Variational maximum likelihood method for parameter extraction of real sinusoids in non-Gaussian noise

A recursive parameter extraction method is presented for the multiple real sinusoidal signals (MRSS) in presence of non-Gaussian noise. It is based on a variational approximation to the maximum likelihood function of hidden mixture Gaussian hyper-parameters. The variational maximum likelihood (VML), based on the trust region algorithm, is then maximized with respect to the parameters of the model as well as to those involved in the approximation. With suitable assumptions, the proposed method reducing to the least mean squares (LMS) method is deduced. The higher performance and the faster convergence of the approach compared to classical LMS methods through numerical experiments are confirmed.