光电参考系系的功能主成分分析
Functional principal component analysis of radio-optical reference frame tie
摘要：
盖亚光学参考系本质上是不确定的全球方向和自旋，所以它需要锚定在基于无线电的国际天体参考系（ICRF），以提供参考和准惯性天体坐标系。两个基本框架之间的联系是通过两个遥远的河外源样本实现的，主要是AGN和类星体，但只有较小的无线电大声ICRF源与光学对应物的样本可用于确定相互方向。这个链接的鲁棒性可以用数学公式表示的功能主成分分析的框架中使用一组矢量球谐函数来表示在天体位置的共同对象的差异。计算最弱的特征向量，其描述链路的最大缺陷。不足或不好确定的条款是特定的矢量场的领域进行最大的误差绝对天体测量使用盖亚在参考ICRF。这一分析为ICRF的未来发展提供了指导方针，以最大限度地提高整个天球上链路的精度。一个最小二乘解决方案，它可以适用于任何线性模型拟合问题的鲁棒性的措施，介绍了帮助区分不同程度的参考系领带模型。
英文摘要：
The Gaia optical reference frame is intrinsically undefined with respect to global orientation and spin, so it needs to be anchored in the radio-based International Celestial Reference Frame (ICRF) to provide a referenced and quasi-inertial celestial coordinate system. The link between the two fundamental frames is realized through two samples of distant extragalactic sources, mostly AGNs and quasars, but only the smaller sample of radio-loud ICRF sources with optical counterparts is available to determine the mutual orientation. The robustness of this link can be mathematically formulated in the framework of functional principal component analysis using a set of vector spherical harmonics to represent the differences in celestial positions of the common objects. The weakest eigenvectors are computed, which describe the greatest deficiency of the link. The deficient or poorly determined terms are specific vector fields on the sphere which carry the largest errors of absolute astrometry using Gaia in reference to the ICRF. This analysis provides guidelines to the future development of the ICRF maximizing the accuracy of the link over the entire celestial sphere. A measure of robustness of a least-squares solution, which can be applied to any linear model fitting problem, is introduced to help discriminate between reference frame tie models of different degrees.
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