Quaternion polynomial matrix diagonalization for the separation of polarized convolutive mixture

Abstract

A generalization of the sequential best rotation algorithm (SBR2) to the quaternion algebra is proposed for convolutive mixture of polarized signals recorded by vector sensors. The new version consists in a quaternion formulation of eigenvalue decomposition of para-Hermitian polynomial matrices which represent convolutive mixtures of polarized waves. The algorithm consists in a sequence of elementary para-unitary quaternion transformations, similar to the Jacobi method for matrix diagonalization. The results of the application of the proposed algorithm on synthetic examples are shown to demonstrate the advantages of the quaternion approach with respect to both conventional scalar and long-vector approaches.