Robust radio interferometric calibration using the t-distribution

Interferometric observations used in radio astronomy are affected by errors due to the propagation medium such as the ionosphere as well as by the instrument such as the beam shape. Hence, calibration of such observations is essential in order to produce high quality data suitable for scientific endeavors. Traditional calibration implicitly relies on an underlying Gaussian noise model. However, outliers in the data due to interference or model errors would have adverse effects on processing based on a Gaussian noise model. In this paper, we propose to improve the robustness of calibration by using a noise model based on the Student´s t distribution. Unlike the Gaussian noise model based calibration, traditional nonlinear least squares minimization would not directly extend to a case when we have a Student´s t noise model. Therefore, we use Expectation Maximization when we have a Student´s t noise model and use the Levenberg-Marquardt algorithm in the maximization step. We give simulation results to show the robustness of the proposed calibration method as opposed to traditional Gaussian noise model based calibration. We also give timing comparisons to show that robust calibration could be used with only a small additional overhead in practice.