APPROXIMATE MAXIMUM-LIKELIHOOD FREQUENCY ESTIMATION

The high-resolution frequency estimators most commonly used, such as M USIC, ESPRIT and Yule-Walker, determine estimates of the sinusoidal fr equencies from the sample covariances of noise-corrupted data. In this paper, a frequency estimation method termed Approximate Maximum Likel ihood (AML) is derived from the approximate likelihood function of sam ple covariances. The statistical performance of AML is studied, both a nalytically and numerically, and compared with the Cramer-Rao bound as well as the statistical performance corresponding to the aforemention ed methods of frequency estimation. AML is shown to provide the minimu m asymptotic error variance in the class of all estimators based on a given set of covariances. The implementation of the AML frequency esti mator is discussed in detail. The paper also introduces an AML-based p rocedure for estimating the number of sinusoidal signals in the measur ed data, which is shown to possess high detection performance.