On Asymptotic Normality of Nonlinear Least Squares for Sinusoidal Parameter Estimation

Abstract

This correspondence revisits the asymptotic normality question of the nonlinear least-squares estimator for sinusoidal parameter estimation and fills a gap in the literature by providing a complete proof of the asymptotic normality under the assumption of additive non-Gaussian white noise. The result shows that the nonlinear least-squares estimator is able to asymptotically attain the Cramer-Rao lower bound derived under the Gaussian white noise assumption in situations where the actual noise distribution is non-Gaussian.