On Asymptotic Normality of Nonlinear Least Squares for Sinusoidal Parameter Estimation

  • Authors:
  • Ta-Hsin Li;Kai-Sheng Song

  • Affiliations:
  • IBM T. J. Watson Res. Center, Yorktown Heights, NY;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2008

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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.