A generalized least squares method for frequency estimation

The application of the generalized-least-squares (GLS) method to the estimation of the frequencies of sinusoids in additive colored noise is discussed. An iterative algorithm is proposed, starting from the assumption that the parameter vector in the model of the sinusoids is symmetric. The algorithm utilizes an adaptive strategy for contracting the poles of the estimated signal model. Expressions for the probability limit and the asymptotic variance of the estimates are derived for the single sinusoid case. Possible convergence points and the asymptotic behavior of the algorithm in the case of low SNRs (signal-to-noise ratios) are analyzed. Extensive simulation results show that the algorithm represents a simple and reliable tool for practical applications.