无线电干涉阵列方向相关校准的可识别性和可估计性
On Identifiability and Estimability of Direction Dependent Calibration of Radio Interferometric Arrays
摘要：
校准是任何射电天文仪器信号处理流程中的关键步骤。这一步骤所需的天空、电离层和仪器模型可能存在各种不完整性。在本文中，我们分析了几个重要的校准方法，忽略了现在的电离层。其目的是使用已建立的统计和信号处理工具，以提供一个通用的方法来评估仪器的校准。我们展示了目前流行的校准技术如何在他们的假设不同，并讨论了他们的理论共性。我们还研究了只使用基线的子集对校准的影响，并提供了理论方法来分析它可能引入的过量噪声和偏差。为了简化结果的物理解释，我们引入了一个新的信号处理模型，该模型能够模拟仪器方向相关的影响和频谱平滑的波束形成站内的个人接收器增益。通过推导Cramér-Rao界（CRB）研究了该模型的统计性质.最后，我们定义了一个数学框架的基础上使用的模型，这是通用的，可用于研究不同的仪器的仪器的校准。这些理论结果，然后使用数值模拟进行验证。
英文摘要：
Calibration is a key step in the signal processing pipeline of any radio astronomical instrument. The required sky, ionospheric and instrumental models for this step can suffer from various kinds of incompleteness. In this paper we analyze several important calibration methods, ignoring for now the ionosphere. The aim is to use established statistical and signal processing tools to provide a generic method to assess calibratability of an instrument. We show how currently popular calibration techniques differ in their assumptions and also discuss their theoretical commonalities. We also study the effect of only using a sub-set of baselines on the calibration and provide theoretical methods to analyze excess noise and biases that it might introduce. In order to simplify the physical interpretation of the results, we introduce a new signal processing model which is capable of modeling instrumental direction dependent effects and spectral smoothness of the individual receiver gain within a beam-formed station. The statistical properties of this model are then studied by deriving the Cramér--Rao bound (CRB). We finally define a mathematical framework for calibratability of an instrument based on the model used which is generic and can be used to study different instruments. These theoretical results are then verified using numerical simulations.
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