Statistical analysis of two non-linear least-squares estimators of sine waves parameters in the colored noise

The authors establish the large-sample accuracy properties of two nonlinear least-squares estimators (NLSEs) of sine waves parameters: the basic NLSE, which ignores the possible correlation of the noise; and the optimal NLSE, which, besides the sine-wave parameters, also estimates the noise correlation (appropriately parameterized). It is shown that these two NLSEs have the same accuracy in large samples. This result provides complete justification for preferring the computationally less-expensive basic NLSE over the optimal NLSE. Both estimators are shown to achieve the Cramer-Rao bound (CRB) as the sample size increases. A simple explicit expression for the CRB matrix is provided which should be useful in studying the performance of sine-wave parameter estimators designed to work in the colored noise case