Impact of numerical stability in Bayesian noise wave calibration on global 21-cm experiments
Abstract
Detecting the global 21-cm signal from the Cosmic Dawn and Epoch of Reionization requires calibration accuracy far below the level of astrophysical foregrounds. REACH models its receiver using the noise wave formalism, with five frequency-dependent low-noise amplifier parameters fitted jointly to multiple calibration sources. We identify a numerical instability in this Bayesian calibration pipeline: the condition number of the posterior covariance matrix reaches κ(V*) ∼ 109--1011, making solutions non-reproducible across computing environments. Singular value decomposition shows that the instability is driven by near-collinearity between the design-matrix columns associated with the excess noise source temperature, XNS, and the load temperature, XL. Using a Chebyshev basis, we develop a two-step mitigation. First, fixing TNS to a scalar removes the degeneracy and reduces κ(V*) to ∼ 60. Second, to retain frequency dependence, we recover TNS(ν) directly from the hot-load calibration measurement. On mock data, this method preserves the stability of the reduced model while achieving comparable calibration accuracy. Masking narrow channels around cable standing-wave degeneracies further removes local artefacts in the design matrix. These steps provide a stable, reproducible, and data-driven calibration procedure. Because the XNS--XL degeneracy is inherent to the noise wave formalism, the method is relevant to other global 21-cm experiments.
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BibTeX
@misc{dasgupta2026impact,
title = {{Impact of numerical stability in Bayesian noise wave calibration on global 21-cm experiments}},
author = {Saswata Dasgupta and Adarsh Kumar Dash and Dominic Anstey and Harry T. J. Bevins and Christian Kirkham and Eloy de Lera Acedo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.26911},
eprint = {2607.26911},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.26911},
}
RIS
TY - UNPB
TI - Impact of numerical stability in Bayesian noise wave calibration on global 21-cm experiments
AU - Saswata Dasgupta
AU - Adarsh Kumar Dash
AU - Dominic Anstey
AU - Harry T. J. Bevins
AU - Christian Kirkham
AU - Eloy de Lera Acedo
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2607.26911
UR - https://arxiv.org/abs/2607.26911
AB - Detecting the global 21-cm signal from the Cosmic Dawn and Epoch of Reionization requires calibration accuracy far below the level of astrophysical foregrounds. REACH models its receiver using the noise wave formalism, with five frequency-dependent low-noise amplifier parameters fitted jointly to multiple calibration sources. We identify a numerical instability in this Bayesian calibration pipeline: the condition number of the posterior covariance matrix reaches κ(V^*) ∼ 10^9--10^11, making solutions non-reproducible across computing environments. Singular value decomposition shows that the instability is driven by near-collinearity between the design-matrix columns associated with the excess noise source temperature, X_NS, and the load temperature, X_L. Using a Chebyshev basis, we develop a two-step mitigation. First, fixing T_NS to a scalar removes the degeneracy and reduces κ(V^*) to ∼ 60. Second, to retain frequency dependence, we recover T_NS(ν) directly from the hot-load calibration measurement. On mock data, this method preserves the stability of the reduced model while achieving comparable calibration accuracy. Masking narrow channels around cable standing-wave degeneracies further removes local artefacts in the design matrix. These steps provide a stable, reproducible, and data-driven calibration procedure. Because the X_NS--X_L degeneracy is inherent to the noise wave formalism, the method is relevant to other global 21-cm experiments.
ER -