Optimal high-order Yule-Walker estimation of sinusoidal frequencies

The asymptotic properties of sinusoidal frequency estimators based on the high-order Yule-Walker (HOYW) equations were analyzed recently. The results of that analysis are used to propose two classes of frequency estimators; one class uses singular value decomposition, and the other uses a sparse matrix solution. Both classes entail two estimation steps: the first step generates initial estimates which are used to obtain an optimal weighting matrix, and the second step generates an optimally weighted estimate. Each two-step method produces asymptotically minimum variance estimates over all estimators of their class. The implementation of the proposed estimators is described in detail, and numerical examples are presented to evaluate their performance