Singular value decomposition and improved frequency estimation using linear prediction

Abstract

Linear-prediction-based (LP) methods for fitting multiple-sinusoid signal models to observed data, such as the forward-backward (FBLP) method of Nuttall [5] and Ulrych and Clayton [6], are very ill-conditioned. The locations of estimated spectral peaks can be greatly affected by a small amount of noise because of the appearance of outliers. LP estimation of frequencies can be greatly improved at low SNR by singular value decomposition (SVD) of the LP data matrix. The improved performance at low SNR is also better than that obtained by using the eigenvector corresponding to the minimum eigenvalue of the correlation matrix, as is done in Pisarenko's method and its variants.