AI 中文总结
该研究针对REACH项目贝叶斯噪声波校准流程的数值不稳定性，开发两步缓解方案，实现稳定可复现的校准，适用于全球21厘米实验。
AI 中文摘要
探测宇宙黎明与再电离时期的全球21厘米信号，需要校准精度远低于天体物理前景的水平。REACH项目采用噪声波形式主义对其接收机建模，通过联合拟合多个校准源的5个频率相关低噪声放大器参数实现校准。我们发现该贝叶斯校准流程存在数值不稳定性：后验协方差矩阵的条件数达到κ(V*)~10^9–10^11，导致不同计算环境下的解不可复现。奇异值分解显示，该不稳定性由过量噪声源温度X_NS与负载温度X_L对应的设计矩阵列近乎共线驱动。我们采用切比雪夫基开发了两步缓解方案：第一步，将T_NS固定为标量以消除退化，将κ(V*)降至~60；第二步，为保留频率相关性，直接从热负载校准测量中恢复T_NS(ν)。在模拟数据上，该方法在维持简化模型稳定性的同时达到了相当的校准精度。屏蔽电缆驻波退化附近的窄通道可进一步消除设计矩阵中的局部伪影。这些步骤提供了稳定、可复现且数据驱动的校准流程。由于X_NS–X_L退化是噪声波形式主义的固有特性，该方法也适用于其他全球21厘米实验。
英文摘要
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 $κ(\mathbf{V}^*) \sim 10^{9}$--$10^{11}$, 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, $X_\mathrm{NS}$, and the load temperature, $X_\mathrm{L}$. Using a Chebyshev basis, we develop a two-step mitigation. First, fixing $T_\mathrm{NS}$ to a scalar removes the degeneracy and reduces $κ(\mathbf{V}^*)$ to $\sim 60$. Second, to retain frequency dependence, we recover $T_\mathrm{NS}(ν)$ 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 $X_\mathrm{NS}$--$X_\mathrm{L}$ degeneracy is inherent to the noise wave formalism, the method is relevant to other global 21-cm experiments.
Comments15 pages, 17 figures, To be submitted to MNRAS
