Self-stabilized gradient algorithms for blind source separation with orthogonality constraints

Developments in self-stabilized algorithms for gradient adaptation of orthonormal matrices have resulted in simple but powerful principal and minor subspace analysis methods. We extend these ideas to develop algorithms for instantaneous prewhitened blind separation of homogeneous signal mixtures. Our algorithms are proven to be self-stabilizing to the Stiefel manifold of orthonormal matrices, such that the rows of the adaptive demixing matrix do not need to be periodically reorthonormalized. Several algorithm forms are developed, including those that are equivariant with respect to the prewhitened mixing matrix. Simulations verify the excellent numerical properties of the proposed methods for the blind source separation task.