HERA Memorandum #84: A Generalized Approach to Redundant Calibration with JAX
HERA Memorandum #84: A Generalized Approach to Redundant Calibration with JAX
复制标题
DOI：
--
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Matyas David Molnar;B. Nikolic
中科院分区：
文献类型：
--
作者：
Matyas David Molnar;B. Nikolic
再电离氢时期阵列（HERA）采用冗余校准方法对数据进行校准，该方法假设了高斯噪声统计，线性化了测量方程，并使χ最小化。我们将这种最大似然估计（MLE）推广到非高斯统计，而不需要线性化，这可以通过重新利用用于机器学习（ML）的开源库（在这种情况下是JAX）来实现良好的计算性能，只需很少的编程工作。作为一个例子，我们显示了高斯和柯西假设的噪声分布之间的比较，在一个样本HERA数据集的校准，与后者显示预期的弹性射频干扰（RFI）。本节中描述的工作代码可以在https://github.com/bnikolic/ simpleredcal上找到。本备忘录中使用的HERA数据示例是在Julian日期（JD）2458098.43869观察到的，并取自H1C_IDR2.2数据集。我们只看EE极化。在§1中，我们回顾了冗余校准，并将其MLE扩展到Cauchy模型。在§2中，我们展示了如何使用JAX显著且轻松地加速其他模型的冗余校准。1稳健的冗余校准具有规则间隔天线的阵列具有许多对天空中相同模式敏感的冗余振子。冗余校准利用冗余基线的真实vibration相等这一事实。假设不存在方向相关的校准效应，我们就得到了所有天线对i和j的方程组：V obs ij（v）= gi（v）g j（v）Uα（v）+ nij（v）（1）其中Uα（v）= V（ri−rj），基线向量bij = ri−rj的可见性对应于我们用α索引的冗余基线集，nij是噪声。对于计划中的完整HERA阵列，六边形核心中将有331个元素，对应于Nbl = 331（331 − 1）/2 = 54，615个基线。核心只有630个唯一的基线，这意味着我们有一个由54615个方程组成的非线性系统来确定630个真实的活力和331个增益。1.1相对校准利用冗余校准先验，可以通过假设观测到的可见性噪声的分布来构造增益和真实可见性的MLE。
The Hydrogen Epoch of Reionization Array (HERA) relies on redundant calibration with redcal to calibrate its data, which assumes Gaussian noise statistics, linearizes the measurement equation and minimizes the χ. We show generalization of this maximum likelihood estimation (MLE) to non-Gaussian statistics and without the need for linearization, which can be achieved at good computational performance with very little programming effort by repurposing open-source libraries intended for machine learning (ML), in this case JAX. As an example, we show a comparison between Gaussian and Cauchy assumed noise distributions in the calibration of a sample HERA dataset, with the latter showing expected resilience to radio-frequency interference (RFI). The code for the work described in this section can be found at https://github.com/bnikolic/ simpleredcal. The example HERA data used throughout this memo was observed on Julian date (JD) 2458098.43869 and taken from the H1C_IDR2.2 dataset. We only look at the EE polarization. In §1, we review redundant calibration and extend its MLE to a Cauchy model. In §2, we show how redundant calibration with other models can be significantly and easily sped up with JAX. 1 Robust redundant calibration An array with regularly spaced antennas has many redundant visibilities that are sensitive to the same modes on the sky. Redundant calibration uses the fact that the true visibilities from redundant baselines are equal. Supposing there are no direction-dependent calibration effects, we therefore have a system of equations for all antenna pairs i and j: V obs ij (ν) = gi(ν)g ∗ j (ν)Uα(ν) + nij(ν) (1) where Uα(ν) = V (ri−rj), the visibility for the baseline vector bij = ri−rj , corresponds to a redundant baseline set that we index by α, and nij is the noise. For the planned full HERA array, there will be 331 elements in the hexagonal core, corresponding to Nbl = 331(331 − 1)/2 = 54, 615 baselines. The core only has 630 unique baselines, which means that we have a non-linear system of 54, 615 equations to determine the 630 true visibilities and 331 gains. 1.1 Relative calibration With the redundant calibration prior, an MLE for the gains and true visibilities can be constructed by assuming a distribution for the observed visibility noise.