Accuracy of high-order Yule–Walker methods for frequency estimation of complex sine waves

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 the elements of this matrix are inversely proportional to the squared signal-to-noise ratio, enjoy a certain invariance to frequency shifts and decrease significantly with increasing the number of YW equations and the model order. These interesting properties are also shared by the MUSIC and ESPRIT methods and, therefore, a performance comparison of the HOYW method with MUSIC and ESPRIT is of interest. A numerical study of the performance of these three methods shows that the HOYW method usually gives the best trade-off between statistical accuracy and computational complexity.