Robust Calibration of Radio Interferometers in Non-Gaussian Environment

Abstract

Abstract-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 noncalibrator 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-theart calibration techniques.

Calibration and 21-cm power spectrum estimation in the presence of antenna beam variations

“…Similar to earlier theoretical work we have not considered the non-Gaussian nature of the noise discussed by Kazemi & Yatawatta (2013); Ollier et al (2017) and (Ollier et al 2018). In this work we study the impact of the variance as the PS only sensitive to that.…”

Statistical performance of radio interferometric calibration

“…For instance, we can have additional terms than just s(θ) for regularization. Other noise models such as Student's t (Kazemi & Yatawatta 2013) or spherically invariant random processes (Ollier et al 2017) will yield other more exotic cost functions. The output y (∈ R D×1 ) is the residual using the calibration solution θ…”

Robust Calibration of Radio Interferometers in Multi-Frequency Scenario

“…, M } 2 which are considered unknown and deterministic in the algorithm, leading to a relaxed version of the ML [23]. Results are directly exposed in non-structured calibration algorithm (NSCA) and details can be found in [11,13]. Let us denote…”

“…To take them into account, a robust calibration technique was introduced in [9] where the noise model is specifically described as a Student's t with independent identically distributed entries. To improve calibration, we proposed, in a previous work [11], to adopt a compound-Gaussian modeling [12] which includes a broad range of different distributions and revealed to be more robust [13].…”