Radio interferometric calibration using the SAGE algorithm

The aim of the new generation of radio synthesis arrays such as LOw Frequency ARray (LOFAR) and Square Kilometre Array (SKA) is to achieve much higher sensitivity, resolution and frequency coverage than what is available now, especially at low frequencies. To accomplish this goal, the accuracy of the calibration techniques used is of considerable importance. Moreover, since these telescopes produce huge amounts of data, speed of convergence of calibration is a major bottleneck. The errors in calibration are due to system noise (sky and instrumental) as well as the estimation errors introduced by the calibration technique itself, which we call ‘solver noise’. We define solver noise as the ‘distance’ between the optimal solution (the true value of the unknowns, uncorrupted by the system noise) and the solution obtained by calibration. We present the Space Alternating Generalized Expectation Maximization (SAGE) calibration technique, which is a modification of the Expectation Maximization algorithm, and compare its performance with the traditional least squares calibration based on the level of solver noise introduced by each technique. For this purpose, we develop statistical methods that use the calibrated solutions to estimate the level of solver noise. The SAGE calibration algorithm yields very promising results in terms of both accuracy and speed of convergence. The comparison approaches that we adopt introduce a new framework for assessing the performance of different calibration schemes.