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Article(id=1322566887901348044, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322566845215912204, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2025.03.064, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1741104000000, receivedDateStr=2025-03-05, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793254118179, onlineDateStr=2026-10-29, pubDate=1771084800000, pubDateStr=2026-02-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793254118179, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793254118179, creator=13701087609, updateTime=1793254118179, updator=13701087609, issue=Issue{id=1322566845215912204, tenantId=1146029695717560320, journalId=1281212831689347082, year='2026', volume='46', issue='2', pageStart='139', pageEnd='261', issueExtLink='null', onlineDate='null', pubDate='1771084800000', pubDateStr='2026-02-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793254108003, creator='13701087609', updateTime=1793254108003, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=227, endPage=233, ext={EN=ArticleExt(id=1322566888098480333, articleId=1322566887901348044, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Performance of PPP Enhanced by Wide-Area Tropospheric Delay Model with Different Inter-Station Spacings, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

The tropospheric delay information of the enhanced precise point positioning (PPP) comes from a small regional reference station network with station spacing of several tens of kilometers, which has the disadvantages of limited service scope and high construction cost. To investigate the impact of wide-area tropospheric delay models with larger station spacing on PPP augmentation performance, observational data from IGS tracking stations in Europe were used to establish tropospheric delay models with average inter-station spacings of approximately 200 km, 260 km, 320 km, and 380 km. These models were then compared with the GPT3 model to evaluate and analyze PPP enhancement performance. The results indicate that the wide-area tropospheric delay models with inter-station spacings of 200 km, 260 km, and 320 km all reduced PPP convergence time to varying degrees, with particularly notable improvements in the height component and its maximum enhancement can reach 39.8%. However, the enhancement effect diminished as average station spacing increased. When the station spacing reached 380 km, the PPP augmentation performance was inferior to that of the global GPT3 model.

, authors=Yumei FANG1, Wujiao DAI1, *, Lin PAN1, Jiabao PAN2, Zhiguo PANG3, authorsList=Yumei FANG, Wujiao DAI, Lin PAN, Jiabao PAN, Zhiguo PANG, authorCompany=null, correspAuthors=Wujiao DAI, authorNote=null, correspAuthorsNote=null, copyrightStatement=All rights reserved. Unauthorized reproduction is prohibited., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322566891164516572, articleId=1322566887901348044, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=不同站间距广域对流层延迟模型对PPP增强性能分析, columnId=1281909276545356011, journalTitle=大地测量与地球动力学, columnName=大地测量学, runingTitle=null, highlight=null, articleAbstract=

精密单点定位(PPP)增强中的对流层延迟信息多来自站间距为几十千米的区域参考站网, 存在服务范围有限、建设成本高等缺点。为研究较大站间距的广域对流层延迟模型对PPP增强效果的影响, 利用欧洲区域IGS跟踪站的观测数据, 分别建立平均站间距约为200 km、260 km、320 km和380 km的对流层延迟模型, 并与GPT3模型对比, 对PPP增强性能进行评估分析。结果表明, 站间距为200 km、260 km和320 km的广域对流层延迟模型均在不同程度上缩短了PPP的收敛时间, 高程方向尤其显著, 最大增强幅度可达39.8%, 但改善效果随平均站间距的增大而减弱, 当模型的站间距扩大至380 km时, PPP的增强效果差于GPT3模型。

, authors=方玉妹1, 戴吾蛟1, *, 潘林1, 潘家宝2, 庞治国3, authorsList=方玉妹, 戴吾蛟, 潘林, 潘家宝, 庞治国, authorCompany=null, correspAuthors=戴吾蛟, authorNote=

方玉妹, 硕士生, 主要研究方向为精密导航定位与应用, E-mail:

, correspAuthorsNote=
戴吾蛟, 博士, 教授, 主要研究方向主要为精密导航定位与应用、变形监测等, E-mail:
, copyrightStatement=版权所有，未经授权，不得转载。, copyrightOwner=大地测量与地球动力学编辑部, extLink=null, articleAbsUrl=null, sourceXml=dSNVEB/BZe8w7mc7ezWvPg==, magXml=VeNnnsfR8V0k4UX9btKnHA==, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=e7Z621B5t3SQSJ0ydbRI8A==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=d0bprrjuFvnI7OytOjoiyQ==, mapNumber=null, fund=null)}, authors=[Author(id=1322566891604918503, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322566887901348044, orderNo=0, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=245011014@csu.edu.cn, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1322566891676221673, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322566887901348044, authorId=1322566891604918503, language=EN, stringName=Yumei FANG, firstName=Yumei, middleName=null, lastName=FANG, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=1, address=1 School of Geosciences and Info-physics, Central South University, Changsha 410083, China, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1322566891739136234, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322566887901348044, authorId=1322566891604918503, language=CN, stringName=方玉妹, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=1, address=1 中南大学地球科学与信息物理学院, 长沙, 410083, bio={"content":"

方玉妹, 硕士生, 主要研究方向为精密导航定位与应用, E-mail:

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方玉妹, 硕士生, 主要研究方向为精密导航定位与应用, E-mail:

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improvement for each coordinate component in enhanced PPP, figureFileSmall=2+lHKqw1z0IEIB/9Ec3RTQ==, figureFileBig=q0hS3g9PeXRwckRRuRKYhQ==, tableContent=null), ArticleFig(id=1322566896218652948, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322566887901348044, language=CN, label=图7, caption=增强PPP各坐标分量定位精度提升结果统计, figureFileSmall=2+lHKqw1z0IEIB/9Ec3RTQ==, figureFileBig=q0hS3g9PeXRwckRRuRKYhQ==, tableContent=null), ArticleFig(id=1322566896302539029, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322566887901348044, language=EN, label=Tab. 1, caption=

Strategy for extracting tropospheric delay information on the server side

, figureFileSmall=null, figureFileBig=null, tableContent=
项目策略
GNSS系统GPS、BDS-3
信号频率GPS: L1、L；BDS-3:BⅡ、B3I
解算模式消电离层组合静态PPP浮点解
截止高度角7.5 °
采样间隔30 s
天线误差igs14.atx
对流层静力学延迟Saastamoninen模型改正
对流层湿延迟GMF投影函数+随机游走估计湿延迟及梯度参数
), ArticleFig(id=1322566896386425110, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322566887901348044, language=CN, label=表1, caption=

服务端对流层延迟信息的提取策略

, figureFileSmall=null, figureFileBig=null, tableContent=
项目策略
GNSS系统GPS、BDS-3
信号频率GPS: L1、L；BDS-3:BⅡ、B3I
解算模式消电离层组合静态PPP浮点解
截止高度角7.5 °
采样间隔30 s
天线误差igs14.atx
对流层静力学延迟Saastamoninen模型改正
对流层湿延迟GMF投影函数+随机游走估计湿延迟及梯度参数
), ArticleFig(id=1322566896457728279, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322566887901348044, language=EN, label=Tab. 2, caption=

Statistical results of average convergence time

, figureFileSmall=null, figureFileBig=null, tableContent=
项目平均收敛时间统计/min
E方向N方向U方向
PPP17.811.520.6
增强PPP-200 km16.211.512.4
增强PPP-260 km16.511.515.2
增强PPP-320 km16.811.517.0
增强PPP-380 km17.611.521.4
增强PPP-GPT317.311.519.9
), ArticleFig(id=1322566896533225752, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322566887901348044, language=CN, label=表2, caption=

平均收敛时间统计结果

, figureFileSmall=null, figureFileBig=null, tableContent=
项目平均收敛时间统计/min
E方向N方向U方向
PPP17.811.520.6
增强PPP-200 km16.211.512.4
增强PPP-260 km16.511.515.2
增强PPP-320 km16.811.517.0
增强PPP-380 km17.611.521.4
增强PPP-GPT317.311.519.9
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不同站间距广域对流层延迟模型对PPP增强性能分析
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方玉妹 1 , 戴吾蛟 1, * , 潘林 1 , 潘家宝 2 , 庞治国 3
大地测量与地球动力学 | 大地测量学 2026,46(2): 227-233
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大地测量与地球动力学 |大地测量学 2026 , 46 (2) : 227 -233
不同站间距广域对流层延迟模型对PPP增强性能分析
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方玉妹1 , 戴吾蛟1, * , 潘林1, 潘家宝2, 庞治国3
作者信息
  • 1 中南大学地球科学与信息物理学院, 长沙, 410083
  • 2 福州市勘测院有限公司, 福州, 350108
  • 3 中国水利水电科学研究院, 北京, 100038
通讯作者:
戴吾蛟, 博士, 教授, 主要研究方向主要为精密导航定位与应用、变形监测等, E-mail:
作者简介:

方玉妹, 硕士生, 主要研究方向为精密导航定位与应用, E-mail:

Performance of PPP Enhanced by Wide-Area Tropospheric Delay Model with Different Inter-Station Spacings
Yumei FANG1 , Wujiao DAI1, * , Lin PAN1, Jiabao PAN2, Zhiguo PANG3
Affiliations
  • 1 School of Geosciences and Info-physics, Central South University, Changsha 410083, China
  • 2 Fuzhou Investigation and Surveying Institute, Fuzhou 350108, China
  • 3 China Institute of Water Resources and Hydropower Research, Beijing 100038, China
出版时间: 2026-02-15 doi: 10.14075/j.jgg.2025.03.064
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摘要
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精密单点定位(PPP)增强中的对流层延迟信息多来自站间距为几十千米的区域参考站网, 存在服务范围有限、建设成本高等缺点。为研究较大站间距的广域对流层延迟模型对PPP增强效果的影响, 利用欧洲区域IGS跟踪站的观测数据, 分别建立平均站间距约为200 km、260 km、320 km和380 km的对流层延迟模型, 并与GPT3模型对比, 对PPP增强性能进行评估分析。结果表明, 站间距为200 km、260 km和320 km的广域对流层延迟模型均在不同程度上缩短了PPP的收敛时间, 高程方向尤其显著, 最大增强幅度可达39.8%, 但改善效果随平均站间距的增大而减弱, 当模型的站间距扩大至380 km时, PPP的增强效果差于GPT3模型。

对流层  /  精密单点定位  /  收敛时间  /  站间距

The tropospheric delay information of the enhanced precise point positioning (PPP) comes from a small regional reference station network with station spacing of several tens of kilometers, which has the disadvantages of limited service scope and high construction cost. To investigate the impact of wide-area tropospheric delay models with larger station spacing on PPP augmentation performance, observational data from IGS tracking stations in Europe were used to establish tropospheric delay models with average inter-station spacings of approximately 200 km, 260 km, 320 km, and 380 km. These models were then compared with the GPT3 model to evaluate and analyze PPP enhancement performance. The results indicate that the wide-area tropospheric delay models with inter-station spacings of 200 km, 260 km, and 320 km all reduced PPP convergence time to varying degrees, with particularly notable improvements in the height component and its maximum enhancement can reach 39.8%. However, the enhancement effect diminished as average station spacing increased. When the station spacing reached 380 km, the PPP augmentation performance was inferior to that of the global GPT3 model.

tropospheric  /  precise point positioning (PPP)  /  convergence time  /  inter-station spacing
方玉妹, 戴吾蛟, 潘林, 潘家宝, 庞治国. 不同站间距广域对流层延迟模型对PPP增强性能分析. 大地测量与地球动力学, 2026 , 46 (2) : 227 -233 . DOI: 10.14075/j.jgg.2025.03.064
Yumei FANG, Wujiao DAI, Lin PAN, Jiabao PAN, Zhiguo PANG. Performance of PPP Enhanced by Wide-Area Tropospheric Delay Model with Different Inter-Station Spacings[J]. Journal of Geodesy and Geodynamics, 2026 , 46 (2) : 227 -233 . DOI: 10.14075/j.jgg.2025.03.064
正文
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精密单点定位(PPP)凭借其高精度、灵活作业方式及低成本等显著优势[1]，在各类测绘与导航场景中得到广泛应用。然而，在PPP解算过程中，初始化和重新初始化过程耗时较长，这一弊端极大地限制了该技术在实际应用中的进一步推广。
对流层延迟误差是影响PPP收敛速度的关键因素之一。研究表明，借助区域CORS(连续运行参考站)网的对流层延迟信息[2]，通过反距离加权内插[3-4]、区域对流层延迟建模[5]等多种方法，能够获取用户端的对流层延迟信息。在PPP观测方程组中，直接对流层延迟参数进行改正或添加虚拟观测方程[6-9]，可有效缩短PPP的收敛时间，加快模糊度固定，最终实现低延时、高精度的定位。但目前，基于对流层延迟信息增强PPP的研究大多集中于站间距为几十千米的小区域参考站网。此类研究存在服务范围有限、建设成本高昂等缺点，并且当通信设备等出现故障时，区域对流层改正信息将无法正常播发。
随着全球对流层延迟建模研究的不断深入与日趋成熟，UNB3m[10]、IGGtrop[11]、GPT3[12]等全球经验模型展现出提升PPP收敛速度的潜力[13]。已有相关研究通过利用全球对流层延迟模型开展PPP增强实验[14-15]，证实其可加速PPP收敛。不过，这些模型的增强效果均受到全球模型自身精度的限制，难以满足PPP快速收敛的实际需求。
综合考量区域实时模型和全球经验模型各自的优势，利用少量且分布均匀的站点构建广域实时对流层延迟模型，并通过卫星播发模型参数，有望实现加速PPP收敛的目标。然而，广域实时对流层延迟模型的精度及实际应用效果与模型的站间距密切相关。为深入探究不同站间距的广域对流层延迟模型对PPP增强效果的影响，本文采用欧洲区域IGS跟踪站的观测数据，构建服务端在不同站间距条件下的广域对流层延迟模型，并对模型精度及其对实时PPP定位的增强效果进行评估，旨在为广域对流层延迟模型增强PPP提供参考。
1 广域对流层信息增强的PPP方法
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1.1 MOFC模型
对于区域对流层延迟高精度建模，通常采用二阶多项式拟合，其公式表达如下：
$\begin{gathered}\text { ZWD }=a_0+a_1 \mathrm{~d} B+a_2 \mathrm{~d} L+a_3 \mathrm{~d} h+ \\a_4 \mathrm{~d} B \mathrm{~d} L+a_5 \mathrm{~d} B \mathrm{~d} h+a_6 \mathrm{~d} L \mathrm{~d} h+ \\a_7 \mathrm{~d} B^2+a_8 \mathrm{~d} L^2+a_9 \mathrm{~d} h^2\end{gathered}$
式中，a0、a1、…、a9分别为多项式系数；dB、dL和dh分别表示基准站相对于参考点的经度差、纬度差和高程差；ZWD表示基准站点的天顶对流层湿延迟。OFC(optimal fitting coefficients)模型是ZWD在数学上的近似表达，忽略了ZWD的物理变化规律。事实上，气压等气象参数随高程增大呈指数趋势衰减，因此在大高差、大范围的区域，仅用OFC模型难以有效拟合ZWD。MOFC(modified optimal fitting coefficients)模型[16]结合了多项式与指数函数，常用于广域对流层延迟背景模型的构建。其公式表达为：
$\begin{gathered}f(\mathrm{~d} L, \mathrm{~d} B)=a_0+a_1 \mathrm{~d} B+a_2 \mathrm{~d} L+ \\a_3 \mathrm{~d} B \mathrm{~d} L+a_4 \mathrm{~d} B^2+a_5 \mathrm{~d} L^2 \\\text { ZWD }=f(\mathrm{~d} L, \mathrm{~d} B) \mathrm{e}^{\frac{h}{H}}\end{gathered}$
式中，h为基准站的大地高；H为在建模区域内用于表征对流层湿延迟高程依赖性的参数，其初始值定为建模区域的平均高程，该参数在建模过程中同a0、a1、…、a5通过最小二乘估计解算得到。相比于OFC模型，MOFC模型在解决高程依赖问题的同时拟合系数由10个减少至7个，在一定程度上对模型进行了简化。
1.2 GPT3模型
全球气压气温(global pressure and temperature，GPT)模型由Böhm等首次提出，而后陆续发展了GPT2、GPT2w和GPT3模型，该系列模型是目前精度最高、应用最广泛的经验对流层模型之一。其中，GPT3引入了梯度法，改正了映射函数在低截止高度角下引起的误差，是一种非常全面的对流层计算模型。该模型以ETOPO5中的平均高程为基准，将全球划分为1°×1°格网，利用最小二乘法进行参数计算。各参数的年、半年周期计算公式如下：
$\begin{gathered}r(t)=A_0+A_1 \cos \left(\frac{2 \pi}{365.25} \mathrm{doy}\right)+ \\B_1 \sin \left(\frac{2 \pi}{365.25} \mathrm{doy}\right)+A_2 \cos \left(\frac{4 \pi}{365.25} \mathrm{doy}\right)+ \\B_2 \sin \left(\frac{4 \pi}{365.25} \mathrm{doy}\right)\end{gathered}$
式中，r(t)为各个气象参数在大地水准面处的估值；doy表示年积日；A0为参数年均值；A1和B1均为参数年振幅；A2和B2均为参数的半年振幅。GPT3模型通过输入测站的坐标及观测时间，利用相应函数计算周围4个格网点的参数，通过高程归化、内插得到测站点的气象参数，最后将所得气象参数中的气压、气温和水汽压带入Askne等[17]的公式计算天顶对流层湿延迟。
1.3 对流层延迟信息增强消电离层组合PPP模型
为了消除电离层误差对实验结果的影响，本文基于无电离层组合的PPP函数模型，引入由对流层延迟信息构造的虚拟观测方程进行联立求解，以期起到约束天顶对流层湿延迟参数的效果，从而加快PPP模型收敛，提高PPP的服务性能。利用先验模型改正对流层静力学延迟后，函数模型如下：
$P_{\mathrm{r}}^{\mathrm{s}}=\rho_{\mathrm{r}}^{\mathrm{s}}+c\left(\mathrm{~d} t_{\mathrm{r}}-\mathrm{d} t^{\mathrm{s}}\right)+m_{\mathrm{r}, \mathrm{w}}^{\mathrm{s}} Z_{\mathrm{r}, \mathrm{w}}+e_{\mathrm{r}}^{\mathrm{s}}$
$\begin{gathered}L_{\mathrm{r}}^{\mathrm{s}}=\rho_{\mathrm{r}}^{\mathrm{s}}+c\left(\mathrm{~d} t_{\mathrm{r}}-\mathrm{d} t^{\mathrm{s}}\right)+m_{\mathrm{r}, \mathrm{w}}^{\mathrm{s}} Z_{\mathrm{r}, \mathrm{w}}+ \\\lambda_i \widetilde{N}_{\mathrm{r}}^{\mathrm{s}}+\varepsilon_{\mathrm{r}}^{\mathrm{s}}\end{gathered}$
$\Delta T_t=Z_{\mathrm{r}, \mathrm{w}}-\widetilde{Z}_{\mathrm{r}, \mathrm{w}}$
式中，Prs、Lrs分别表示消电离层组合的伪距、相位观测值；ρrs表示卫星与接收机间的几何距离；c为真空中的光速；dtr和dts分别为无电离层组合的接收机钟差和卫星钟差；mr, ws表示天顶对流层湿延迟对应的投影函数；Zr, w和$\widetilde{Z}_{\mathrm{r}, \mathrm{w}}$分别对应天顶ZWD的近似值和经验模型值；$\widetilde{N}_{\mathrm{r}}^{\mathrm{s}}$为第i个频率上的载波相位整周模糊度；λi为第i个频率上的载波波长；ers和εrs均为观测噪声。其中，钟差、模糊度参数分别吸收了对应硬件延迟。
PPP解算过程中，需给予伪距、载波相位观测值不同的权重来反映其质量好坏。本文采用基于余弦函数模型的高度角定权法：
$\sigma^2=a^2+b^2 \cos ^2(\mathrm{el})$
式中，σ2为观测值方差；el代表卫星高度角；a和b均基于经验值给定，本文伪距观测值定权时a和b均取值0.3 m，载波相位观测值定权时a和b均取值0.003 m。对于虚拟观测方程方差，采用逐步松弛的方式，逐渐减弱对流层增强信息对后续定位的影响。
2 实验数据与处理策略
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选取欧洲区域IGS跟踪站的观测数据，建立不同站间距下的广域对流层延迟模型并开展PPP增强实验。研究时段为2023-12-12(doy346)00：00—24：00，在此基础上还引入同时段的GPT3模型对流层延迟产品，进一步作对比分析。为探究不同站间距的广域对流层延迟模型对PPP增强效果的影响，本文共设计了4种不同站间距(测站数)的广域对流层延迟模型(建模点数/站间距(单位个/km)分别为12/380、18/320、25/260、34/200)，并均匀选取5个固定站点测试模型精度。具体站点分布见图 1。
服务端使用基于RTKLIB的自研软件，并采用双系统双频的消电离层组合静态PPP浮点解策略，提取时间分辨率为30 s的高精度ZWD信息，为建立对流层延迟模型提供数据来源，同时作为对流层延迟模型精度检验的标准。在PPP解算时，采用欧洲航天局(ESA)提供的精密轨道和精密钟差产品、利用IGS发布的地球自转参数和差分码偏差文件对相应误差进行修正，其他的误差项如相对论效应、Sagnac效应、固体潮等都由现有的模型进行改正，其他具体提取策略如表 1所示。但在实际解算过程中，由于ZWD收敛较慢，未收敛的ZWD精度难以满足模型构建及精度检验的要求，因此在本次研究中，剔除前200个历元的ZWD解算值。
用户端通过模拟接收广域或全球对流层延迟模型参数(全球模型特指GPT3模型，广域模型参数当前为事后建模结果，未实现实时播发)计算站点的ZWD值，并构建虚拟观测方程约束静态PPP解算，以比较不同站间距下高精度对流层延迟信息对PPP定位效果的增强性能。为提高数据利用率，用户端将1 d的数据划分为多个2 h片段进行解算。具体实验流程和策略见图 2。
3 实验结果分析
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实验结果分析包括广域对流层延迟模型精度评估和PPP增强性能评估两个方面。其中，对流层延迟模型精度定义为测试站点的ZWD与对应模型值的残差均方根(RMS)；PPP增强效果从收敛时间和定位精度两个维度进行衡量，收敛时间定义为自定位解算起，连续15个历元内的水平误差持续小于5 cm、高程误差小于10 cm；定位精度的判断标准为自定位解算起，第10 min时的坐标误差。
3.1 对流层延迟模型精度评估
图 3展示了基于不同站间距的建模策略下部分IGS站点的对流层湿延迟及其残差序列, 其中对流层湿延迟真值由静态PPP结算提取获得。可以看出，对流层湿延迟误差基本围绕0值线上下波动，且随着建模站间距的增大，其整体的拟合误差越大，波动性越强。由此可见，对流层湿延迟模型整体精度随站间距的增大而减小。
图 4展示了平均站间距为200 km、260 km、320 km和380 km的对流层延迟模型中各IGS站点的RMSE值。可以看出，随着模型站间距的增大，该区域站点的总体RMSE上升，由模型精度的统计结果可知，随着站间距的增大，对流层延迟模型精度降低，站间距为200 km、260 km、320 km和380 km的对流层延迟模型精度分别为12.6 mm、13.1 mm、15.8 mm和16.1 mm，其原因主要为较密集的站点分布能够更好地捕捉对流层延迟信息的空间相关性，从而提升模型的精度；而在对流层延迟随空间变化较大的情况下，站间距的增加会减弱测试点与建模点之间的相关性，导致模型精度下降。
由图 4还可以看出，站点的总体精度呈现出北低南高的分布特点，引起这一现象发生的主要原因有两点：一是气压、温度等气象参数随海拔高度呈指数变化，尤其在地形变化较大的区域，其ZWD波动较大，会导致模型拟合的准确性下降；二是大气中的水汽含量随纬度减小而增加，导致ZWD值增大且起伏较大，拟合精度降低。由此可见，欧洲西部南高北低的地势差异和基准点间纬度差异对模型精度有明显影响，南部海拔高且纬度低使得ZWD精度偏低，而北部区域站点ZWD精度较高, 且随模型站间距变化波动较小。
3.2 PPP增强性能分析
图 5分别展示了2个不同示例站点(GRAC与WTZ3)在不同尺度对流层增强策略下的PPP误差随时间变化的对比结果。为直观显示实验效果，仅展示了其中一个收敛序列在东(E)、北(N)、高程(U)方向上的收敛时间序列片段。实验结果表明，对于GRAC站点(图 5(a))，在不同尺度对流层增强策略的作用下，PPP性能均得到了有效提升。这主要是因为，在针对GRAC站点采用的不同尺度建模策略中，拟合效果均表现良好。这一结果也从侧面印证了高精度对流层延迟信息能够切实有效地增强PPP性能。从图 5(b)看出，实验进一步揭示随着模型尺度的增大，广域模型所提供的对流层延迟信息精度会逐渐降低，进而导致PPP增强的收敛速度变慢。其中，GPT3模型的增强效果稍弱于广域对流层延迟模型，同时随着对流层尺度的增大，其收敛序列的波动幅度也显著增大，而站间距较小的对流层延迟模型增强PPP的收敛序列更加平滑。
此外，从方向性来看，引入对流层延迟模型显著缩短了U方向的收敛时间，其次是E方向，而对N方向的收敛速度几乎没有影响。这是由于对流层延迟与高程强相关，定位解算时通常需要较长时间才能有效分离高程误差与对流层湿延迟，加入对流层延迟增强信息后，在一定程度上削弱了二者的相关性，有助于快速分离U方向的误差与对流层湿分量，从而加速高程方向的收敛。
表 2展示了在不同尺度的对流层延迟模型增强下，PPP各个方向的平均收敛时间。可以看出，随着区域建模站间距的增大，对应收敛时间的提升幅度降低。由数值结果可知，U方向的平均收敛时间的提升幅度最大，最高可达39.8%；E方向次之；N方向的收敛性能几乎没有提升。同时，当模型的站间距达380 km时，其对PPP收敛时间的增强效果差于全球GPT3模型，甚至比传统PPP的收敛时间还要长。
图 6展示了不同尺度的对流层延迟模型约束策略下，PPP解算第10 min各坐标分量的误差值。可以看出，不同模型约束下，E、N坐标分量对流层延迟变化的敏感度弱，定位精度没有明显变化规律且其差值基本保持在±2 cm之内。反之，由于对流层延迟与高程强相关，引入对流层延迟模型约束，PPP在U方向的定位精度得到明显提升，其平均定位精度由10.4 cm最大提升至4.0 cm。
图 7分别展示了WTZZ、GRAC、JOZE和PTBB站点各分量第10 min的定位精度，图中左Y轴表示不同策略下的增强PPP与PPP精度的差异，正数值代表改善精度值，负数值代表精度降低值；右Y轴表示传统消电离层组合PPP的精度。由图可知，随着对流层尺度的加大，其定位增强效果降低，当约束信息与实际对流层延迟偏差过大时，还会导致定位精度降低。
4 结语
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为研究不同站间距的广域对流层延迟模型对PPP增强的影响，利用欧洲区域IGS跟踪站的观测数据，以全球对流层延迟模型GPT3为对比模型，分析不同尺度的广域模型对PPP的增强性能。结果表明：
1) 引入广域对流层延迟模型的增强信息，可加速PPP收敛，其中U方向的增强效果最佳，最大增强幅度可达39.8%；E方向次之；N方向的收敛性能几乎不受影响。
2) PPP增强的收敛性能随模型站间距的增大而降低，且其收敛序列波动也随之变大。但当站间距扩大至380 km时，广域模型增强效果差于全球GPT3模型，甚至比传统PPP收敛速度还要慢。
3) 在收敛阶段，PPP增强的U方向平均定位精度可从10.4 cm提升至4.0 cm，但提升幅度随站间距增大而下降，引入站间距达380 km或GPT3模型时，总体定位结果精度降低或发散。
总之，在对流层延迟模型增强PPP应用中，可通过建立稀疏站点的参考站网来降低成本，但当参考站站间距超过320 km时，建议采用高精度的全球对流层延迟模型增强PPP；若参考站所处区域的气候复杂多变或地形起伏较大，可适当减小广域对流层延迟模型的模型站间距阈值。
基金
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  • 中国水利水电科学研究院"揭榜挂帅"专项(9002241)
  • 福建省科技计划(2021Y3001)
文献
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2026年第46卷第2期
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doi: 10.14075/j.jgg.2025.03.064
  • 接收时间：2025-03-05
  • 首发时间：2026-10-29
  • 出版时间：2026-02-15
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  • 收稿日期：2025-03-05
基金
中国水利水电科学研究院"揭榜挂帅"专项(9002241)
福建省科技计划(2021Y3001)
作者信息
    1 中南大学地球科学与信息物理学院, 长沙, 410083
    2 福州市勘测院有限公司, 福州, 350108
    3 中国水利水电科学研究院, 北京, 100038

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戴吾蛟, 博士, 教授, 主要研究方向主要为精密导航定位与应用、变形监测等, E-mail:
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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
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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
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