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Article(id=1322506580612985692, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322506567065383670, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.07.345, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1721059200000, receivedDateStr=2024-07-16, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793239739801, onlineDateStr=2026-10-29, pubDate=1752508800000, pubDateStr=2025-07-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793239739801, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793239739801, creator=13701087609, updateTime=1793239739801, updator=13701087609, issue=Issue{id=1322506567065383670, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='7', pageStart='661', pageEnd='770', issueExtLink='null', onlineDate='null', pubDate='1752508800000', pubDateStr='2025-07-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793239736572, creator='13701087609', updateTime=1793239736572, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=718, endPage=724, ext={EN=ArticleExt(id=1322506580814312285, articleId=1322506580612985692, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Comparison and Analysis of PPP Performance Enhanced by Several Typical LEO Constellations in China, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

A constellation performance evaluation is conducted using the number of visible satellite and position dilution of precision(PDOP) of three low Earth orbit(LEO) constellations Hongyan, CentiSpace, and Hongyun in China. Simulated LEO data is combined with GNSS observation data from 12 evenly distributed stations to enhance precise point positioning(PPP). The performance enhancement effects of three LEO constellations on GPS/GLONASS/BDS/Galileo PPP are compared and analyzed in static and simulated dynamic modes. The results show that after the enhancement of Hongyan, CentiSpace, and Hongyun LEO constellations, the average static PPP convergence time of all stations is reduced by 64%, 77%, and 80%, the static PPP accuracy is improved by 33%, 36%, and 43%, respectively. The dynamic PPP convergence time is reduced by 67%, 76%, and 86%, the dynamic PPP accuracy is improved by 10%, 17%, and 16%, respectively. Overall, the PPP enhancement performance of CentiSpace and Hongyun LEO constellations is more significant compared to Hongyan constellation, and the enhancement performance is generally positively correlated with constellation size.

, authors=Chengjian CHEN1, Changsheng CAI1, *, Lin PAN1, Wujiao DAI1, authorsList=Chengjian CHEN, Changsheng CAI, Lin PAN, Wujiao DAI, authorCompany=null, correspAuthors=Changsheng CAI, authorNote=

CHEN Chengjian, postgraduate, majors in GNSS PPP enhanced by LEO constellations, E-mail:

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针对国内的微厘空间、鸿雁和虹云工程3个低轨星座，从可见卫星数和位置精度衰减因子(PDOP)两个方面进行星座性能评估，并使用仿真的低轨数据结合全球均匀分布的12个测站实测的GNSS观测数据进行增强精密单点定位(PPP)处理，对比分析3个低轨星座在静态和模拟动态模式下对GPS/GLONASS/BDS/Galileo四星座PPP性能的增强效果。结果表明，通过鸿雁、微厘空间、虹云工程低轨星座增强后，所有测站平均静态PPP收敛时间分别降低64%、77%和80%，静态PPP定位精度分别提升33%、36%和43%；动态PPP收敛时间分别降低67%、76%和86%，动态PPP定位精度分别提升10%、17%和16%。综合来看，微厘空间和虹云工程两个低轨星座PPP性能增强效果相比鸿雁星座更为显著，增强程度总体上与星座规模呈正相关。

, authors=陈成俭1, 蔡昌盛1, *, 潘林1, 戴吾蛟1, authorsList=陈成俭, 蔡昌盛, 潘林, 戴吾蛟, authorCompany=null, correspAuthors=蔡昌盛, authorNote=

陈成俭，硕士生，主要从事低轨增强GNSS精密单点定位研究，E-mail:

, correspAuthorsNote=

蔡昌盛，博士，教授，博士生导师，主要从事GNSS导航和精密定位研究，E-mail:

CAI Changsheng, PhD, professor, PhD supervisor, majors in GNSS navigation and precise positioning, E-mail:

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CHEN Chengjian, postgraduate, majors in GNSS PPP enhanced by LEO constellations, E-mail:

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Journal of Navigation and Positioning, 2022, 10 (2): 58- 67, articleTitle=null, refAbstract=null)], funds=[Fund(id=1322506594328359854, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506580612985692, awardId=2020YFA0713501, language=EN, fundingSource=National Key Research and Development Program of China(2020YFA0713501), fundOrder=null, country=null), Fund(id=1322506594399663023, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506580612985692, awardId=2020YFA0713501, language=CN, fundingSource=国家重点研发计划(2020YFA0713501), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1322506584857621360, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506580612985692, xref=null, ext=[AuthorCompanyExt(id=1322506584870204273, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506580612985692, companyId=1322506584857621360, language=EN, country=null, province=null, city=null, 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error time series of four positioning schemes at AJAC, BRST, and DJIG stations, figureFileSmall=lKWplYJagZ4rqzQldq32uQ==, figureFileBig=KwOO+qrvOIJ2WkZyOv4FMw==, tableContent=null), ArticleFig(id=1322506592927462309, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506580612985692, language=CN, label=图8, caption=AJAC、BRST、DJIG测站4种定位方案动态PPP误差时间序列, figureFileSmall=lKWplYJagZ4rqzQldq32uQ==, figureFileBig=KwOO+qrvOIJ2WkZyOv4FMw==, tableContent=null), ArticleFig(id=1322506593002959782, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506580612985692, language=EN, label=Tab. 1, caption=

Parameters of CentiSpace, Hongyan, and Hongyun constellations

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LEO星座 微厘空间 鸿雁 虹云工程
卫星总数 120 30 72 156
轨道面数 12 3 9 13
相位因子 0 0 1 1
轨道高度/km 975 1 200 1 120 1 040
轨道倾角/(°) 55 85 86.5 80
), ArticleFig(id=1322506593086845863, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506580612985692, language=CN, label=表1, caption=

微厘空间、鸿雁和虹云工程星座参数

, figureFileSmall=null, figureFileBig=null, tableContent=
LEO星座 微厘空间 鸿雁 虹云工程
卫星总数 120 30 72 156
轨道面数 12 3 9 13
相位因子 0 0 1 1
轨道高度/km 975 1 200 1 120 1 040
轨道倾角/(°) 55 85 86.5 80
), ArticleFig(id=1322506593770517416, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506580612985692, language=EN, label=Tab. 2, caption=

Simulation parameters setting

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类别 设置
精密星历采样间隔 30 s
轨道径向/切向/法向误差 1/1/1 cm
钟差标准差 0.006 ns
观测值采样间隔 1 s
观测数据 实测GREC数据/仿真LEO数据
仿真观测值类型 非差伪距和载波相位观测值
仿真观测值频段 L1/L2
伪距/载波相位噪声 0.3 m/1 cm
), ArticleFig(id=1322506593879569321, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506580612985692, language=CN, label=表2, caption=

仿真参数设置

, figureFileSmall=null, figureFileBig=null, tableContent=
类别 设置
精密星历采样间隔 30 s
轨道径向/切向/法向误差 1/1/1 cm
钟差标准差 0.006 ns
观测值采样间隔 1 s
观测数据 实测GREC数据/仿真LEO数据
仿真观测值类型 非差伪距和载波相位观测值
仿真观测值频段 L1/L2
伪距/载波相位噪声 0.3 m/1 cm
), ArticleFig(id=1322506593955066794, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506580612985692, language=EN, label=Tab. 3, caption=

Precise point positioning solution strategies

, figureFileSmall=null, figureFileBig=null, tableContent=
类别 处理策略或配置
日期 2024-01-01
卫星系统 GREC/GRECL
定位模式 静态/动态；模糊度浮点解
函数模型 双频无电离层组合
随机模型 高度角随机模型
估计器 扩展Kalman滤波
滤波形式 前向滤波
卫星截止高度角 7°
重初始化 每4 h对所有待求参数进行初始化
卫星轨道 IGS精密产品/仿真LEO轨道
卫星钟差 IGS精密产品/仿真LEO钟差
卫星天线PCO/PCV igs14.atx文件改正
相对论效应 模型改正
电离层延迟误差 双频消电离层
对流层延迟误差 Saastamoinen模型改正干延迟/随机游走估计湿延迟
接收机钟差 白噪声估计
ISB或IFB 白噪声估计
地球潮汐 改正地球固体潮和极潮
), ArticleFig(id=1322506594030564267, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506580612985692, language=CN, label=表3, caption=

PPP解算策略

, figureFileSmall=null, figureFileBig=null, tableContent=
类别 处理策略或配置
日期 2024-01-01
卫星系统 GREC/GRECL
定位模式 静态/动态；模糊度浮点解
函数模型 双频无电离层组合
随机模型 高度角随机模型
估计器 扩展Kalman滤波
滤波形式 前向滤波
卫星截止高度角 7°
重初始化 每4 h对所有待求参数进行初始化
卫星轨道 IGS精密产品/仿真LEO轨道
卫星钟差 IGS精密产品/仿真LEO钟差
卫星天线PCO/PCV igs14.atx文件改正
相对论效应 模型改正
电离层延迟误差 双频消电离层
对流层延迟误差 Saastamoinen模型改正干延迟/随机游走估计湿延迟
接收机钟差 白噪声估计
ISB或IFB 白噪声估计
地球潮汐 改正地球固体潮和极潮
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Average positioning accuracy and convergence time of kinematic PPP at each station for 4 schemes

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测站 星座方案
GREC/GREC+鸿雁/GREC+微厘空间/GREC+虹云工程
E/cm N/cm U/cm 收敛时间/min
AJAC 2.4/2.2/1.2/1.5 1.4/1.3/1.4/1.2 3.5/3.4/4.8/3.6 19.5/4.3/5.4/2.1
BRST 2.5/1.5/1.4/1.3 1.5/1.5/1.7/1.8 4.7/4.2/4.8/4.8 23.5/6.2/3.2/3.1
DJIG 3.2/3.4/2.2/2.6 1.5/1.5/1.5/1.4 5.8/5.2/5.0/4.7 20.3/5.1/3.2/1.4
GAMG 1.9/1.8/1.5/1.5 1.6/1.6/1.5/1.4 3.0/3.1/3.1/3.2 17.6/6.2/4.2/2.2
KERG 2.5/1.6/1.4/1.7 2.3/2.1/2.1/2.0 6.9/4.8/4.3/4.8 23.1/7.7/5.8/2.2
LMMF 2.3/2.1/2.3/2.2 2.4/2.4/2.8/2.6 6.2/5.6/5.1/5.2 28.5/5.8/5.8/4.6
MAR6 2.9/1.8/1.2/1.3 1.3/1.1/1.2/1.2 4.3/4.5/4.2/3.9 13.0/2.7/3.3/2.9
NKLG 3.6/3.1/2.5/3.1 1.4/1.2/1.1/1.2 5.2/4.0/3.5/3.7 19.5/7.4/2.5/1.9
PTGG 2.3/2.6/1.7/2.3 1.9/1.9/1.5/1.6 5.7/5.5/4.3/5.0 13.4/6.3/3.5/2.0
SCRZ 2.5/2.7/2.3/2.7 2.4/2.3/2.2/2.1 8.1/5.1/4.3/4.4 17.9/4.3/4.0/5.9
THTI 4.7/3.5/2.9/3.2 1.9/2.2/2.4/2.5 9.3/8.6/6.4/5.5 20.4/11.5/7.9/2.9
YEL2 1.9/1.3/1.3/1.3 2.1/1.5/1.4/1.2 4.3/3.8/3.9/4.3 14.8/6.9/4.7/1.3
), ArticleFig(id=1322506594236085165, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506580612985692, language=CN, label=表4, caption=

4种方案动态PPP各测站平均定位精度与收敛时间

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测站 星座方案
GREC/GREC+鸿雁/GREC+微厘空间/GREC+虹云工程
E/cm N/cm U/cm 收敛时间/min
AJAC 2.4/2.2/1.2/1.5 1.4/1.3/1.4/1.2 3.5/3.4/4.8/3.6 19.5/4.3/5.4/2.1
BRST 2.5/1.5/1.4/1.3 1.5/1.5/1.7/1.8 4.7/4.2/4.8/4.8 23.5/6.2/3.2/3.1
DJIG 3.2/3.4/2.2/2.6 1.5/1.5/1.5/1.4 5.8/5.2/5.0/4.7 20.3/5.1/3.2/1.4
GAMG 1.9/1.8/1.5/1.5 1.6/1.6/1.5/1.4 3.0/3.1/3.1/3.2 17.6/6.2/4.2/2.2
KERG 2.5/1.6/1.4/1.7 2.3/2.1/2.1/2.0 6.9/4.8/4.3/4.8 23.1/7.7/5.8/2.2
LMMF 2.3/2.1/2.3/2.2 2.4/2.4/2.8/2.6 6.2/5.6/5.1/5.2 28.5/5.8/5.8/4.6
MAR6 2.9/1.8/1.2/1.3 1.3/1.1/1.2/1.2 4.3/4.5/4.2/3.9 13.0/2.7/3.3/2.9
NKLG 3.6/3.1/2.5/3.1 1.4/1.2/1.1/1.2 5.2/4.0/3.5/3.7 19.5/7.4/2.5/1.9
PTGG 2.3/2.6/1.7/2.3 1.9/1.9/1.5/1.6 5.7/5.5/4.3/5.0 13.4/6.3/3.5/2.0
SCRZ 2.5/2.7/2.3/2.7 2.4/2.3/2.2/2.1 8.1/5.1/4.3/4.4 17.9/4.3/4.0/5.9
THTI 4.7/3.5/2.9/3.2 1.9/2.2/2.4/2.5 9.3/8.6/6.4/5.5 20.4/11.5/7.9/2.9
YEL2 1.9/1.3/1.3/1.3 2.1/1.5/1.4/1.2 4.3/3.8/3.9/4.3 14.8/6.9/4.7/1.3
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国内几种典型低轨星座增强PPP性能对比分析
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陈成俭 1 , 蔡昌盛 1, * , 潘林 1 , 戴吾蛟 1
大地测量与地球动力学 | 现代大地测量 2025,45(7): 718-724
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大地测量与地球动力学 |现代大地测量 2025 , 45 (7) : 718 -724
国内几种典型低轨星座增强PPP性能对比分析
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陈成俭1 , 蔡昌盛1, * , 潘林1, 戴吾蛟1
作者信息
  • 1 中南大学地球科学与信息物理学院, 长沙市麓山南路932号, 410083
通讯作者:

蔡昌盛，博士，教授，博士生导师，主要从事GNSS导航和精密定位研究，E-mail:

CAI Changsheng, PhD, professor, PhD supervisor, majors in GNSS navigation and precise positioning, E-mail:

作者简介:

陈成俭，硕士生，主要从事低轨增强GNSS精密单点定位研究，E-mail:

Comparison and Analysis of PPP Performance Enhanced by Several Typical LEO Constellations in China
Chengjian CHEN1 , Changsheng CAI1, * , Lin PAN1, Wujiao DAI1
Affiliations
  • 1 School of Geosciences and Info-Physics, Central South University, 932 South-Lushan Road, Changsha 410083, China

    • CHEN Chengjian, postgraduate, majors in GNSS PPP enhanced by LEO constellations, E-mail:

出版时间: 2025-07-15 doi: 10.14075/j.jgg.2024.07.345
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摘要
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针对国内的微厘空间、鸿雁和虹云工程3个低轨星座，从可见卫星数和位置精度衰减因子(PDOP)两个方面进行星座性能评估，并使用仿真的低轨数据结合全球均匀分布的12个测站实测的GNSS观测数据进行增强精密单点定位(PPP)处理，对比分析3个低轨星座在静态和模拟动态模式下对GPS/GLONASS/BDS/Galileo四星座PPP性能的增强效果。结果表明，通过鸿雁、微厘空间、虹云工程低轨星座增强后，所有测站平均静态PPP收敛时间分别降低64%、77%和80%，静态PPP定位精度分别提升33%、36%和43%；动态PPP收敛时间分别降低67%、76%和86%，动态PPP定位精度分别提升10%、17%和16%。综合来看，微厘空间和虹云工程两个低轨星座PPP性能增强效果相比鸿雁星座更为显著，增强程度总体上与星座规模呈正相关。

低轨星座  /  GNSS  /  PPP  /  定位精度  /  收敛时间

A constellation performance evaluation is conducted using the number of visible satellite and position dilution of precision(PDOP) of three low Earth orbit(LEO) constellations Hongyan, CentiSpace, and Hongyun in China. Simulated LEO data is combined with GNSS observation data from 12 evenly distributed stations to enhance precise point positioning(PPP). The performance enhancement effects of three LEO constellations on GPS/GLONASS/BDS/Galileo PPP are compared and analyzed in static and simulated dynamic modes. The results show that after the enhancement of Hongyan, CentiSpace, and Hongyun LEO constellations, the average static PPP convergence time of all stations is reduced by 64%, 77%, and 80%, the static PPP accuracy is improved by 33%, 36%, and 43%, respectively. The dynamic PPP convergence time is reduced by 67%, 76%, and 86%, the dynamic PPP accuracy is improved by 10%, 17%, and 16%, respectively. Overall, the PPP enhancement performance of CentiSpace and Hongyun LEO constellations is more significant compared to Hongyan constellation, and the enhancement performance is generally positively correlated with constellation size.

LEO constellation  /  GNSS  /  PPP  /  positioning accuracy  /  convergence time
陈成俭, 蔡昌盛, 潘林, 戴吾蛟. 国内几种典型低轨星座增强PPP性能对比分析. 大地测量与地球动力学, 2025 , 45 (7) : 718 -724 . DOI: 10.14075/j.jgg.2024.07.345
Chengjian CHEN, Changsheng CAI, Lin PAN, Wujiao DAI. Comparison and Analysis of PPP Performance Enhanced by Several Typical LEO Constellations in China[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (7) : 718 -724 . DOI: 10.14075/j.jgg.2024.07.345
正文
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随着全球导航卫星系统(GNSS)的广泛应用，定位、导航和授时(PNT)服务已经成为现代社会的重要基础设施[1]。精密单点定位(PPP)作为GNSS主流技术之一，收敛后定位精度可达cm级。然而，受GNSS自身星座构型的限制，较长的收敛时间会极大地限制PPP的应用[2]。低地球轨道(LEO)卫星相较于GNSS中高轨卫星，轨道高度更低、运行速度更快，具有短时延和低功耗的特点，若LEO卫星和中高轨卫星发射相同功率的信号，抵达地球表面的信号功率将比中高轨卫星高出30 dB(即1 000倍)，这种更强的落地信号功率可以在复杂地形环境和电磁环境下改善定位效果，提升抗干扰和反欺骗能力[3]。此外，LEO卫星运行1 min所经历的几何变化相当于中轨卫星运行20 min的情况，短时间的快速几何变化可降低PPP滤波矩阵的病态性，加快模糊度方差阵几何相关分量的收敛，从而提升模糊度的短时估计精度，并加快位置参数的收敛[4]。随着LEO卫星技术的发展，许多商业LEO卫星星座也在规划设计中，研究人员将LEO卫星引入导航定位中，分析和评估通过LEO卫星增强能否为用户提供更好的导航定位服务。未来导航科技有限公司在2018年公布了微厘空间一号LEO导航增强星座的设计；2018-06武汉大学发射的珞珈1号实验星具备导航增强功能；2018-12中国航天科工集团成功发射了虹云工程技术验证卫星；中国航天科技集团于2018-12成功发射了鸿雁星座首发星重庆号，并进行载荷星地通信实验，接收机利用首发星播发的增强信号进行实时PPP，鸿雁星座未来还计划将卫星数量增加至300多颗，提升其服务性能。此外，时空道宇公司于2019年启动“未来出行”商用LEO导航增强星座的建设，2024-02未来出行星座第2个轨道面以一箭11星的方式成功发射。国家星网工程大力发展LEO通信与导航增强卫星网络，计划于2030年之前完成10%卫星的发射。
在LEO卫星导航增强研究方面，Su等[5]针对北斗三号系统设计一个LEO星座并进行增强PPP实验，收敛时间从30 min左右缩短到1 min。Shi等[6]提出一种适用于LEO卫星多普勒定位的单历元算法，基于仿真的LEO卫星多普勒观测数据进行非差多普勒定位，定位精度可达m级。Li等[7]提出一种LEO卫星精密定轨和时间同步方法，建立并验证LEO增强数据处理框架，使用微厘空间2颗LEO卫星进行增强PPP，结果显示，加入LEO卫星后PPP收敛时间得到显著改善，但定位精度无明显提高。Xu等[8]使用微厘空间5颗LEO卫星的双频数据，研究分析其与GPS/Galileo/BDS三系统组合对PPP收敛时间和定位精度的影响，结果表明，使用LEO卫星进行导航增强能明显提升PPP模糊度固定解技术性能。综合来看，近年来众多学者通过模拟数据对LEO卫星在导航增强方面的效果进行研究，但不同学者采取的仿真策略并不一样，其结论也有一定差异。随着各机构LEO卫星星座计划的逐步展开，也有学者基于零星几颗实测的LEO卫星数据进行PPP增强研究，但由于目前实际观测的LEO卫星数量有限，各LEO星座真实的增强性能尚不明确[9]。
本文以国内已公开的航天科技的鸿雁星座、未来导航的微厘空间和航天科工的虹云工程3个LEO星座计划为原型构建星座，以可见卫星数、位置精度衰减因子(PDOP)、收敛时间和定位精度为指标，对各星座增强GNSS四星座PPP性能进行对比分析和评估。
1 LEO星座系统参数与数据仿真
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微厘空间星座由120颗倾斜轨道卫星和30颗近极地轨道卫星混合而成；鸿雁星座由72颗近极地轨道卫星构成；虹云工程星座构型与鸿雁星座类似，由156颗轨道倾角为80°的卫星构成[10]。3个LEO星座的构型图与具体参数分别见图 1和表 1。需要说明的是，由于这些星座尚处于发展阶段，部分参数可能根据技术进展与实际需求进行调整。
由于目前大部分搭载导航增强载荷的LEO星座建设还处于实验论证阶段，公开的LEO卫星观测数据和资料极其有限，故本实验对LEO卫星轨道、钟差和观测数据进行仿真。在轨道仿真中，先根据星座构型确定初始轨道参数，得到卫星初始位置和速度后，通过动力学积分方法确定卫星全天的轨道位置。对于卫星钟差仿真部分，先对德国地学研究中心(GFZ)多系统精密钟差文件中的卫星进行筛选，剔除部分历元缺少钟差信息的卫星，将剩余卫星的钟差序列按导航卫星伪随机噪声码(PRN)进行排列，分配给所有待仿真卫星，由于待仿真的卫星数大于精密钟差文件中的卫星数，对于超出钟差序列的待仿真卫星采用取余数的方式确定索引进行分配。考虑到精密钟差和轨道估计也包含误差，为使仿真数据更贴合实际，在仿真后的轨道和钟差数据中加入不同量级的有色噪声。在观测值模拟中，由于卫星轨道、卫星钟差和测站位置已知，据此可计算出测站与卫星的几何距离，然后在此基础上加上硬件延迟、天线相位中心偏差、地球潮汐改正、对流层延迟和电离层延迟等误差并考虑观测噪声，从而得到模拟的伪距和载波相位观测数据，具体的仿真参数设置见表 2[11]。
LEO卫星的差分码偏差(DCB)按照GNSS的DCB数值进行仿真，LEO系统的天线相位中心偏差按照国际GNSS服务(IGS)提供的atx文件中相应的卫星和接收机天线类型进行仿真。固体潮位移采用模型进行计算，极潮位移使用IGS提供的erp文件结合模型进行计算。LEO卫星的电离层延迟仿真采用全球电离层格网数据进行内插，对流层延迟仿真中的干延迟采用Saastamoinen模型[12]结合全球压力和温度模型(GPT)，投影函数采用全球投影函数模型(GMF)[13]。
2 LEO星座增强PPP定位模型
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本文采用双频无电离层组合模型进行PPP解算，GNSS/LEO无电离层组合定位模型如式(1)~(3)所示[14]：
$\left\{\begin{array}{l}P_{\mathrm{IF}}^{\mathrm{G}}=\rho_{\mathrm{r}}^{\mathrm{G}}-t^{\mathrm{G}}+t_{\mathrm{r}}+T^{\mathrm{G}}+b_{\mathrm{IF}}^{\mathrm{G}}+b_{\mathrm{r}, \mathrm{IF}}+e_{\mathrm{IF}}^{\mathrm{G}} \\P_{\mathrm{IF}}^{\mathrm{R}}=\rho_{\mathrm{r}}^{\mathrm{R}}-t^{\mathrm{R}}+t_{\mathrm{r}}+T^{\mathrm{R}}+\mathrm{ISB}_{\mathrm{R}}+b_{\mathrm{IF}}^{\mathrm{R}}+b_{\mathrm{r}, \mathrm{IF}}+e_{\mathrm{IF}}^{\mathrm{R}} \\P_{\mathrm{IF}}^{\mathrm{E}}=\rho_{\mathrm{r}}^{\mathrm{E}}-t^{\mathrm{E}}+t_{\mathrm{r}}+T^{\mathrm{E}}+\mathrm{ISB}_{\mathrm{E}}+b_{\mathrm{IF}}^{\mathrm{E}}+b_{\mathrm{r}, \mathrm{IF}}+e_{\mathrm{IF}}^{\mathrm{E}} \\P_{\mathrm{IF}}^{\mathrm{C}}=\rho_{\mathrm{r}}^{\mathrm{C}}-t^{\mathrm{C}}+t_{\mathrm{r}}+T^{\mathrm{C}}+\mathrm{ISB}_{\mathrm{C}}+b_{\mathrm{IF}}^{\mathrm{C}}+b_{\mathrm{r}, \mathrm{IF}}+e_{\mathrm{IF}}^{\mathrm{C}} \\P_{\mathrm{IF}}^{\mathrm{L}}=\rho_{\mathrm{r}}^{\mathrm{L}}-t^{\mathrm{L}}+t_{\mathrm{r}}+T^{\mathrm{L}}+\mathrm{ISB}_{\mathrm{L}}+b_{\mathrm{IF}}^{\mathrm{L}}+b_{\mathrm{r}, \mathrm{IF}}+e_{\mathrm{IF}}^{\mathrm{L}}\end{array}\right.$
$\left\{\begin{array}{l}\mathit\Phi_{\mathrm{IF}}^{\mathrm{G}}=\rho_{\mathrm{r}}^{\mathrm{G}}-t^{\mathrm{G}}+t_{\mathrm{r}}+T^{\mathrm{G}}+\lambda_{\mathrm{IF}}^{\mathrm{G}} \widetilde{N}_{\mathrm{IF}}^{\mathrm{G}}+ \\~~~B_{\mathrm{r}, \mathrm{IF}}-B_{\mathrm{IF}}^{\mathrm{G}}+\varepsilon_{\mathrm{IF}}^{\mathrm{G}} \\\mathit\Phi_{\mathrm{IF}}^{\mathrm{R}}=\rho_{\mathrm{r}}^{\mathrm{R}}-t^{\mathrm{R}}+t_{\mathrm{r}}+T^{\mathrm{R}}+\mathrm{ISB}_{\mathrm{R}}+ \\~~~\lambda_{\mathrm{IF}}^{\mathrm{R}} \widetilde{N}_{\mathrm{IF}}^{\mathrm{R}}+B_{\mathrm{r}, \mathrm{IF}}-B_{\mathrm{IF}}^{\mathrm{R}}+\varepsilon_{\mathrm{IF}}^{\mathrm{R}} \\\mathit\Phi_{\mathrm{IF}}^{\mathrm{E}}=\rho_{\mathrm{r}}^{\mathrm{E}}-t^{\mathrm{E}}+t_{\mathrm{r}}+T^{\mathrm{E}}+\mathrm{ISB}_{\mathrm{E}}+ \\~~~\lambda_{\mathrm{IF}}^{\mathrm{E}} \widetilde{N}_{\mathrm{IF}}^{\mathrm{E}}+B_{\mathrm{r}, \mathrm{IF}}-B_{\mathrm{IF}}^{\mathrm{E}}+\varepsilon_{\mathrm{IF}}^{\mathrm{E}} \\\mathit\Phi_{\mathrm{IF}}^{\mathrm{C}}=\rho_{\mathrm{r}}^{\mathrm{C}}-t^{\mathrm{C}}+t_{\mathrm{r}}+T^{\mathrm{C}}+\mathrm{ISB}_{\mathrm{C}}+ \\~~~\lambda_{\mathrm{IF}}^{\mathrm{C}} \widetilde{N}_{\mathrm{IF}}^{\mathrm{C}}+B_{\mathrm{r}, \mathrm{IF}}-B_{\mathrm{IF}}^{\mathrm{C}}+\varepsilon_{\mathrm{IF}}^{\mathrm{C}} \\\mathit\Phi_{\mathrm{IF}}^{\mathrm{L}}=\rho_{\mathrm{r}}^{\mathrm{L}}-t^{\mathrm{L}}+t_{\mathrm{r}}+T^{\mathrm{L}}+\mathrm{ISB}_{\mathrm{L}}+ \\~~~\lambda_{\mathrm{IF}}^{\mathrm{L}} \widetilde{N}_{\mathrm{IF}}^{\mathrm{L}}+B_{\mathrm{r}, \mathrm{IF}}-B_{\mathrm{IF}}^{\mathrm{L}}+\varepsilon_{\mathrm{IF}}^{\mathrm{L}}\end{array}\right.$
$\widetilde{N}_{\mathrm{IF}}^{\mathrm{s}}=N_{\mathrm{IF}}^{\mathrm{s}}+\frac{B_{\mathrm{IF}}^{\mathrm{s}}-B_{\mathrm{r}, \mathrm{IF}}}{\lambda_{\mathrm{IF}}}$
式中，r表示接收机；G、R、E、C、L分别表示GNSS四大卫星系统和LEO系统；PIFs、ΦIFs分别为仿真的伪距和载波相位无电离层组合观测值(s=G/R/E/C/L, 下同)；ρrs为考虑地球潮汐、相对论效应、地球自转改正、天线PCO和PCV的星地距；Ts为对流层延迟；ISB为系统间偏差；bIFs和br, IF分别为卫星端和接收机端的无电离层组合伪距硬件延迟；λ为载波波长；NIFs为整周模糊度；BIFs和Br, IF分别为卫星端和接收机端的无电离层组合相位硬件延迟；eIFs和εIFs分别为伪距和载波相位观测值的测量噪声，包含多路径效应。
3 数据处理结果与分析
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3.1 实验数据来源及处理策略
为评估LEO增强PPP的性能，本实验选取全球均匀分布的12个IGS测站(图 2)，收集2024-01-01四系统(GPS/GLONASS/BDS/Galileo)观测数据。考虑到LEO卫星的快速运动，测站可连续观测到LEO卫星的时间通常小于半小时，因此使用采样间隔为1 s的GNSS和LEO观测值，卫星截止高度角设为7°；采用可见卫星数、PDOP值、收敛时间和定位精度等指标评估各星座的定位性能；以IGS提供的snx文件中的测站坐标作为真值。具体解算策略见表 3。
3.2 可见卫星数与PDOP值
确定3种LEO卫星星座构型之后，对其总体性能展开评估。可见卫星数量与PDOP值是衡量星座性能的关键指标，其中，PDOP值大小可直接反映定位精度优劣，即PDOP值越小，定位精度越高。
图 3为各个星座在0°经线上不同纬度地区的平均可见卫星数，可以看出，各星座组合在南北半球的可见卫星数相等。从整体来看，可见卫星数随纬度增加而增多，这是因为GNSS星座和LEO星座在设计时的轨道倾角均较高，低纬度地区的轨道间距较大，可见卫星数较少。根据3个LEO星座的模拟计算结果可知，鸿雁和虹云工程星座构型相似，且鸿雁星座的可见卫星数几乎是虹云工程星座的一半，两者在各纬度的平均可见卫星数成倍数关系。此外，微厘空间星座与虹云工程星座规模相近，两者在赤道地区均可见3颗卫星，在中低纬区域(15°~45°N)分别平均可见4.9和3.9颗卫星，在两极地区分别平均可见2.2和14.8颗卫星。而鸿雁星座在两极地区的平均可见卫星数比微厘空间星座要多，为6.8颗，这主要是因为微厘空间星座的主星座轨道倾角只有55°，在高纬区域的可见卫星数较少。由于3个LEO星座的设计不同，导致其与GNSS组合后可见卫星数量存在显著差异。
图 4为各LEO星座增强GREC的全球PDOP值分布情况，可以看出，加入LEO星座后，PDOP值得到明显改善，GREC/鸿雁、GREC/微厘空间和GREC/虹云工程星座的全球PDOP最大值从0.85分别降为0.77、0.83、0.72。相比微厘空间LEO星座，鸿雁和虹云工程LEO星座在高纬地区对PDOP值的改善程度更高，这是因为其LEO卫星数量更多。4个星座的全球PDOP平均值分别为0.70、0.67、0.64、0.62，3个LEO星座的PDOP平均值分别降低4%、9%和11%。
3.3 静态PPP收敛时间与定位精度
为验证LEO卫星增强静态PPP的效果，本文采用实测的四星座GNSS数据与仿真的LEO数据进行组合解算，以4 h为一个定位时段。将静态定位收敛时间定义为E、N、U三个方向的定位误差收敛到±10 cm以内，并在后续10 min均保持在±10 cm以内所花费的时间，取最后30 min的定位误差统计计算RMS值。
图 5为12个IGS测站的收敛过程，可以看出，3个LEO星座的加入对GREC四系统PPP的收敛时间均有不同程度的改善。四系统定位时，SCRZ和THTI测站U方向的定位误差波动明显，这可能与不同测站间的观测数据质量不同有关，但在加入LEO星座之后收敛时间得到极大改善。鸿雁星座对四系统PPP的增强效果与其他2个星座相比稍有不及，这是因为其星座规模不及其他2个星座，可见卫星数较少。总体而言，LEO卫星的加入均能显著改善四系统定位的收敛时间。
图 6为12个IGS测站采用GREC、GREC/鸿雁、GREC/微厘空间、GREC/虹云工程4种方案进行静态PPP解算的平均收敛时间。可以看出，12个IGS测站4种定位方案的平均收敛时间分别为19.2 min、6.6 min、4.1 min和3.8 min，3个LEO星座的加入均能显著缩短各测站的收敛时间。在加入鸿雁、微厘空间、虹云工程星座后，所有测站平均收敛时间分别降低64%、77%、80%。提升效果最小的NKLG测站的收敛时间也降低了55%、75%、75%。同时可以看出，鸿雁星座对收敛时间的改善效果不及其他2个星座，微厘空间和虹云工程2个星座对收敛时间的改善效果相近。
图 7为各测站在不同定位方案下的定位精度。相比于GREC四系统定位，加入3个LEO星座后，12个IGS测站的平均定位精度在E方向分别提升14%、45%、46%，N方向分别提升24%、28%、46%，U方向分别提升28%、33%、37%。定位精度提升较小的LMMF测站E方向分别提升12%、15%、0%，N方向分别提升30%、52%、18%，U方向分别提升10%、47%、42%。在大部分情况下，LEO卫星的加入能提升定位精度，且总体上定位精度的提升程度与LEO星座的规模成正比。
3.4 动态PPP收敛时间与定位精度
为验证LEO卫星在动态导航中的应用，开展静态仿动态PPP实验。实验方案与上节一致，不同的是将动态定位收敛时间定义为E、N、U三个方向的定位误差收敛到±20 cm以内，并在后续30 min均保持在±20 cm以内所花费的时间[8]。
限于篇幅，仅展示3个测站(AJAC、BRST、DJIG)的收敛过程(图 8)。可以看出，与静态PPP不同，进行动态PPP时，U方向定位误差的波动情况与其他2个方向相比要大得多，LEO星座的加入可以缩短收敛时间，但对定位精度的提升并不明显，LEO卫星的增强效果主要体现在收敛时间上。
表 4为12个IGS测站采用GREC、GREC/鸿雁、GREC/微厘空间、GREC/虹云工程4种方案进行动态PPP解算的平均收敛时间和定位精度。可以看出，12个IGS测站4种定位方案的平均收敛时间分别为19.28 min、6.20 min、4.48 min、2.71 min，3个LEO星座的加入均能显著缩短各测站的收敛时间。在加入鸿雁、微厘空间、虹云工程星座后，所有测站的平均收敛时间分别降低67%、76%、86%。提升效果较差的THTI测站的收敛时间也降低44%、61%、86%。可以看出，虹云工程星座对收敛时间的改善效果最好，微厘空间星座其次，鸿雁星座最差，增强效果与星座规模成正比。在定位精度方面，U方向的定位精度明显差于其他2个方向。相比于GREC四系统定位，加入3个LEO星座后，12个IGS测站的平均定位精度在E方向分别提升15%、32%、24%，N方向分别提升32%、5%、8%，U方向分别提升11%、14%、16%。与静态PPP相比，在动态PPP中加入LEO星座对定位精度的提升效果并不显著。
4 结语
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本文对国内已公布计划的鸿雁、微厘空间、虹云工程3个LEO星座进行仿真，讨论不同LEO星座对全球可见卫星数、PDOP值的改善情况；使用仿真的LEO观测数据结合12个IGS测站实测的GNSS观测数据进行增强静态/动态PPP，评估3个LEO星座在增强静态和动态四系统PPP中对收敛时间和定位精度的改善效果。
结果表明，微厘空间星座与虹云工程星座在赤道地区均可见3颗卫星，在中低纬区域(15°~45°N)分别可见4.9和3.9颗卫星，在两极地区分别可见2.2和14.8颗卫星。鸿雁星座规模在中低纬区域是其他星座的一半，但在两极地区的平均可见卫星数比微厘空间星座要多，可见星座构型对可见卫星数有很大影响。GREC联合LEO定位可改善全球PDOP值，鸿雁和虹云工程星座在高纬地区对PDOP值的改善程度比微厘空间星座要高，鸿雁、微厘空间、虹云工程星座的全球PDOP平均值分别降低4%、9%和11%。与四系统定位相比，加入鸿雁、微厘空间、虹云工程星座后，所有测站的平均静态收敛时间分别降低64%、77%、80%，静态定位精度分别提升33%、36%、43%，动态收敛时间分别降低67%、76%、86%，动态定位精度分别提升10%、17%、16%，微厘空间和虹云工程星座对收敛时间的改善效果相近，鸿雁星座次之。在静态PPP中，LEO卫星的加入均能提升定位精度，且总体上定位精度的提升程度与LEO星座的规模成正比，而在动态PPP中LEO星座的加入对定位精度的提升效果并不显著。综合来看，虹云工程LEO星座对PPP的增强效果最优；微厘空间LEO星座的增强效果与虹云工程星座相近，但对高纬地区测站的改善效果略差；鸿雁LEO星座受限于卫星数量，增强效果与其他2个LEO星座相比略有不及。
基金
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  • 国家重点研发计划(2020YFA0713501)
文献
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doi: 10.14075/j.jgg.2024.07.345
  • 接收时间：2024-07-16
  • 首发时间：2026-10-29
  • 出版时间：2025-07-15
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  • 收稿日期：2024-07-16
基金
National Key Research and Development Program of China(2020YFA0713501)
国家重点研发计划(2020YFA0713501)
作者信息
    1 中南大学地球科学与信息物理学院, 长沙市麓山南路932号, 410083

通讯作者:

蔡昌盛，博士，教授，博士生导师，主要从事GNSS导航和精密定位研究，E-mail:

CAI Changsheng, PhD, professor, PhD supervisor, majors in GNSS navigation and precise positioning, E-mail:

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https://castjournals.cast.org.cn/joweb/ddcl/CN/10.14075/j.jgg.2024.07.345
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