StEFCal — An Alternating Direction Implicit method for fast full polarization array calibration

Alternating Direction Implicit (ADI) methods provide a computationally efficient way to solve for antenna based gains in full polarization. In this paper, we analyze the convergence of such methods in simulations. We show that convergence of a basic implementation can be quite slow and we propose two forms of relaxation to improve convergence behavior. The algorithm can be shown to be statistically efficient in low-SNR scenarios, which makes this approach particularly suitable for calibration of large radio astronomical arrays like the Square Kilometre Array (SKA). This also led to the name Statistically Efficient and Fast Calibration (StEFCal). The algorithm was implemented in several stages of the Low Frequency Array (LOFAR) calibration pipeline. We report on calibration performance improvement achieved with StEFCal in this pipeline.