Optimum Parameter Estimation Under Additive Cauchy-Gaussian Mixture Noise

In this paper, a mixture process is proposed for modelling the summation of Cauchy and Gaussian random variables. The probability density function (PDF) of the mixture can be derived as the Voigt profile. To further study the noise, the estimation of the constant model is taken as an illustration. Here the scenarios of both known and unknown density parameters are considered. The maximum likelihood estimator (MLE) with Voigt function is first employed to devised the optimal estimator. Then an M-estimator with pseudo-Voigt function is developed to improve the computational complexity of MLE. Simulation results indicate the superior of both proposals, which can attain the Cramer-Rao lower bound.