Iterative inverse filtering approach to the estimation of frequencies of noisy sinusoids

A signal modeling approach is proposed to reduce the problem of estimating frequencies of noisy sinusoids to the parameter estimation problem. Both white and colored noise are considered. The maximum likelihood approach leads to an algorithm computationally inefficient for low values of signal-to-noise ratio. Based on the equation-error formulation, an iterative inverse filtering algorithm is derived in the case of colored noise, and a generalized least-squares algorithm in the case of white noise. It is shown, on the basis of numerous experimental results, that the iterative inverse filtering algorithm provides highly accurate estimates of unknown frequencies for low values of signal-to-noise ratio, even in the case of a small number of sampling points.