A Bayesian approach to high-fidelity interferometric calibration – I. Mathematical formalism
A Bayesian approach to high-fidelity interferometric calibration – I. Mathematical formalism
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高保真干涉校准的贝叶斯方法 — I. 数学形式主义
DOI：
10.1093/mnras/stac1861
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发表时间：
2022
影响因子：
4.8
通讯作者：
Sievers, Jonathan L.
中科院分区：
文献类型：
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作者：
Sims, Peter H.;Pober, Jonathan C.;Sievers, Jonathan L.
在另一篇论文中，我们提出了一种减轻干涉校准中天空模型不完备性的数学形式bayescal。在本文中，我们演示了使用bayescalto校准full-Stokes模拟观测的退化增益参数，该参数具有类似hera的六边形紧密填充冗余阵列，用于校准天空模型的优先已知分量的三个假设完备度。我们将贝叶斯尺度校准解决方案与通过校准退化增益参数恢复的解决方案进行比较，这些退化增益参数只有校准天空模型的优先级已知分量，在增益幅度解决方案上施加或不施加物理动机先验，以及在其上校准的基线长度范围的两种选择。我们发现，在数据中可获得的整个光谱尺度范围内，贝叶斯尺度提供的校准解决方案在伪增益幅度波动方面的功率比使用替代方法获得的相同数据集的校准解决方案低4个数量级，并且比平均退化增益幅度小~ 107到~ 1010倍。此外，我们发现在模拟的场景中，仅贝叶斯尺度具有足够高保真度的校准解，可以在大光谱尺度上无偏恢复21 cm功率谱（k∥> 0.15hMpc−1）。在所有其他情况下，在研究的完备性体系中，这些尺度都受到了污染。
In a companion paper, we presentedbayescal, a mathematical formalism for mitigating sky-model incompleteness in interferometric calibration. In this paper, we demonstrate the use ofbayescalto calibrate the degenerate gain parameters of full-Stokes simulated observations with a HERA-like hexagonal close-packed redundant array, for three assumed levels of completeness of thea prioriknown component of the calibration sky model. We compare thebayescalcalibration solutions to those recovered by calibrating the degenerate gain parameters with only thea prioriknown component of the calibration sky model both with and without imposing physically motivated priors on the gain amplitude solutions and for two choices of baseline length range over which to calibrate. We find thatbayescalprovides calibration solutions with up to 4 orders of magnitude lower power in spurious gain amplitude fluctuations than the calibration solutions derived for the same data set with the alternate approaches, and between ∼107and ∼1010times smaller than in the mean degenerate gain amplitude, on the full range of spectral scales accessible in the data. Additionally, we find that in the scenarios modelled onlybayescalhas sufficiently high fidelity calibration solutions for unbiased recovery of the 21-cm power spectrum on large spectral scales (k∥≲ 0.15hMpc−1). In all other cases, in the completeness regimes studied, those scales are contaminated.