Robust nonlinear power iteration algorithm for adaptive blind separation of independent signals

In this paper, we elaborate an extension of classical power iteration method to nonlinear power iteration for blind separation of multiple independent sources from observed array output signals. The present algorithm, referred to as NPI, considers the estimating of the separating matrix as a nonlinear power iteration problem. By naturally choosing the positive definite normalizer for nonlinear power term, the resulting algorithm not only yields robust convergence behavior but also guarantees the orthonormality of the separating matrix at each iteration. To circumvent the difficulty of solving the inverse square root for the normalizer, an efficient adaptive singular value decomposition (SVD) technique is also adopted to obtain a fast implementation of NPI. The estimation accuracy and convergence speed of the present algorithm are illustrated through simulation results and compared with the existing adaptive algorithms.