阿伦方差在天文学和大地测量学时间序列分析中的应用：综述
Application of the Allan Variance to Time Series Analysis in Astrometry and Geodesy: A Review
AI总结：
综述阿伦方差及其改进方法在处理天文大地时间序列中的应用，强调其在处理非均匀加权和多维数据中的重要性。
摘要：
阿伦方差（AVAR）于50年前被引入作为评估频率标准偏差的统计工具。过去几十年中，AVAR在大地测量学和天文学中被越来越多用于评估大地测量和天文学时间序列中的噪声特性。与钟测量相比，天文学和大地测量测量通常与不确定性相关，因此在数据分析中应适当加权。此外，一些物理上相连的标量时间序列自然形成多维向量序列。例如，三个站坐标时间序列X、Y和Z可以结合分析三维站位变化。经典的AVAR并非为处理非均匀加权和/或多维数据而设计。因此，引入了阿伦方差的改进方法，即加权阿伦方差（WAVAR）、多维阿伦方差（MAVAR）和加权多维阿伦方差（WMAVAR），以克服这些不足。本文简要回顾了在处理天文大地时间序列中使用AVAR及其改进方法的经验。
英文摘要：
The Allan variance (AVAR) was introduced 50 years ago as a statistical tool for assessing of the frequency standards deviations. For the past decades, AVAR has increasingly being used in geodesy and astrometry to assess the noise characteristics in geodetic and astrometric time series. A specific feature of astrometric and geodetic measurements, as compared with the clock measurements, is that they are generally associated with uncertainties; thus, an appropriate weighting should be applied during data analysis. Besides, some physically connected scalar time series naturally form series of multi-dimensional vectors. For example, three station coordinates time series $X$, $Y$, and $Z$ can be combined to analyze 3D station position variations. The classical AVAR is not intended for processing unevenly weighted and/or multi-dimensional data. Therefore, AVAR modifications, namely weighted AVAR (WAVAR), multi-dimensional AVAR (MAVAR), and weighted multi-dimensional AVAR (WMAVAR), were introduced to overcome these deficiencies. In this paper, a brief review is given of the experience of using AVAR and its modifications in processing astro-geodetic time series.
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