Robust Calibration of Radio Interferometers in Non-Gaussian Environment

The development of new phased-array systems in radio astronomy, as the low-frequency array (LOFAR) and the square kilometre array (SKA), formed of a large number of small and flexible elementary antennas has led to significant challenges. Among them, model calibration is a crucial step in order to provide accurate and, thus, meaningful images and requires the estimation of all the perturbation effects introduced along the signal propagation path for a specific source direction and antenna position. Usually, it is common to perform model calibration using the a priori knowledge regarding a small number of known strong calibrator sources but under the assumption of Gaussianity of the noise. Nevertheless, observations in the context of radio astronomy are known to be affected by the presence of outliers, which are due to several causes, e.g., weak non-calibrator sources or man-made radio frequency interferences. Consequently, the classical Gaussian noise assumption is violated leading to severe degradation in performances. In order to take into account the outlier effects, we assume that the noise follows a spherically invariant random distribution. Based on this modeling, a robust calibration algorithm is presented in this paper. More precisely, this new scheme is based on the design of an iterative relaxed concentrated maximum likelihood estimation procedure that allows us to obtain closed-form expressions for the unknown parameters with a reasonable computational cost. Numerical simulations reveal that the proposed algorithm outperforms the state-of-the-art calibration techniques.