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Article(id=1322940580627624295, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322940449979244751, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.04.149, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1712073600000, receivedDateStr=2024-04-03, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793343213468, onlineDateStr=2026-10-30, pubDate=1741968000000, pubDateStr=2025-03-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793343213468, onlineIssueDateStr=2026-10-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793343213468, creator=13701087609, updateTime=1793343213468, updator=13701087609, issue=Issue{id=1322940449979244751, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='3', pageStart='221', pageEnd='330', issueExtLink='null', onlineDate='null', pubDate='1741968000000', pubDateStr='2025-03-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793343182320, creator='13701087609', updateTime=1793343182320, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=284, endPage=289, ext={EN=ArticleExt(id=1322940582296957289, articleId=1322940580627624295, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Analysis of Time Frequency Characteristics of Modern GPS_Ⅲ Spaceborne Atomic Clock, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

We use the precise clock offset data released by IGS to analyze the key performance indicators of six GPS-Ⅲ satellite clocks that have been launched and operated in orbit, including frequency accuracy, frequency drift rate, and frequency stability, and compare them with the previous GPS clocks. The results show that rubidium clocks carried by GPS-Ⅲ are generally stable in operation and have good data quality, which is related to the improvement of anti-interference ability. There is no significant change or difference in time frequency performance, which is basically consistent with the previous generation Block ⅡF rubidium clocks. The frequency stability of GPS-Ⅲ rubidium clocks are better, which helps to improve the accuracy of PNT services. The research can provide reference and guidance for the upgrading and transformation of other GNSS system satellites.

, authors=Hanlong CHEN1, Yupu WANG1, Xiaoqing JIANG1, Rui LI1, Zhenfan ZHOU1, authorsList=Hanlong CHEN, Yupu WANG, Xiaoqing JIANG, Rui LI, Zhenfan ZHOU, authorCompany=null, correspAuthors=null, authorNote=

CHEN Hanlong, engineer, majors in satellite navigation and time frequency, E-mail:

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利用IGS发布的精密钟差数据，对已发射并在轨运行的6颗GPS_Ⅲ星钟的频率准确度、频率漂移率和频率稳定度等关键性能指标进行分析，并与前期GPS星钟进行对比。结果表明，GPS_Ⅲ搭载的铷钟整体运行稳定且数据质量较好，可能与抗干扰能力的提升有关，时频性能并无重大变化或明显不同，基本与上一代Block ⅡF铷钟一致，但频率稳定度更优，有助于提升PNT服务精度。研究成果可为其他GNSS系统空间段卫星的升级改造提供借鉴和参考。

, authors=陈汗龙1, 王宇谱1, 蒋孝卿1, 李睿1, 周真帆1, authorsList=陈汗龙, 王宇谱, 蒋孝卿, 李睿, 周真帆, authorCompany=null, correspAuthors=null, authorNote=

陈汗龙，工程师，主要从事卫星导航和时间频率研究，E-mail:

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Journal of Navigation and Positioning, 2023, 11 (6): 28- 33, articleTitle=null, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1322940590798811520, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, xref=null, ext=[AuthorCompanyExt(id=1322940591021109633, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, companyId=1322940590798811520, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1 Beijing Satellite Navigation Center, P O Box 5128, Yongfeng Road, Beijing 100094, China), AuthorCompanyExt(id=1322940591042081154, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, companyId=1322940590798811520, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1 北京卫星导航中心, 北京市永丰路5128信箱, 100094)])], figs=[ArticleFig(id=1322940595219607979, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=EN, label=Fig. 1, caption=GPS satellite clock offsets and RMSE, figureFileSmall=zf72BqHErs1vzzWHqBbLkQ==, figureFileBig=TirswehAyyPS15VKYxSOrw==, tableContent=null), ArticleFig(id=1322940595311882668, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=CN, label=图1, caption=GPS卫星钟差和均方根误差, figureFileSmall=zf72BqHErs1vzzWHqBbLkQ==, figureFileBig=TirswehAyyPS15VKYxSOrw==, tableContent=null), ArticleFig(id=1322940595773256110, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=EN, label=Fig. 2, caption=Clock offsets and RMSE after preprocessing, figureFileSmall=sl1xhc409udqS23V20T+Iw==, figureFileBig=2v13dEcmOpt59Zf6JoF86Q==, tableContent=null), ArticleFig(id=1322940595848753583, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=CN, label=图2, caption=预处理后的钟差和均方根误差, figureFileSmall=sl1xhc409udqS23V20T+Iw==, figureFileBig=2v13dEcmOpt59Zf6JoF86Q==, tableContent=null), ArticleFig(id=1322940596154937777, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=EN, label=Fig. 3, caption=Calculation results of frequency accuracy of GPS satellite clocks, figureFileSmall=E5ns/dfOvpeHLVMAEAV3DQ==, figureFileBig=0iUa2PBHtYB2Nt7pl5RekA==, tableContent=null), ArticleFig(id=1322940596226240946, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=CN, label=图3, caption=GPS星钟频率准确度计算结果, figureFileSmall=E5ns/dfOvpeHLVMAEAV3DQ==, figureFileBig=0iUa2PBHtYB2Nt7pl5RekA==, tableContent=null), ArticleFig(id=1322940596318515635, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=EN, label=Fig. 4, caption=Calculation results of frequency drift of GPS satellite clocks, figureFileSmall=FzET0jY8rw8K2dz+0djkow==, figureFileBig=LswaRDp/AU+rl87qJOHWdQ==, tableContent=null), ArticleFig(id=1322940596377235892, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=CN, label=图4, caption=GPS星钟频率漂移率计算结果, figureFileSmall=FzET0jY8rw8K2dz+0djkow==, figureFileBig=LswaRDp/AU+rl87qJOHWdQ==, tableContent=null), ArticleFig(id=1322940596452733365, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=EN, label=Fig. 5, caption=Calculation results of GPS satellite clocks using overlapping Allan deviation, figureFileSmall=nwuNXLelMobXjY5JqmUT1w==, figureFileBig=93L3/8iV+iGwn4ApL81KFQ==, tableContent=null), ArticleFig(id=1322940596540813750, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=CN, label=图5, caption=GPS星钟重叠阿仑方差计算结果, figureFileSmall=nwuNXLelMobXjY5JqmUT1w==, figureFileBig=93L3/8iV+iGwn4ApL81KFQ==, tableContent=null), ArticleFig(id=1322940596909912503, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=EN, label=Fig. 6, caption=Calculation results of GPS satellite clocks using overlapping Hadamard deviation, figureFileSmall=6uMst2B1Sdg9dDvRAlXywQ==, figureFileBig=GBv9I3Z5x9Oka7jIXjO9hA==, tableContent=null), ArticleFig(id=1322940596977021368, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=CN, label=图6, caption=GPS星钟重叠哈达玛方差计算结果, figureFileSmall=6uMst2B1Sdg9dDvRAlXywQ==, figureFileBig=GBv9I3Z5x9Oka7jIXjO9hA==, tableContent=null), ArticleFig(id=1322940597052518841, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=EN, label=Tab. 1, caption=

Basic information of constellation in GPS modern space segment

, figureFileSmall=null, figureFileBig=null, tableContent=
序号 类型 卫星型号 在轨总数/颗 卫星PRN 原子钟类型
1 传统星座 Block ⅡR 7 G02    G13    G16    G19    G20    G21    G22 铷钟
2 现代星座 Block ⅡR-M 7 G05    G07    G12    G15    G17    G29    G31 铷钟
3 现代星座 Block ⅡF 11 G03    G06    G09    G24    G25    G26    G27    G30    G32 铷钟
G08    G10 铯钟
4 现代星座 GPS_Ⅲ 6 G04    G11    G14    G18    G23    G28 铷钟
), ArticleFig(id=1322940597123822011, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=CN, label=表1, caption=

GPS现代化空间段星座基本信息

, figureFileSmall=null, figureFileBig=null, tableContent=
序号 类型 卫星型号 在轨总数/颗 卫星PRN 原子钟类型
1 传统星座 Block ⅡR 7 G02    G13    G16    G19    G20    G21    G22 铷钟
2 现代星座 Block ⅡR-M 7 G05    G07    G12    G15    G17    G29    G31 铷钟
3 现代星座 Block ⅡF 11 G03    G06    G09    G24    G25    G26    G27    G30    G32 铷钟
G08    G10 铯钟
4 现代星座 GPS_Ⅲ 6 G04    G11    G14    G18    G23    G28 铷钟
), ArticleFig(id=1322940597316759997, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=EN, label=Tab. 2, caption=

Statistics of RMSE

, figureFileSmall=null, figureFileBig=null, tableContent=
类型 卫星PRN及均方根误差/ns 最大/ns 最小/ns 平均/ns
Block ⅡR G02 G13 G16 G19 G21 G22 3.45 0.82 1.526
1.32 3.45 0.96 1.25 1.36 0.82
Block ⅡR-M G05 G07 G12 G15 G29 G31 5.90 0.99 2.595
1.62 1.96 1.05 0.99 4.05 5.90
Block ⅡF G06 G08 G09 G10 G24 G25 6.08 0.89 2.381
0.89 6.08 1.10 5.00 3.98 1.01
G26 G30 G32 - - -
1.16 1.30 0.91 - - -
GPS_Ⅲ G04 G11 G14 G18 G23 G28 1.15 0.78 0.912
0.83 0.90 0.92 0.89 0.78 1.15
), ArticleFig(id=1322940597400646078, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=CN, label=表2, caption=

RMDE统计

, figureFileSmall=null, figureFileBig=null, tableContent=
类型 卫星PRN及均方根误差/ns 最大/ns 最小/ns 平均/ns
Block ⅡR G02 G13 G16 G19 G21 G22 3.45 0.82 1.526
1.32 3.45 0.96 1.25 1.36 0.82
Block ⅡR-M G05 G07 G12 G15 G29 G31 5.90 0.99 2.595
1.62 1.96 1.05 0.99 4.05 5.90
Block ⅡF G06 G08 G09 G10 G24 G25 6.08 0.89 2.381
0.89 6.08 1.10 5.00 3.98 1.01
G26 G30 G32 - - -
1.16 1.30 0.91 - - -
GPS_Ⅲ G04 G11 G14 G18 G23 G28 1.15 0.78 0.912
0.83 0.90 0.92 0.89 0.78 1.15
), ArticleFig(id=1322940597476143551, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=EN, label=Tab. 3, caption=

Comparison of time frequency characteristics between GPS_Ⅲ and other GPS satellite clocks

, figureFileSmall=null, figureFileBig=null, tableContent=
序号 星载钟类型 评估总数/颗 剔除星数/颗 频率准确度(均值) 天漂移率(均值) 频率稳定度(均值)
100 s 1 000 s 3 600 s 1万s 1 d
1 Block ⅡR 7 1 5.01×10-12 7.70×10-15 1.79×10-12 2.69×10-13 7.96×10-14 5.24×10-14 9.87×10-15
2 Block ⅡR-M 7 1 3.21×10-12 4.39×10-15 1.97×10-12 2.63×10-13 7.59×10-14 5.89×10-14 1.30×10-14
3 Block ⅡF 11 2 5.37×10-12 1.84×10-14 5.58×10-13 1.72×10-13 8.89×10-14 6.52×10-14 1.79×10-14
4 GPS_Ⅲ 6 0 1.03×10-11 2.48×10-14 1.71×10-13 4.44×10-14 2.38×10-14 2.25×10-14 6.00×10-15
), ArticleFig(id=1322940597740384704, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940580627624295, language=CN, label=表3, caption=

GPS_Ⅲ与其他GPS星钟时频特性结果对比

, figureFileSmall=null, figureFileBig=null, tableContent=
序号 星载钟类型 评估总数/颗 剔除星数/颗 频率准确度(均值) 天漂移率(均值) 频率稳定度(均值)
100 s 1 000 s 3 600 s 1万s 1 d
1 Block ⅡR 7 1 5.01×10-12 7.70×10-15 1.79×10-12 2.69×10-13 7.96×10-14 5.24×10-14 9.87×10-15
2 Block ⅡR-M 7 1 3.21×10-12 4.39×10-15 1.97×10-12 2.63×10-13 7.59×10-14 5.89×10-14 1.30×10-14
3 Block ⅡF 11 2 5.37×10-12 1.84×10-14 5.58×10-13 1.72×10-13 8.89×10-14 6.52×10-14 1.79×10-14
4 GPS_Ⅲ 6 0 1.03×10-11 2.48×10-14 1.71×10-13 4.44×10-14 2.38×10-14 2.25×10-14 6.00×10-15
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现代化GPS_Ⅲ星载原子钟时频特性分析
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陈汗龙 1 , 王宇谱 1 , 蒋孝卿 1 , 李睿 1 , 周真帆 1
大地测量与地球动力学 | 现代大地测量 2025,45(3): 284-289
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大地测量与地球动力学 |现代大地测量 2025 , 45 (3) : 284 -289
现代化GPS_Ⅲ星载原子钟时频特性分析
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陈汗龙1 , 王宇谱1, 蒋孝卿1, 李睿1, 周真帆1
作者信息
  • 1 北京卫星导航中心, 北京市永丰路5128信箱, 100094
作者简介:

陈汗龙，工程师，主要从事卫星导航和时间频率研究，E-mail:

Analysis of Time Frequency Characteristics of Modern GPS_Ⅲ Spaceborne Atomic Clock
Hanlong CHEN1 , Yupu WANG1, Xiaoqing JIANG1, Rui LI1, Zhenfan ZHOU1
Affiliations
  • 1 Beijing Satellite Navigation Center, P O Box 5128, Yongfeng Road, Beijing 100094, China

    • CHEN Hanlong, engineer, majors in satellite navigation and time frequency, E-mail:

出版时间: 2025-03-15 doi: 10.14075/j.jgg.2024.04.149
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摘要
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利用IGS发布的精密钟差数据，对已发射并在轨运行的6颗GPS_Ⅲ星钟的频率准确度、频率漂移率和频率稳定度等关键性能指标进行分析，并与前期GPS星钟进行对比。结果表明，GPS_Ⅲ搭载的铷钟整体运行稳定且数据质量较好，可能与抗干扰能力的提升有关，时频性能并无重大变化或明显不同，基本与上一代Block ⅡF铷钟一致，但频率稳定度更优，有助于提升PNT服务精度。研究成果可为其他GNSS系统空间段卫星的升级改造提供借鉴和参考。

GPS_Ⅲ  /  星载原子钟  /  时频特性  /  频率稳定度

We use the precise clock offset data released by IGS to analyze the key performance indicators of six GPS-Ⅲ satellite clocks that have been launched and operated in orbit, including frequency accuracy, frequency drift rate, and frequency stability, and compare them with the previous GPS clocks. The results show that rubidium clocks carried by GPS-Ⅲ are generally stable in operation and have good data quality, which is related to the improvement of anti-interference ability. There is no significant change or difference in time frequency performance, which is basically consistent with the previous generation Block ⅡF rubidium clocks. The frequency stability of GPS-Ⅲ rubidium clocks are better, which helps to improve the accuracy of PNT services. The research can provide reference and guidance for the upgrading and transformation of other GNSS system satellites.

GPS_Ⅲ  /  spaceborne atomic clock  /  time frequency characteristics  /  frequency stability
陈汗龙, 王宇谱, 蒋孝卿, 李睿, 周真帆. 现代化GPS_Ⅲ星载原子钟时频特性分析. 大地测量与地球动力学, 2025 , 45 (3) : 284 -289 . DOI: 10.14075/j.jgg.2024.04.149
Hanlong CHEN, Yupu WANG, Xiaoqing JIANG, Rui LI, Zhenfan ZHOU. Analysis of Time Frequency Characteristics of Modern GPS_Ⅲ Spaceborne Atomic Clock[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (3) : 284 -289 . DOI: 10.14075/j.jgg.2024.04.149
正文
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截至2023-12，GPS空间段共有31颗卫星在轨运行并提供服务，包含4种新旧类型的导航卫星，分别为Block Ⅱ R、Block Ⅱ R-M、Block Ⅱ F和GPS_Ⅲ，除Block Ⅱ R为传统体制卫星外，其余均为现代化卫星，早期的Block ⅡA卫星已于2019年全部退役，GPS星座组成具体信息如表1[1]所示。
Block Ⅱ R为旧体制卫星，共7颗在轨提供服务，均搭载铷钟，在1997—2004年投入运行。Block Ⅱ R-M、Block Ⅱ F为新体制卫星，分别有7颗和11颗，除Block Ⅱ F搭载2颗铯钟外，其余均搭载铷钟，在2005—2016年陆续投入运行[1]。GPS_Ⅲ为最新体制卫星，其设计和产生一方面是为满足不断增长的民用PNT服务需求[2]，另一方面是为获取军事上绝对的制太空权和制导航权。
GPS_Ⅲ新体制卫星作为GPS系统现代化改造的重要组成部分，计划生产10颗，卫星采用最先进的技术手段，精度和抗干扰能力与前期GPS卫星相比分别提高3倍和8倍，同时可在原有信号基础上播发新的L1C民用信号，与Galileo等国际全球卫星导航系统兼容。2018年至今，已有6颗GPS_Ⅲ卫星发射并提供在轨服务。星载原子钟(以下简称星钟)是导航卫星的重要载荷，负责建立和维持星上单元的时间基准，其性能会直接影响PNT服务的精度和可用性。贾小林等[3]对GPS系统Block Ⅱ F和Block Ⅱ R等类型星钟进行评估；文献[4-5]对北斗星钟性能进行研究；韩有文[6]对Galileo星钟特性进行分析；文献[7-8]对GPS_Ⅲ星钟进行研究，但当时GPS_Ⅲ卫星数量不多且在轨运行时间不长。针对GPS_Ⅲ星钟时频性能相关研究较少的问题，本文利用国际GNSS服务组织(international GNSS service, IGS)发布的精密钟差产品，对在轨运行的GPS星钟关键时频性能进行评估，并对比GPS_Ⅲ与前期GPS星钟的性能指标，深入了解GPS现代化星钟性能现状，分析其未来发展方向，为其他卫星导航系统星钟建设提供参考。
1 数据来源和预处理
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1.1 数据来源
高质量的卫星钟差数据是分析星钟时频特性的基础，为客观准确地分析GPS_Ⅲ星钟性能，需要获取较长时间的稳定连续精密钟差数据。当前国际上精度最高的钟差数据产品由多GNSS实验项目(multi-GNSS experiment, MGEX)提供，截至2024-03，IGS共有6个全球数据中心，515个监测站点，产品测量标准差为20 ps。选取MGEX德国地学研究中心(GFZ)发布的采样间隔为30 s的事后GPS精密卫星钟差产品对星钟时频特性进行分析评估，数据时间段为2024-01-01—30。
1.2 星钟数据预处理
卫星钟差数据预处理包括获取完好的卫星钟差序列和计算均方根误差(root mean square error, RMSE)。获取完好的GPS卫星钟差序列主要是对IGS发布的每日GPS钟差数据进行整合，补偿和平滑台阶跳项，剔除钟差野值和跳变值，通过线性拟合对缺漏数值进行内插，然后扣除30 d的相位均值。RMSE可衡量测量值与真实值之间的偏差，根据RMSE结果可将明显异常的星钟剔除，避免因单一星钟异常而影响整体评估结果。考虑到GPS星钟绝大部分使用铷原子钟，存在明显的频率漂移，将最小二乘法拟合结果作为真值进行计算，RMSE结果较大或明显偏离均值的卫星可能存在调频、变频或监测异常，不参与评估并将其剔除。GPS四种新旧体制卫星剔除异常星钟前后的完好钟差序列、RMSE结果如图1、2所示。除GPS_Ⅲ外，其他3种类型卫星中各有1颗卫星由于RMSE过大(≥10 ns)且存在调频或明显异常被剔除出评估钟组，表2为RMSE统计结果。
从表2可以看出，即使剔除钟差数据异常的星钟，前3种类型卫星的RMSE结果仍然较大，约为GPS_Ⅲ的2~3倍，RMSE均值分别为1.526 ns、2.595 ns、2.381 ns和0.912 ns，表明GPS_Ⅲ类型星钟整体波动幅度最小。此外，RMSE结果小于1 ns的星钟共有10颗，其中GPS_Ⅲ占比50%，说明GPS_Ⅲ星钟基本保持在同一水平，性能更加接近，而Block Ⅱ F最大值与最小值之差达到5.19 ns，各星钟差距较大。根据数据预处理结果，认为可以对GPS_Ⅲ星钟时频特性做进一步的对比评估分析。
2 GPS_Ⅲ星钟时频特性评估
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GPS_Ⅲ星钟时频特性评估主要是对时频关键性能指标进行分析，包含频率准确度、频率漂移率和频率稳定度3个部分内容。为获得客观、综合的评价结果，同样将2024-01表现异常的星钟剔除，然后利用§1.2预处理后的精密钟差数据，计算所有GPS星钟关键性能指标，并按照不同类型进行分类，采取对比分析法对GPS_Ⅲ与其他3种新旧体制类型星钟进行评估分析。
2.1 GPS_Ⅲ频率准确度
频率准确度在时域上通常有3种计算方法：最小二乘线性拟合法、相位差平均法和端点相差法[9]。第1种方法最常用，优势在于可以更好地分辨出调相白噪声；第2种方法使用较普遍，适用于调频白噪声计算；第3种方法较简单，利用数据序列的首尾值之差进行计算，但可信度不高。本文采用最常用的最小二乘线性拟合法对GPS_Ⅲ及其他类型GPS星钟的频率准确度进行对比计算，结果如图3所示，图中红色为GPS_Ⅲ星钟，蓝色为其余类型星钟。从图中可以看出，GPS_Ⅲ星钟的频率准确度并不高，在7.48×10-12~1.40×10-11之间，均值为1.03×10-11，整体上不如其他类型星钟；Block Ⅱ R-M的频率准确度最高，均值为3.21×10-12，其中G29和G31星钟更是达到10-13量级；Block Ⅱ R和Block Ⅱ F的频率准确度相差不大，均值分别为5.01×10-12和5.37× 10-12。原因可能为：一是GPS_Ⅲ星钟在轨运行时间整体不长，未对频率准确度进行系统性校准和修正；二是当前GPS星钟的频率准确度已经能够满足使用需求，并且可以通过星钟模型进行精确预报和消除，未在设计上对频率准确度进行更多优化。
2.2 GPS_Ⅲ频率漂移率
频率漂移率在时域上通常有4种计算方法[10]：最小二乘二次拟合法、第二差相位平均法、三点差法和Greenhall方法。第1种方法应用最广，是标准的漂移率计算方法；第2种方法适用于随机游走噪声计算；第3种方法取数据序列的首尾值和中间值，适用于调频白噪声和随机游走噪声计算；第4种方法不常用，但适用于多种类型噪声计算。本文采用标准的最小二乘二次拟合法对频率漂移率进行计算，结果如图4所示，图中红色为GPS_Ⅲ星钟，蓝色为其他类型星钟。由图可知，GPS_Ⅲ星钟的天漂移率在8.81×10-15~4.47×10-14之间，GPS_Ⅲ与Block Ⅱ F的天漂移率均值分别为2.48×10-14和1.84×10-14，明显大于Block Ⅱ R和Block Ⅱ R-M，两者均值分别为7.7×10-15和4.39×10-15。可以看出，GPS_Ⅲ未对频率漂移率相关性能进行提升和优化，与Block Ⅱ F基本处于同一水平，在技术设计上延续了Block Ⅱ F铷钟的性能，而频率漂移率只要进行精确测量同样可以通过模型进行扣除和预报，不会影响各类PNT服务精度。
2.3 GPS_Ⅲ频率稳定度
频率稳定度既可以在时域进行分析，也可以在频域进行分析，因瞬时频率难以测量，通常在时域进行计算。时域上频率稳定度分析最经典的方法为阿仑方差，后续基于该方法又延伸出多种方差类型，如哈达玛方差、修正阿仑方差和总方差等[11-12]。目前时域上频率稳定度评估方法主要集中在阿仑(或重叠阿仑)方差、哈达玛(或重叠哈达玛)方差中的一种或两种，导致在研究过程中缺乏横向比较，如单独使用阿仑方差无法区分出调相白噪声和调相闪烁噪声对星钟的影响[9]。由于星载铷钟的频率漂移率较高，需要考虑其对评估结果的影响，本文采用重叠阿仑方差和重叠哈达玛方差同时对GPS_Ⅲ星钟频率稳定度进行计算，结果如图5~6所示。
图5、6中红色线条为GPS_Ⅲ星钟频率稳定度对数曲线，其余线条为其他类型星钟计算结果。从重叠阿仑方差结果可以看出，GPS_Ⅲ在3万s以下时频率稳定度优于Block Ⅱ R和Block Ⅱ R-M，百秒和千秒频率稳定度均在2×10-13和5×10-14以内，但在4万s以上时频率稳定度开始逐渐变差，明显低于后两者；而重叠哈达玛方差结果显示，GPS_Ⅲ频率稳定度整体上优于Block Ⅱ R和Block Ⅱ R-M，不仅短期稳定度好，且中长期(3万s至10万s)稳定度仍然保持在5×10-15~1×10-14之间，Block Ⅱ F与GPS_Ⅲ的频率稳定度大体一致，但Block Ⅱ F搭载铯原子钟的G08和G10表现较差，如图6中上方2条黑色线条所示。通过分析可知，GPS_Ⅲ星载铷钟具有典型的频率漂移现象，利用重叠哈达玛方差扣除频率漂移影响后，无论是短期还是中长期稳定度都表现最优，可以将星钟模型随机项的波动值降到最低，显著提升星钟模型预报精度，进而提高PNT服务精度。
对GPS_Ⅲ及其他类型GPS星钟的频率准确度、频率漂移率和频率稳定度结果进行汇总和对比，其中频率稳定度选取重叠哈达玛方差结果，该结果可以明显抑制铷钟频率漂移带来的影响，具体对比结果如表3所示。
从表3可以看出，在频率准确度方面，GPS_Ⅲ表现较差，频率准确度对应星钟二次多项式模型中A1值，说明以标称频率为参考，GPS_Ⅲ实际输出频率在单位时间内单调递增或递减的幅度更大；在频率漂移率方面，GPS_Ⅲ与Block Ⅱ F相当，同处1×10-14量级，频率漂移率对应星钟二次多项式模型中A2值，反映出GPS_Ⅲ星钟输出频率随时间单调变化的速度较大；在频率稳定度方面，GPS_Ⅲ表现最好，明显优于其他3种类型星钟，特别是在3 600 s以下时，最多高出近1个数量级。
3 结语
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根据GPS现代化建设相关计划，结合GPS_Ⅲ星钟时频特性评估结果，可以得到以下结论：1)现代化GPS_Ⅲ铷钟的时频性能并无重大变化或明显不同，整体性能指标与Block Ⅱ F铷钟基本相当，总体技术沿用上一代铷钟，能满足当前的服务需求；2)GPS_Ⅲ在时频性能上更注重频率稳定度的表现，并未将性能提升的关注点放在可预报的频率准确度和频率漂移率上，因为后者可以通过精确建模进行预报和消除，而前者会直接影响PNT服务精度，GPS_Ⅲ无论是短期还是中长期的频率稳定度均最优；3)GPS_Ⅲ运行稳定且整体数据质量较好，当月无任何星钟被剔除或设置为不可用，从RMSE结果还可以看出，GPS_Ⅲ星钟波动最小，有助于提升PNT服务精度，这可能与现代化GPS抗干扰性能的提升有关；4)由GPS_Ⅲ的RMSE波动趋势一致可以判断，目前星地钟差的测量不确定度已经制约短期频率稳定度的提升，这种情况通常是由同一种测量噪声所造成[12]。GPS系统空间段的现代化升级还在持续进行，可持续关注其星钟时频性能、技术状态和发展趋势，为其他GNSS系统空间段卫星的升级改造提供借鉴和参考。

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2025年第45卷第3期
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doi: 10.14075/j.jgg.2024.04.149
  • 接收时间：2024-04-03
  • 首发时间：2026-10-30
  • 出版时间：2025-03-15
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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