Optimum linear regression in additive Cauchy-Gaussian noise

We study the estimation problem of linear regression in the presence of a new impulsive noise model, which is a sum of Cauchy and Gaussian random variables in time domain. The probability density function (PDF) of this mixture noise, referred to as the Voigt profile, is derived from the convolution of the Cauchy and Gaussian PDFs. To determine the linear regression parameters, the maximum likelihood estimator (MLE) is developed first. Since the Voigt profile suffers from a complicated analytical form, an M-estimator with the pseudo-Voigt function is also derived. In our algorithm development, both scenarios of known and unknown density parameters are considered. For the latter case, we estimate the density parameters by utilizing the empirical characteristic function prior to applying the MLE. Simulation results show that the performance of both proposed methods can attain the Cramer-Rao lower bound. HighlightsNew additive mixture noise is studied and the corresponding noise PDF is derived.MLE is employed to estimate the parameters of a linear regression model under noise.To reduce the computational complexity of MLE, an M-estimator is proposed.Both scenarios of known and unknown density parameters are considered.The estimation performance of the developed estimators attains the CRLB.

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