SOME ALGORITHMS FOR EIGENSUBSPACE ESTIMATION

An important tool in signal processing is the use of eigenvalue and si ngular value decompositions for extracting information from time-serie s/sensor array data. These tools are used in the so-called subspace me thods that underlie solutions to the harmonic retrieval problem in tim e series and the directions-of-arrival (DOA) estimation problem in arr ay processing. The subspace methods require the knowledge of eigenvect ors of the underlying covariance matrix to estimate the parameters of interest. Eigenstructure estimation in signal processing has two impor tant classes: (i) estimating the eigenstructure of the given covarianc e matrix and (ii) updating the eigenstructure estimates given the curr ent estimate and new data. In this paper, we survey some algorithms fo r both these classes useful for harmonic retrieval and DOA estimation problems. We begin by surveying key results in the literature and then describe, in some detail, energy function minimization approaches tha t underlie a class of feedback neural networks. Our approaches estimat e some or all of the eigenvectors corresponding to the repeated minimu m eigenvalue and also multiple orthogonal eigenvectors corresponding t o the ordered eigenvalues of the covariance matrix. Our presentation i ncludes some supporting analysis and simulation results. We may point out here that eigensubspace estimation is a vast area and all aspects of this cannot be fully covered in a single paper. (C) 1995 Academic P ress, Inc.