Efficient Calibration of Radio Interferometers Using Block LDU Decomposition

TL;DR

This paper introduces efficient, fast-converging calibration algorithms for large-scale radio telescopes, utilizing block-LDU decomposition and Gauss-Newton methods to reduce computational complexity and improve accuracy.

Contribution

The paper presents novel calibration algorithms combining block-LDU decomposition with Gauss-Newton iterations, enabling faster convergence and lower storage requirements for next-generation radio telescopes.

Findings

Algorithms converge rapidly in simulations.

Significant reduction in per-iteration complexity.

Effective extension to direction-dependent calibration.

Abstract

Having an accurate calibration method is crucial for any scientific research done by a radio telescope. The next generation radio telescopes such as the Square Kilometre Array (SKA) will have a large number of receivers which will produce exabytes of data per day. In this paper we propose new direction-dependent and independent calibration algorithms that, while requiring much less storage during calibration, converge very fast. The calibration problem can be formulated as a non-linear least square optimization problem. We show that combining a block-LDU decomposition with Gauss-Newton iterations produces systems of equations with convergent matrices. This allows significant reduction in complexity per iteration and very fast converging algorithms. We also discuss extensions to direction-dependent calibration. The proposed algorithms are evaluated using simulations.