sample analysis of the polarimetric Capon method is also provided showing that it converges, up to a multiplicative factor that depends on the interference-plus-noise power, to the polarimetric MUSIC method in the high SINR regime. Such a result gives a new insight into the well-known Capon and MUSIC methods. This paper also shows that employing manifold separation in robust Capon beamforming as well as in transmit beamforming schemes leads to improved performance in terms of received SINR when array calibration measurements are used. Extensive numerical results employing real-world polarimetric arrays are given. Results show that employing manifold separation leads to improved performance in many array processing tasks.