Joint diagonalization of correlation matrices by using gradient methods with application to blind signal separation

Joint diagonalization of several correlation matrices is a powerful tool for blind signal separation. This paper addresses the blind signal separation problem for the case where the source signals are non-stationary and / or non-white, and the sensors are possibly noisy. We present cost functions for jointly diagonalizing several correlation matrices. The corresponding gradients are derived and used in a gradient-based joint-diagonalization algorithms. Several variations are given, depending on desired properties of the separation matrix, e.g., unitary separation matrix. These constraints are either imposed by adding a penalty term to the cost function or by projecting the gradient onto the desired manifold. The performance of the proposed joint-diagonalization algorithm is verified by simulating a blind signal separation application.