Density parameter estimation for additive Cauchy-Gaussian mixture

In this paper, a mixture noise model, which is a sum of symmetric Cauchy and zero-mean Gaussian random variables in time domain, is studied. The Cauchy and Gaussian distributions are characterized by the unknown median γ and variance σ², respectively. The probability density function (PDF) and characteristic function (CF) of the mixture are also investigated which are calculated by the convolution of the two PDFs, and product of the two CFs, respectively. Due to the complication of the resultant PDF, typical approaches such as maximum likelihood estimator may not be able to estimate γ and σ² reliably. Based on the resultant CF, we propose to employ the fractional lower-order moment estimator for their computation. Simulation results show the mean square error performance of the proposed method and a comparison with the Cramér-Rao lower bound is also provided.