Bayesian noise wave calibration for 21-cm global experiments

TL;DR

This paper introduces a Bayesian noise wave calibration algorithm for 21-cm global experiments, enhancing sensitivity and systematic calibration using Bayesian evidence and machine learning, achieving an RMS error of 8 mK.

Contribution

It presents a novel Bayesian calibration method with machine learning techniques, improving calibration accuracy and efficiency for 21-cm experiments.

Findings

Achieved 8 mK RMS calibration error on a 50 Ω load.

Method supports frequency variation detection and parameter correlation.

Applicable to global 21-cm experiments and adaptable to other telescopes.

Abstract

Detection of millikelvin-level signals from the 'Cosmic Dawn' requires an unprecedented level of sensitivity and systematic calibration. We report the theory behind a novel calibration algorithm developed from the formalism introduced by the EDGES collaboration for use in 21-cm experiments. Improvements over previous approaches are provided through the incorporation of a Bayesian framework and machine learning techniques such as the use of Bayesian evidence to determine the level of frequency variation of calibration parameters that is supported by the data, the consideration of correlation between calibration parameters when determining their values and the use of a conjugate-prior based approach that results in a fast algorithm for application in the field. In self-consistency tests using empirical data models of varying complexity, our methodology is used to calibrate a 50 $\Omega$ ambient-temperature load. The RMS error between the calibration solution and the measured temperature of the load is 8 mK, well within the 1$\sigma$ noise level. Whilst the methods described here are more applicable to global 21-cm experiments, they can easily be adapted and applied to other applications, including telescopes such as HERA and the SKA.