Performance analysis of some cumulant-based estimators: harmonics in noise

We consider the problem of estimating the parameters of harmonics (with non-random parameters) observed in zero mean (colored/white, Gaussian/non-Gaussian) stationary mixing noise. A new fourth-order moment based non-parametric estimator is introduced, and it is shown that this estimator is superior to the conventional second-order estimator at all SNR´s. The variance of the frequency estimator is shown to converge as 1/T³; for the harmonic with frequency ω ₀, and amplitude A₀, the peak amplitude of the normalized fourth-order spectrum is shown to be α(ω₀ )(|A₀|²/2σ_υ² +1)² where α(ω₀) is the local SNR, and σ_υ² is the noise variance