On the accuracy of high-order Yule-Walker methods for cisoids

The asymptotic properties of the high-order Yule-Walker (HOYW) estimators of the frequencies of complex sine waves are investigated. An explicit formula is derived for the covariance matrix of the corresponding estimation errors. An analytical study of the HOYW error covariance matrix shows that its elements are inversely proportional to the squared signal-to-noise ratio, enjoy a certain invariance to frequency shifts, and decrease significantly as the number of YW equations and the model order increases. These properties are also shared by the MUSIC and ESPRIT methods. A numerical study of the performance of these three methods shows that the HOYW method usually gives the best tradeoff between statistical accuracy and computational complexity