Statistical analysis of MUSIC and ESPRIT estimates of sinusoidal frequencies

The large-sample second-order properties of multiple signal classification (MUSIC) and subspace rotation methods such as ESPRIT for sinusoidal frequency estimation are analyzed. Both MUSIC and ESPRIT are based on the eigendecomposition of a sample data covariance matrix. Explicit expressions for the covariance elements of the estimation errors associated with either method are derived. These expressions of covariances are used to analyze and compare the statistical performance of the MUSIC and ESPRIT methods. It is shown that ESPRIT is usually slightly more accurate than MUSIC. Since MUSIC is computationally more demanding than ESPRIT, it appears that the ESPRIT method for frequency estimation should be preferred to MUSIC in most cases