Abstract: Equivariant adaptive blind source separation algorithms require a serial update rule for the demixing matrix. From the point of view of relative gradient proposed by Cardoso, we optimize a nonlinear principal component analysis criterion. Then a modified recursive least-squares (RLS) algorithm for serial updating of the demixing matrix is presented. The equivariant property is guaranteed due to the serial updating rule used at each iteration. To speed up the convergence, the singular value decomposition is employed together with the stiefel manifold projection of the demixing matrix. Computer simulation results demonstrate the effectiveness of the algorithm.

Key words: blind source separation (BSS), relative gradient, equivariant property, serial update, singular value decomposition (SVD)