Articolo in rivista, 2015, ENG, 10.1016/j.sigpro.2014.07.028

Optimum linear regression in additive Cauchy-Gaussian noise

Chen J. Y.; Kuruoglu E.E.; So H.C.

Department of Electronic Engineering, City University of Hong Kong, Hong Kong, Hong Kong; CNR-ISTI, Pisa, Italy; Department of Electronic Engineering, City University of Hong Kong, Hong Kong, Hong Kong

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 Cramér-Rao lower bound. © 2014 Elsevier B.V.

Signal processing (Print) 106 , pp. 312–318

Keywords

Cauchy distribution, Gaussian distribution, Impulsive noise

CNR authors

Kuruoglu Ercan Engin

CNR institutes

ISTI – Istituto di scienza e tecnologie dell'informazione "Alessandro Faedo"

ID: 295344

Year: 2015

Type: Articolo in rivista

Creation: 2015-01-28 13:39:24.000

Last update: 2021-04-08 00:35:01.000

External IDs

CNR OAI-PMH: oai:it.cnr:prodotti:295344

DOI: 10.1016/j.sigpro.2014.07.028

Scopus: 2-s2.0-84907342611

ISI Web of Science (WOS): 000344210200030