Robust Frequency Estimation Under Additive Symmetric α-Stable Gaussian Mixture Noise

Here the estimating problem of a single sinusoidal signal in the additive symmetric alpha-stable Gaussian (AS alpha SG) noise is investigated. The AS alpha SG noise here is expressed as the additive of a Gaussian noise and a symmetric alpha-stable distributed variable. As the probability density function (PDF) of the AS alpha SG is complicated, traditional estimators cannot provide optimum estimates. Based on the Metropolis-Hastings (M-H) sampling scheme, a robust frequency estimator is proposed for AS alpha SG noise. Moreover, to accelerate the convergence rate of the developed algorithm, a new criterion of reconstructing the proposal covariance is derived, whose main idea is updating the proposal variance using several previous samples drawn in each iteration. The approximation PDF of the AS alpha SG noise, which is referred to the weighted sum of a Voigt function and a Gaussian PDF, is also employed to reduce the computational complexity. The computer simulations show that the performance of our method is better than the maximum likelihood and the lp-norm estimators.