  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 which allows to obtain closed-form expressions for the
unknown parameters with a reasonable computational cost. This is of importance
as the number of estimated parameters depends on the number of antenna
elements, which is large for the new generation of radio interferometers.
Numerical simulations reveal that the proposed algorithm outperforms the
state-of-the-art calibration techniques.
