A criterion for identifying dominant singular values in the SVD based method of harmonic retrieval

Abstract

The problem of determining the dominant singular values in the singular value decomposition (SVD) based state-space approach to harmonic retrieval is considered. A common difficulty encountered in harmonic retrieval methods is that the covariance matrix is full rank due to noise and estimation errors, instead of the ideal low rank. Then, from the singular value decomposition of this noisy and estimated covariance matrix, a low rank approximation is normally sought by retaining the dominant singular values and zeroing out the rest. A criterion is proposed, based on the distribution of the norms of the perturbation matrix associated with the estimated covariance matrix, to identify these dominant singular values.<>