Accounting for noise and singularities in Bayesian calibration methods for global 21-cm cosmology experiments

ABSTRACT Due to the large dynamic range involved with separating the cosmological 21-cm signal from the Cosmic Dawn from galactic foregrounds, a well-calibrated instrument is essential to avoid biases from instrumental systematics. In this paper, we present three new methods for calibrating a global 21-cm cosmology experiment using the noise wave parameter formalization to characterize a low-noise amplifier including a careful consideration of how calibrator temperature noise and singularities will bias the result. The first method presented in this paper builds upon the existing conjugate priors method by weighting the calibrators by a physically motivated factor, thereby avoiding singularities and normalizing the noise. The second method fits polynomials to the noise wave parameters by marginalizing over the polynomial coefficients and sampling the polynomial orders as parameters. The third method introduces a physically motivated noise model to the marginalized polynomial method. Running these methods on a suite of simulated data sets based on the Radio Experiment for the Analysis of Cosmic Hydrogen receiver design and a lab data set, we found that our methods produced a calibration solution which is equally as or more accurate than the existing conjugate priors method when compared with an estimate of the calibrator’s noise. We find in the case of the measured lab data set the conjugate priors method is biased heavily by the large noise on the shorted load calibrator, resulting in incorrect noise wave parameter fits. This is mitigated by the methods introduced in this paper which calibrate the validation source spectra to within 5 per cent of the noise floor at best.