This paper revisits the asymptotic normality of the nonlinear least-squares estimator for sinusoidal parameter estimation and fills two voids in the literature. First, it provides a complete proof of the asymptotic normality of the nonlinear least-squares estimator for sinusoidal signals in additive non-Gaussian white noise. Second, it uncovers the necessity of re-interpreting and re-defining the signal-to-noise ratio when applying the asymptotic theory to practical situations where the sample sizes are finite and the noise distribution has heavy tails. Simulation results are given to demonstrate the findings.
By: Ta-Hsin Li; Kai-Sheng Song
Published in: RC24340REV in 2007
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