Asymptotic properties of the high-order Yule-Walker estimates of sinusoidal frequencies

The asymptotic properties of the high-order Yule-Walker (HOYW) estimator of sinusoidal frequencies are analyzed. An explicit formula for the covariance matrix of the HOYW frequency estimation error is derived. The effects on estimation accuracy of the number of YW equations, the model order, and a certain weighting matrix are investigated analytically. The optimally weighted HOYW estimator is described. The analysis presented together with the already existing empirical evidence provides enough motivation for the use of an overdetermined and high-order Yule-Walker estimator.>