Low complexity adaptive algorithm for generalized eigenvalue decomposition

It is well known that the generalized eigenvalue decomposition (GEVD) can be used in a number of signal processing applications, for example, subspace tracking and estimation in the presence of colored noise. In this paper, we propose a new approach to extract the principle generalized eigenvectors (PGEs) for GEVD. Resorting to a weighted non-quadratic criterion (WNQC), the designed algorithm has a steep land-scape, such that the desired point can be obtained from fast gradient-based method. Applying the projection approximation and recursive least squares (RLS) technique, we develop an adaptive algorithm with low computational complexity to parallelly estimate the PGEs. Finally, numerical results are provided to demonstrate the effectiveness of the proposed studies.