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Article(id=1322506292325888000, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322506263716541212, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.09.437, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1726675200000, receivedDateStr=2024-09-19, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793239671069, onlineDateStr=2026-10-29, pubDate=1757865600000, pubDateStr=2025-09-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793239671069, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793239671069, creator=13701087609, updateTime=1793239671069, updator=13701087609, issue=Issue{id=1322506263716541212, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='9', pageStart='881', pageEnd='990', issueExtLink='null', onlineDate='null', pubDate='1757865600000', pubDateStr='2025-09-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793239664248, creator='13701087609', updateTime=1793239664248, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=905, endPage=909, ext={EN=ArticleExt(id=1322506292527214593, articleId=1322506292325888000, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Impact of VLBI Observation Frequency on the Accuracy of UT1 Determination, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

This paper introduces the data preprocessing and interpolation methods for universal time(UT1) and analyzes the factors affecting the interpolation accuracy of UT1, including different interpolation methods and differences in data preprocessing. The study combines international products with domestic co-observation data to analyze the interpolation accuracy of UT1 under different observation frequencies of very long baseline interferometry(VLBI). The results show that among different interpolation methods, cubic spline interpolation is superior. The interpolation process of UT1 must consider the influence of Earth's solid tides, while high-frequency corrections can be neglected. Compared with daily observations, when the observation interval is less than 2 days, the deviation of UT1 can be stabilized at around 0.05 ms. Increasing the observation interval further will lead to a more pronounced increase of UT1 deviation. Verification using domestic observational data shows that with an observation interval of 2 days, the accuracy of UT1 can reach around 0.05 ms.

, authors=Zhuoxi MA1, 2, Guangyun LI1, *, Dang YAO3, Dan JIANG2, authorsList=Zhuoxi MA, Guangyun LI, Dang YAO, Dan JIANG, authorCompany=null, correspAuthors=Guangyun LI, authorNote=

MA Zhuoxi, PhD, engineer, majors in spatial geodetic data processing, E-mail:

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介绍世界时(UT1)的数据预处理和加密方法，并分析不同加密方法、数据预处理差异等因素对UT1加密精度的影响。结合国际产品和国内联合观测的实测数据，对不同甚长基线干涉测量(VLBI)观测频次下的UT1加密精度进行分析。结果表明，不同加密方法之间，三次样条插值方法较优，且UT1插值过程中必须考虑地球固体潮影响，而高频项修正可以忽略。与每天观测相比，当观测间隔小于2 d时，UT1的偏差可稳定在0.05 ms左右，继续增大观测间隔，UT1的偏差将出现较明显的增大。国内实测数据验证表明，观测间隔为2 d的情况下，UT1的精度可达0.05 ms左右。

, authors=马卓希1, 2, 李广云1, *, 姚当3, 江丹2, authorsList=马卓希, 李广云, 姚当, 江丹, authorCompany=null, correspAuthors=李广云, authorNote=

马卓希，博士，工程师，主要从事空间大地测量数据处理研究，E-mail:

, correspAuthorsNote=

李广云，博士，教授，博士生导师，主要从事大地测量与测量工程、导航与位置服务等研究，E-mail:

LI Guangyun, PhD, professor, PhD supervisor, majors in geodesy and survey engineering, navigation and positioning services, E-mail:

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MA Zhuoxi, PhD, engineer, majors in spatial geodetic data processing, E-mail:

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MA Zhuoxi, PhD, engineer, majors in spatial geodetic data processing, E-mail:

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densification errors through domestic observations, figureFileSmall=nWkRk5Kj547N7ghUGvoUEg==, figureFileBig=0y9BK3BTFUparP29PWNgVg==, tableContent=null), ArticleFig(id=1322506299854663736, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506292325888000, language=CN, label=图4, caption=国内UT1测定和加密误差, figureFileSmall=nWkRk5Kj547N7ghUGvoUEg==, figureFileBig=0y9BK3BTFUparP29PWNgVg==, tableContent=null), ArticleFig(id=1322506299930161209, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506292325888000, language=EN, label=Tab. 1, caption=

Statistics of the average differences between desification results using different methods

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采样间隔/d 线性插值法/ms 三次样条法/ms 拉格朗日法/ms LOD外推/ms
1 0.051 0.006 0.015 0.053
2 0.100 0.019 0.045 0.100
3 0.160 0.042 0.094 0.142
4 0.227 0.097 0.169 0.176
5 0.301 0.197 0.259 0.202
), ArticleFig(id=1322506300177625146, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506292325888000, language=CN, label=表1, caption=

不同加密方法加密结果的平均互差统计

, figureFileSmall=null, figureFileBig=null, tableContent=
采样间隔/d 线性插值法/ms 三次样条法/ms 拉格朗日法/ms LOD外推/ms
1 0.051 0.006 0.015 0.053
2 0.100 0.019 0.045 0.100
3 0.160 0.042 0.094 0.142
4 0.227 0.097 0.169 0.176
5 0.301 0.197 0.259 0.202
), ArticleFig(id=1322506300257316923, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506292325888000, language=EN, label=Tab. 2, caption=

UT1 errors of different interpolation methods

, figureFileSmall=null, figureFileBig=null, tableContent=
采样间隔/d 方案1/ms 方案2/ms 方案3/ms
1 0.013 0.013 0.013
2 0.019 0.018 0.018
3 0.069 0.054 0.054
4 0.118 0.075 0.074
5 0.193 0.096 0.095
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不同预处理方法的UT1互差

, figureFileSmall=null, figureFileBig=null, tableContent=
采样间隔/d 方案1/ms 方案2/ms 方案3/ms
1 0.013 0.013 0.013
2 0.019 0.018 0.018
3 0.069 0.054 0.054
4 0.118 0.075 0.074
5 0.193 0.096 0.095
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Statistics of UT1 accuracy at different sampling intervals

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采样间隔/d 最大偏差/ms 平均偏差/ms 样本数 A B/%
1 0.031 0.013 1 360 1 360 100
2 0.089 0.018 1 360 1 360 100
3 0.164 0.054 1 360 1 158 85.1
4 0.406 0.075 1 360 1 068 78.5
5 0.844 0.096 1 360 990 72.8
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不同采样间隔下UT1精度统计

, figureFileSmall=null, figureFileBig=null, tableContent=
采样间隔/d 最大偏差/ms 平均偏差/ms 样本数 A B/%
1 0.031 0.013 1 360 1 360 100
2 0.089 0.018 1 360 1 360 100
3 0.164 0.054 1 360 1 158 85.1
4 0.406 0.075 1 360 1 068 78.5
5 0.844 0.096 1 360 990 72.8
), ArticleFig(id=1322506300680941631, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506292325888000, language=EN, label=Tab. 4, caption=

Statistics of UT1 accuracy under different observation conditions

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观测 平均观测量 平均偏差(插值前)/ms 平均偏差(插值后)/ms
观测1 249 0.033 0.046
观测2 72 0.035 0.031
), ArticleFig(id=1322506300756439104, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506292325888000, language=CN, label=表4, caption=

不同观测下UT1精度统计

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观测 平均观测量 平均偏差(插值前)/ms 平均偏差(插值后)/ms
观测1 249 0.033 0.046
观测2 72 0.035 0.031
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VLBI观测频次对UT1加密精度的影响
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马卓希 1, 2 , 李广云 1, * , 姚当 3 , 江丹 2
大地测量与地球动力学 | 现代大地测量 2025,45(9): 905-909
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大地测量与地球动力学 |现代大地测量 2025 , 45 (9) : 905 -909
VLBI观测频次对UT1加密精度的影响
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马卓希1, 2 , 李广云1, * , 姚当3, 江丹2
作者信息
  • 1 信息工程大学地理空间信息学院，郑州市科学大道62号，450001
  • 2 61363部队，西安市，710054
  • 3 中国科学院国家授时中心，西安市书院东路3号，710600
通讯作者:

李广云，博士，教授，博士生导师，主要从事大地测量与测量工程、导航与位置服务等研究，E-mail:

LI Guangyun, PhD, professor, PhD supervisor, majors in geodesy and survey engineering, navigation and positioning services, E-mail:

作者简介:

马卓希，博士，工程师，主要从事空间大地测量数据处理研究，E-mail:

Impact of VLBI Observation Frequency on the Accuracy of UT1 Determination
Zhuoxi MA1, 2 , Guangyun LI1, * , Dang YAO3, Dan JIANG2
Affiliations
  • 1 School of Surveying and Mapping, Information Engineering University, 62 Kexue Road, Zhengzhou 450001, China
  • 2 61363 Troops, Xi'an 710054, China
  • 3 National Time Service Center, CAS, 3 East-Shuyuan Road, Xi'an 710600, China

    • MA Zhuoxi, PhD, engineer, majors in spatial geodetic data processing, E-mail:

出版时间: 2025-09-15 doi: 10.14075/j.jgg.2024.09.437
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介绍世界时(UT1)的数据预处理和加密方法，并分析不同加密方法、数据预处理差异等因素对UT1加密精度的影响。结合国际产品和国内联合观测的实测数据，对不同甚长基线干涉测量(VLBI)观测频次下的UT1加密精度进行分析。结果表明，不同加密方法之间，三次样条插值方法较优，且UT1插值过程中必须考虑地球固体潮影响，而高频项修正可以忽略。与每天观测相比，当观测间隔小于2 d时，UT1的偏差可稳定在0.05 ms左右，继续增大观测间隔，UT1的偏差将出现较明显的增大。国内实测数据验证表明，观测间隔为2 d的情况下，UT1的精度可达0.05 ms左右。

VLBI  /  加强观测  /  UT1参数  /  精度评估

This paper introduces the data preprocessing and interpolation methods for universal time(UT1) and analyzes the factors affecting the interpolation accuracy of UT1, including different interpolation methods and differences in data preprocessing. The study combines international products with domestic co-observation data to analyze the interpolation accuracy of UT1 under different observation frequencies of very long baseline interferometry(VLBI). The results show that among different interpolation methods, cubic spline interpolation is superior. The interpolation process of UT1 must consider the influence of Earth's solid tides, while high-frequency corrections can be neglected. Compared with daily observations, when the observation interval is less than 2 days, the deviation of UT1 can be stabilized at around 0.05 ms. Increasing the observation interval further will lead to a more pronounced increase of UT1 deviation. Verification using domestic observational data shows that with an observation interval of 2 days, the accuracy of UT1 can reach around 0.05 ms.

VLBI  /  intensive observation  /  UT1 parameter  /  precision evaluation
马卓希, 李广云, 姚当, 江丹. VLBI观测频次对UT1加密精度的影响. 大地测量与地球动力学, 2025 , 45 (9) : 905 -909 . DOI: 10.14075/j.jgg.2024.09.437
Zhuoxi MA, Guangyun LI, Dang YAO, Dan JIANG. Impact of VLBI Observation Frequency on the Accuracy of UT1 Determination[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (9) : 905 -909 . DOI: 10.14075/j.jgg.2024.09.437
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地球定向参数(earth orientation parameter，EOP)是实现地球参考框架与天球参考框架相互转换的关键参数，用于描述地球自转轴及其指向的变化。这些参数包括2个极移参数、世界时(universal time，UT1)与协调世界时(coordinated universal time，UTC)的差值(UT1-UTC)以及2个章动改正参数[1]。EOP参数在卫星导航、深空探测等航天工程领域具有重要应用价值[2]。
目前，国际上EOP产品主要由国际地球自转和参考系统服务组织(International Earth Rotation and Reference Systems Service，IERS)发布，通过全球导航卫星系统(GNSS)、甚长基线干涉测量(very long baseline interferometry, VLBI)和卫星激光测距(satellite laser range，SLR)等多种空间大地测量观测数据的解算和融合获得。其中，GNSS和SLR等卫星测量技术虽无法直接测量UT1，但可测定日长变化(length of day，LOD)，为地球自转的高频信息提供重要参考[2]。VLBI技术是唯一能够解算全部EOP参数并监测UT1变化的空间大地测量技术[3]，但其观测成本高、数据处理复杂且数据传输困难，难以实现每日连续、整点的UT1测定。因此，通过加密手段实现UT1的高精度预测至关重要。
自1984年起，国际上开始实施VLBI加强观测，通常利用单条东西走向的基线或区域观测网络进行1~2 h的观测以解算UT1参数。目前，多国已开展UT1快速服务研究，如国际VLBI服务组织(IVS)的INT系列、Ultra-rapid系列，俄罗斯的quasar、美国的VLBA等观测项目[4-8]。近年来，随着VLBI全球观测系统(VGOS)的发展，自2021年起，基于VGOS台站的观测(如VGOS-INT-A/B/C/S/G/Y等)为连续VLBI测定提供了有力补充。在不同观测系列的支持下，已基本实现UT1的每日观测[9-10]。
为推动我国自主EOP产品的研发，依托中国科学院系统的中国VLBI网(CVN)、国家授时中心VLBI网(NTSC)以及西安测绘研究所的中国新一代VLBI网(CNVN)等观测设施，国内多个机构已开展并组织了观测试验，并对我国的UT1快速服务能力进行了系统评估[1, 11-12]。然而，综合考虑观测成本和台站损耗，短期内我国仍难以实现UT1的每日连续观测。在此背景下，分析VLBI观测频次对UT1加密精度的影响，对于后续国内UT1测量计划的制定具有重要参考价值。
本文介绍UT1的数据预处理及加密方法，并分析影响UT1加密精度的因素。最后，利用国际和国内实测数据，分析和验证不同观测频次设置对UT1加密精度的影响。
1 UT1的数据预处理及加密算法
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VLBI加强观测的UT1测定结果，需要通过数据预处理及加密，提供连续的UTC 0时的结果。其中，数据预处理主要包括跳秒改正、潮汐改正和高频项改正。加密一般有内插算法和外推算法两种。UT1的数据预处理和加密算法的流程见图 1。
1.1 数据预处理
数据预处理的主要目的是剔除地球固体潮等对UT1的影响。IERS技术报告[13]中的固体潮改正包含除周日、半周日等高频变化外的5 d~18.6 a周期项变化，共62项。由于IERS公布的UT1/LOD未包括海潮改正中的周日、半周日项(共计71项)和顺行周日章动改正(共计10项)，为更好进行评估，需要将上述改正作为高频项进行修正。
1.2 内插算法
UT1插值结果的优劣取决于插值算法与UT1的符合程度，目前常采用数学插值算法(包括线性插值法、样条插值法、拉格朗日插值法等)获得待定节点的UT1参数。
1.3 外推算法
UT1的外推算法需要建立在GNSS技术提供LOD值的基础上，LOD的预处理步骤与UT1相同。当已知第T天的UT1和LOD值时，采用以下公式：
$\begin{gathered}\mathrm{UT} 1_{T+n}=\mathrm{UT} 1_T-\mathrm{LOD}_T-\cdots-\mathrm{LOD}_{T+n-1}, \\n=1, 2, \cdots\end{gathered}$
$\begin{gathered}\mathrm{UT} 1_{T-n}=\mathrm{UT} 1_T+\mathrm{LOD}_{T-1}+\cdots+\mathrm{LOD}_{T-n-1}, \\n=1, 2, \cdots\end{gathered}$
2 加密精度的影响因素分析
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2.1 加密算法的差异
为了验证不同算法间加密精度的差异，采用数值仿真方式进行分析。UT1参数序列来源于IERS 2015—2023年发布的C04序列。分别间隔1~5 d选取C04序列的UT1参数作为已知节点，内插得到中间各天节点结果，并统计内插点与已知序列的互差。采用相同的内插方法和日长外推的方法，并统计外推1~5 d的互差，插值方法与外推方法的统计结果见表 1。
为了更加直观地显示不同加密方法的差异，图 2(a)、2(b)显示了在采样间隔分别为2 d、3 d的情况下，不同插值方法的插值点与已知点的互差情况。
由表 1和图 2可以看出：1)对比不同内插方法。总体上看，三次样条法最优，拉格朗日法次之；随着采样间隔的增大，插值方法的精度衰减程度逐渐增大，当已知节点的间隔大于4 d时，精度衰减程度显著增大。2)对比内插算法和外推算法。外推算法的外推精度与日长参数的测定精度有关，本文采用的仿真方法建立在LOD精度较高的情况下，在实际数据处理过程中，其精度会较仿真结果略低。从结果看，内插和外推两种加密方法的精度在同一量级，但外推法4 d内的插值误差明显低于内插算法，长期外推的精度优于内插算法。3)在加密精度方面，采用三次样条法，采样间隔为2 d时的加密点误差较为稳定，误差总体优于0.1 ms；当继续增大采样间隔时，加密点误差将持续放大，超过0.1 ms。
2.2 数据预处理差异
以2015—2023年美国戈达德宇宙飞行中心(Goddard Space Flight Center，GSFC)发布的加强型EOP观测产品(EOP-I产品)中的连续UT1测定值作为分析对象。加密方法采用三次样条插值法，对不同数据预处理策略的差异进行分析。对于没有观测的天数，采用IERS C04的UT1值进行补充以保证分析对象的完整性，为尽可能还原统计结果的准确性，在结果统计中不统计这些虚拟点前后3个节点的解算值。
采用以下3种方案：方案1，不作任何数据预处理，直接插值；方案2，进行跳秒改正和固体潮改正；方案3，在方案2的基础上，增加高频项改正。
同样分别间隔1~4 d选取已知节点，内插得到中间各天节点结果，并统计内插点与IERS C04序列的互差，结果见表 2。
由表 2可见，若不考虑地球固体潮影响，其误差会随着采样间隔的增大而明显增大，因此在UT1插值过程中必须要考虑地球固体潮影响。而UT1高频项的修正量级在10-3 ms以内，对插值精度几乎没有影响。此外，笔者分别对固体潮改正中的短周期项(5~35 d，共41项)和长周期项(35 d~18.6 a，共21项)进行分析，发现固体潮的长周期项对采样5 d以内的插值影响量级也在10-3 ms以内。
3 数据测试及验证
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3.1 国际数据测试验证
采用§2.2描述的EOP-I产品作为分析对象。试验方法方面，分别提取间隔1~5 d的5种节点设置方式的UT1测定值作为已知节点，用于模拟不同VLBI观测频次的测定值，采用三次样条插值方法获得每日0时的UT1加密值；精度评估方面，将加密值与已知IERS C04序列进行互差，统计最大偏差、平均偏差和较差在±0.1 ms区间内的占比，其结果见表 3(表中，A列表示较差在±0.1 ms区间内的个数，B列表示A列个数占样本数的比)。对不同采样间隔下的不同区间段误差占比进行进一步统计，结果见图 3，图中横轴代表UT1误差，纵轴代表误差区间内样本占样本总数之比。
从图 3和表 3可以看出，当VLBI观测的采样间隔少于2 d时，较差在±0.05 ms的个数占样本数的比例超过96%，随着采样间隔的延长，采样间隔3~5 d的较差在±0.05 ms的占比分别衰减至73.4%、61.9%和51.9%，在±0.1 ms间的占比分别为85.1%、78.5%和72.8%。因此，每周间隔观测3次的情况下，可保证加密精度的衰减程度较小。可根据实际情况，综合考虑人员、观测成本和精度，设置合适的观测频次。
3.2 国内数据测试验证
从2023-05起，为致力于UT1参数的自主快速测定，由西安测绘研究所组织，中国科学院上海天文台实施，利用国内3个13 m口径的VGOS观测站(上海佘山站、乌鲁木齐南山站和上海天马站)，以每周3次(周一、周三、周五)的观测频次进行UT1测量工作，观测时长为1 h。但受观测条件制约，组织的观测并不连续，本文利用其中较连续的时间段数据进行了初步验证。观测时间为2023-05-24—07-31，其中05-24—06-27采用3站观测的方式，共13次观测，计为观测1；07-07—07-31采用上海佘山-乌鲁木齐南山站的“单基线”观测方式，共11次观测，计为观测2。每次观测的时间间隔在2~3 d。
解算配置方面，采用CALC/SOLVE 11.0软件，采用单次解模式，固定测站坐标、射电源位置及极移分量等参数，仅解算测站钟差(采用二次多项式拟合的方法)、测站天顶对流层延迟(每个测站估计一个参数)及UT1-UTC参数，极移分量及UT1-UTC的先验值采用USNO的预报值，且在求解过程中不添加约束。
通过三次样条法进行UT1加密获得每天连续的UT1数值，对测定值和内插值进行统计，评估指标仍为与已知序列的偏差，统计结果见图 4。对观测1、观测2的平均观测量和插值前后的平均偏差进行统计，结果见表 4。
通过实验样本分析，不同观测下的UT1测定值的平均偏差总体优于0.05 ms，最大偏差在0.12 ms左右，且不同类型观测的测定误差差别不显著；在2~3 d观测频次下，UT1的插值误差总体小于0.1 ms。
理论上，平均观测量越多，采用的测站数量越多，观测的质量应该越好。但对比观测2，采用3个台站“双基线”UT1的测定精度低于2个台站“单基线”观测，其原因可能归结为实验样本有限，且国内台站建成时间较短，站址坐标的变化仍然较大。因此，关于国内VLBI台站的测定能力还有待于进一步分析和评估。
4 结语
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本文对VLBI观测频次对UT1加密精度的影响进行讨论，利用数据仿真的方法分析不同加密方法的差异，并利用国际和国内观测数据，对不同VLBI观测频次下UT1的加密精度进行分析。结果表明，不同加密方法之间，三次样条插值方法较优，且UT1插值过程中必须要考虑地球固体潮影响，而高频项修正可以忽略；观测频次方面，同每天观测相比，当观测间隔小于2 d时，UT1的偏差可稳定在0.05 ms左右，继续增大观测间隔，UT1的偏差将出现明显增大。国内实测数据验证表明，观测间隔为2 d的情况下，UT1的精度可达0.05 ms左右。本文结果可为后续国内UT1测量和EOP常态化保障提供技术参考。
基金
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  • 国家自然科学基金(42304044)
文献
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参考文献 引证文献
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Geiger P, Fey A, Dieck C, et al. Intensifying the Intensives with the VLBA[C]. IVS 2018 General Meeting, Longyearbyen, 2018
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2025年第45卷第9期
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文章信息
doi: 10.14075/j.jgg.2024.09.437
  • 接收时间：2024-09-19
  • 首发时间：2026-10-29
  • 出版时间：2025-09-15
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  • 收稿日期：2024-09-19
基金
National Natural Science Foundation of China(42304044)
国家自然科学基金(42304044)
作者信息
    1 信息工程大学地理空间信息学院，郑州市科学大道62号，450001
    2 61363部队，西安市，710054
    3 中国科学院国家授时中心，西安市书院东路3号，710600

通讯作者:

李广云，博士，教授，博士生导师，主要从事大地测量与测量工程、导航与位置服务等研究，E-mail:

LI Guangyun, PhD, professor, PhD supervisor, majors in geodesy and survey engineering, navigation and positioning services, E-mail:

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