Estimating the parameters of a random amplitude sinusoid from its sample covariances

In this paper, we consider the best asymptotic accuracy that can be achieved when estimating the parameters of a random-amplitude sinusoid from its sample covariances. An estimator, based upon matching in a weighted least-squares sense the sample correlation sequence to the theoretical sequence is presented. The asymptotic properties of the estimator are analyzed. A lower bound on the estimation of the parameters from sample covariances is derived. This bound is shown to be attainable by appropriately choosing the weighting matrix. Numerical simulations illustrate the performance of the proposed estimator and the validity of the theoretical analysis. Finally, a comparison with Yule-Walker methods is given