Statistical analysis of Pisarenko's method for sinusoidal frequency estimation

Statistical analysis is performed for Pisarenko's method of sinusoidal frequency estimation by using the periodogram technique. Under the assumption that the data consist of several sinusoids plus white noise, we give an asymptotic expression of the error variance of the sinusoidal frequency estimator. Also, a modified method is proposed. This is computationally efficient but the statistical property is not improved. We also present simulation results and compare them to the theoretical ones. Lastly, we point out that the Pisarenko's method can be implemented as an (on-line) bias compensated least-squares algorithm, thus avoiding the eigenvalue and eigenvector calculations.