Estimating Parameters of One-dimensional Gaussian Mixture Models Using Fourier Approach

A novel algorithm is proposed to estimate the parameters, including the number of components, variance, means, and weights, in one-dimensional Gaussian mixture models by leveraging the Hankel structure in the Fourier data obtained from i.i.d. samples. The algorithm does not require prior knowledge of the number of components or good initial guesses, and it demonstrates superior performance in estimation accuracy and computational cost compared to classic methods like the method of moments and maximum likelihood.