Study of the statistical performance of the Pisarenko harmonic decomposition method

A self-contained statistical analysis of the Pisarenko method for estimating sinusoidal frequencies from signal measurements corrupted by white noise is presented. An explicit formula is provided for the asymptotic covariance matrix of the joint estimation errors of the minimum eigenvalue and the minimum eigenfilter coefficients of the data covariance matrix. Our theoretical results extend and reinforce previous results obtained by Sakai [1]. A numerical study of the performance of the Pisarenko method, and a comparison with the performance achieved by the Yule-Walker method are also reported.