A fast maximum likelihood algorithm for frequency estimation of a sinusoid based on Newton´s method

A fast algorithm to estimate the frequency of a sinusoid is presented here. It is based on Newton´s method for finding the root of an equation, and it is shown that under easily met conditions, the root mean-square error (RMSE) of the estimator is practically equal to the Cramer-Rao bound after only two iterations of Newton´s method for all signal-to-noise ratios (SNR´s) above threshold. The estimator´s probability density function is computed analytically, and the RMSE is calculated for one and two iterations of Newton´s method. Its computational load is shown to be significantly less than other conventional algorithms.