General method for sinusoidal frequencies estimation using ARMA algorithms with nonlinear prediction error transformation

A new general approach to estimating the frequencies of sinusoidal signals corrupted by an additive nonGaussian noise is presented. The mixture of sinusoids and noise is modeled by an autoregressive moving average (ARMA) model with nonGaussian model noise. A class of ARMA recursive algorithms with nonlinear prediction error transformation is proposed for frequencies estimation. For a given probability density function of the model noise, known except for the scale parameter, the presented method enables the derivation of the algorithms ensuring the fastest convergence of the covariance error matrix to the asymptotic one. The robust version of the algorithms is also discussed. The performance of the ARMA nonlinear algorithms is illustrated by simulation results