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Article(id=1322567131519107102, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322567020940481144, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2025.06.198, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1749657600000, receivedDateStr=2025-06-12, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793254176262, onlineDateStr=2026-10-29, pubDate=1776182400000, pubDateStr=2026-04-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793254176262, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793254176262, creator=13701087609, updateTime=1793254176262, updator=13701087609, issue=Issue{id=1322567020940481144, tenantId=1146029695717560320, journalId=1281212831689347082, year='2026', volume='46', issue='4', pageStart='392', pageEnd='521', issueExtLink='null', onlineDate='null', pubDate='1776182400000', pubDateStr='2026-04-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793254149899, creator='13701087609', updateTime=1793254149899, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=503, endPage=509, ext={EN=ArticleExt(id=1322567131670102047, articleId=1322567131519107102, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=GNSS Observation Environment Complexity Assessment Method Based on Subjective and Objective Weighted CODAS, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Aiming at the quantitative evaluation of observation environment complexity in GNSS high-precision positioning, a comprehensive subjective and objective weighted combinative distance-based assessment (CODAS) method based on data quality indicators such as data integrity rate, cycle slip ratio, pseudorange multipath error, carrier-to-noise ratio and PDOP is proposed. According to different weighting strategies, the CODAS, TOPSIS and VIKOR methods are used to evaluate the observation environment complexity of 120 monitoring stations, and the Spearman correlation coefficient is used to measure the correlation between evaluation results of each method and the accuracy of PPP kinematics solution. The results show that the comprehensive subjective and objective weighting can improve the accuracy of CODAS method compared with the single weighting. The Spearman correlation coefficients of evaluation results of CODAS method with RMSE and ME are 0.897 and 0.924, respectively, which are better than TOPSIS and VIKOR methods. Parameter sensitivity analysis shows that the mean standard deviation of evaluation results of CODAS method under different trade-off parameters is less than 1.5, indicating good stability.

, authors=Mingzhuang HUANG1, Wujiao DAI1, *, Wenkun YU1, Yaxin WEN2, authorsList=Mingzhuang HUANG, Wujiao DAI, Wenkun YU, Yaxin WEN, 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=1322567132949364780, articleId=1322567131519107102, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=基于主客观赋权CODAS的GNSS观测环境复杂度评估方法, columnId=1281909276545356011, journalTitle=大地测量与地球动力学, columnName=大地测量学, runingTitle=null, highlight=null, articleAbstract=

针对GNSS高精度定位中观测环境复杂度的量化评估问题, 提出一种基于数据完整率、周跳比、伪距多路径误差、载噪比和PDOP等数据质量指标的综合主客观赋权组合距离评估法(CODAS)。基于不同赋权策略, 利用CODAS、TOPSIS和VIKOR方法对120个监测站的观测环境复杂度进行评估, 并采用Spearman相关系数衡量各方法评估结果与PPP动态解算精度的相关性。结果表明, 相较于单一赋权, 综合主客观赋权可提升CODAS方法准确性; CODAS方法的评估结果与均方根误差和平均误差的Spearman相关系数分别为0.897和0.924, 优于TOPSIS和VIKOR方法。参数敏感性分析表明, CODAS方法在不同折衷系数下的评估结果标准差均值小于1.5, 具备良好的稳定性。

, authors=黄明庄1, 戴吾蛟1, *, 余文坤1, 温亚鑫2, authorsList=黄明庄, 戴吾蛟, 余文坤, 温亚鑫, authorCompany=null, correspAuthors=戴吾蛟, authorNote=

黄明庄, 硕士生, 主要从事GNSS导航定位研究, E-mail:

, correspAuthorsNote=
戴吾蛟, 教授, 主要从事GNSS导航定位研究, E-mail:
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黄明庄, 硕士生, 主要从事GNSS导航定位研究, E-mail:

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companyId=1322567133419126832, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2 空天信息大学(筹)导航与物联网学院, 济南, 250299)])], figs=[ArticleFig(id=1322567137722482771, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=EN, label=Fig. 1, caption=Flow chart of GNSS observation environment complexity assessment method, figureFileSmall=dHTXMx54cH+SoJi/cApZDA==, figureFileBig=dkhkmnkSDWoRg+67LtyltA==, tableContent=null), ArticleFig(id=1322567137814757460, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=CN, label=图1, caption=GNSS观测环境复杂度评估方法流程, figureFileSmall=dHTXMx54cH+SoJi/cApZDA==, figureFileBig=dkhkmnkSDWoRg+67LtyltA==, tableContent=null), ArticleFig(id=1322567138011889749, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=EN, label=Fig. 2, caption=Spearman correlation coefficients 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evaluation results of CODAS method under different trade-off coefficients, figureFileSmall=sPf366biMQVgj35T3yTqoQ==, figureFileBig=9gVRukqn8rCHVOAyK9qJIQ==, tableContent=null), ArticleFig(id=1322567138477457500, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=CN, label=图5, caption=CODAS方法在不同折衷系数下的监测站评估结果排序, figureFileSmall=sPf366biMQVgj35T3yTqoQ==, figureFileBig=9gVRukqn8rCHVOAyK9qJIQ==, tableContent=null), ArticleFig(id=1322567138552954973, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=EN, label=Fig. 6, caption=Ranking of monitoring station evaluation results of VIKOR method under different trade-off coefficients, figureFileSmall=rxxAVURzg92D9DgaGvfs7Q==, figureFileBig=LiNvh64u8Jfp9Cv+zYAsBg==, tableContent=null), ArticleFig(id=1322567138624258142, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=CN, label=图6, caption=VIKOR方法在不同折衷系数下的监测站评估结果排序, figureFileSmall=rxxAVURzg92D9DgaGvfs7Q==, figureFileBig=LiNvh64u8Jfp9Cv+zYAsBg==, tableContent=null), ArticleFig(id=1322567138691367007, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=EN, label=Tab. 1, caption=

Weights of GNSS data quality indicators under different weighting methods

, figureFileSmall=null, figureFileBig=null, tableContent=
质量指标 经验权重 熵权法权重 CRITIC法权重 综合主客观权重
数据完整率 0.4 0.053 0.137 0.295
周跳比 0.1 0.497 0.223 0.149
伪距多路径MP1 0.075 0.086 0.111 0.089
伪距多路径MP2 0.075 0.100 0.117 0.092
载噪比SNR1 0.04 0.057 0.119 0.070
载噪比SNR2 0.04 0.108 0.215 0.110
PDOP 0.27 0.099 0.078 0.193
), ArticleFig(id=1322567138766864480, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=CN, label=表1, caption=

不同赋权方法下GNSS数据质量指标的权重

, figureFileSmall=null, figureFileBig=null, tableContent=
质量指标 经验权重 熵权法权重 CRITIC法权重 综合主客观权重
数据完整率 0.4 0.053 0.137 0.295
周跳比 0.1 0.497 0.223 0.149
伪距多路径MP1 0.075 0.086 0.111 0.089
伪距多路径MP2 0.075 0.100 0.117 0.092
载噪比SNR1 0.04 0.057 0.119 0.070
载噪比SNR2 0.04 0.108 0.215 0.110
PDOP 0.27 0.099 0.078 0.193
), ArticleFig(id=1322567138833973345, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=EN, label=Tab. 2, caption=

Data quality indicators of monitoring stations

, figureFileSmall=null, figureFileBig=null, tableContent=
监测站 数据完整率/% 周跳比 MP1/cm MP2/cm SNR1 SNR2 PDOP
JC007 74.81 1 157 33.2 27.20 36.94 30.10 1.14
JC021 72.32 1 058 19.4 19.20 37.14 30.44 1.09
JC060 80.35 825 27.8 25.65 37.19 29.76 1.04
JC066 83.34 105 17.9 16.45 46.58 46.63 1.02
JC084 74.29 17 416 28.3 20.85 42.39 43.98 1.10
JC091 69.41 8 033 35.7 31.50 42.22 44.21 1.21
JC101 52.50 2 202 40.3 40.95 42.67 44.90 1.56
JC116 66.30 23 092 38.6 34.35 41.95 42.49 1.20
), ArticleFig(id=1322567138909470818, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=CN, label=表2, caption=

监测站数据质量指标

, figureFileSmall=null, figureFileBig=null, tableContent=
监测站 数据完整率/% 周跳比 MP1/cm MP2/cm SNR1 SNR2 PDOP
JC007 74.81 1 157 33.2 27.20 36.94 30.10 1.14
JC021 72.32 1 058 19.4 19.20 37.14 30.44 1.09
JC060 80.35 825 27.8 25.65 37.19 29.76 1.04
JC066 83.34 105 17.9 16.45 46.58 46.63 1.02
JC084 74.29 17 416 28.3 20.85 42.39 43.98 1.10
JC091 69.41 8 033 35.7 31.50 42.22 44.21 1.21
JC101 52.50 2 202 40.3 40.95 42.67 44.90 1.56
JC116 66.30 23 092 38.6 34.35 41.95 42.49 1.20
), ArticleFig(id=1322567138993356899, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=EN, label=Tab. 3, caption=

Data quality indicators and RMSE of monitoring stations

, figureFileSmall=null, figureFileBig=null, tableContent=
监测站 数据完整率/% 周跳比 MP1/cm MP2/cm SNR1 SNR2 PDOP RMSE/m
JC004 83.73 100 000 1.9 2.65 46.91 46.87 0.95 0.099
JC024 71.21 735.29 33.9 29.10 36.99 30.14 1.15 0.353
JC029 73.43 3.00 51.4 81.45 46.68 47.83 1.10 0.526
JC054 70.94 308.64 52.7 45.30 37.08 30.68 1.17 3.643
JC058 79.63 735.29 25.8 25.50 37.07 29.75 1.05 0.185
JC059 81.05 892.86 22.5 22.15 36.87 29.85 1.05 0.144
JC063 79.04 781.25 29.1 34.00 37.38 30.24 1.06 0.133
JC065 68.30 699.30 61.5 53.10 37.01 30.93 1.30 1.813
JC082 70.54 50 000 24.7 22.55 43.21 45.17 1.17 0.336
JC093 69.90 100 000 28.2 25.15 43.22 45.37 1.19 0.306
), ArticleFig(id=1322567139056271460, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=CN, label=表3, caption=

监测站数据质量指标及RMSE

, figureFileSmall=null, figureFileBig=null, tableContent=
监测站 数据完整率/% 周跳比 MP1/cm MP2/cm SNR1 SNR2 PDOP RMSE/m
JC004 83.73 100 000 1.9 2.65 46.91 46.87 0.95 0.099
JC024 71.21 735.29 33.9 29.10 36.99 30.14 1.15 0.353
JC029 73.43 3.00 51.4 81.45 46.68 47.83 1.10 0.526
JC054 70.94 308.64 52.7 45.30 37.08 30.68 1.17 3.643
JC058 79.63 735.29 25.8 25.50 37.07 29.75 1.05 0.185
JC059 81.05 892.86 22.5 22.15 36.87 29.85 1.05 0.144
JC063 79.04 781.25 29.1 34.00 37.38 30.24 1.06 0.133
JC065 68.30 699.30 61.5 53.10 37.01 30.93 1.30 1.813
JC082 70.54 50 000 24.7 22.55 43.21 45.17 1.17 0.336
JC093 69.90 100 000 28.2 25.15 43.22 45.37 1.19 0.306
), ArticleFig(id=1322567139131768933, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=EN, label=Tab. 4, caption=

Standard deviation of monitoring station evaluation results of CODAS and VIKOR methods under different trade-off coefficients

, figureFileSmall=null, figureFileBig=null, tableContent=
监测站 VIKOR CODAS
JC004 1.656 1.176
JC024 2.487 2.001
JC029 3.016 0.772
JC054 0.802 0.816
JC058 0.899 0.002
JC059 1.386 0.189
JC063 0.398 0.002
JC065 1.990 1.731
JC082 5.223 3.797
JC093 5.289 3.855
均值 2.315 1.434
), ArticleFig(id=1322567139203072102, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567131519107102, language=CN, label=表4, caption=

CODAS与VIKOR方法在不同折衷系数下的测站评估结果的标准差

, figureFileSmall=null, figureFileBig=null, tableContent=
监测站 VIKOR CODAS
JC004 1.656 1.176
JC024 2.487 2.001
JC029 3.016 0.772
JC054 0.802 0.816
JC058 0.899 0.002
JC059 1.386 0.189
JC063 0.398 0.002
JC065 1.990 1.731
JC082 5.223 3.797
JC093 5.289 3.855
均值 2.315 1.434
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基于主客观赋权CODAS的GNSS观测环境复杂度评估方法
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黄明庄 1 , 戴吾蛟 1, * , 余文坤 1 , 温亚鑫 2
大地测量与地球动力学 | 大地测量学 2026,46(4): 503-509
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大地测量与地球动力学 |大地测量学 2026 , 46 (4) : 503 -509
基于主客观赋权CODAS的GNSS观测环境复杂度评估方法
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黄明庄1 , 戴吾蛟1, * , 余文坤1, 温亚鑫2
作者信息
  • 1 中南大学地球科学与信息物理学院, 长沙, 410083
  • 2 空天信息大学(筹)导航与物联网学院, 济南, 250299
通讯作者:
戴吾蛟, 教授, 主要从事GNSS导航定位研究, E-mail:
作者简介:

黄明庄, 硕士生, 主要从事GNSS导航定位研究, E-mail:

GNSS Observation Environment Complexity Assessment Method Based on Subjective and Objective Weighted CODAS
Mingzhuang HUANG1 , Wujiao DAI1, * , Wenkun YU1, Yaxin WEN2
Affiliations
  • 1 School of Geosciences and Info-Physics, Central South University, Changsha 410083, China
  • 2 School of Navigation and Internet of Things, Aerospace Information Technology University, Jinan 250299, China
出版时间: 2026-04-15 doi: 10.14075/j.jgg.2025.06.198
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摘要
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针对GNSS高精度定位中观测环境复杂度的量化评估问题, 提出一种基于数据完整率、周跳比、伪距多路径误差、载噪比和PDOP等数据质量指标的综合主客观赋权组合距离评估法(CODAS)。基于不同赋权策略, 利用CODAS、TOPSIS和VIKOR方法对120个监测站的观测环境复杂度进行评估, 并采用Spearman相关系数衡量各方法评估结果与PPP动态解算精度的相关性。结果表明, 相较于单一赋权, 综合主客观赋权可提升CODAS方法准确性; CODAS方法的评估结果与均方根误差和平均误差的Spearman相关系数分别为0.897和0.924, 优于TOPSIS和VIKOR方法。参数敏感性分析表明, CODAS方法在不同折衷系数下的评估结果标准差均值小于1.5, 具备良好的稳定性。

GNSS观测环境复杂度  /  数据质量分析  /  CRITIC  /  综合赋权  /  CODAS

Aiming at the quantitative evaluation of observation environment complexity in GNSS high-precision positioning, a comprehensive subjective and objective weighted combinative distance-based assessment (CODAS) method based on data quality indicators such as data integrity rate, cycle slip ratio, pseudorange multipath error, carrier-to-noise ratio and PDOP is proposed. According to different weighting strategies, the CODAS, TOPSIS and VIKOR methods are used to evaluate the observation environment complexity of 120 monitoring stations, and the Spearman correlation coefficient is used to measure the correlation between evaluation results of each method and the accuracy of PPP kinematics solution. The results show that the comprehensive subjective and objective weighting can improve the accuracy of CODAS method compared with the single weighting. The Spearman correlation coefficients of evaluation results of CODAS method with RMSE and ME are 0.897 and 0.924, respectively, which are better than TOPSIS and VIKOR methods. Parameter sensitivity analysis shows that the mean standard deviation of evaluation results of CODAS method under different trade-off parameters is less than 1.5, indicating good stability.

GNSS observation environment complexity  /  data quality analysis  /  CRITIC  /  comprehensive weighting  /  CODAS
黄明庄, 戴吾蛟, 余文坤, 温亚鑫. 基于主客观赋权CODAS的GNSS观测环境复杂度评估方法. 大地测量与地球动力学, 2026 , 46 (4) : 503 -509 . DOI: 10.14075/j.jgg.2025.06.198
Mingzhuang HUANG, Wujiao DAI, Wenkun YU, Yaxin WEN. GNSS Observation Environment Complexity Assessment Method Based on Subjective and Objective Weighted CODAS[J]. Journal of Geodesy and Geodynamics, 2026 , 46 (4) : 503 -509 . DOI: 10.14075/j.jgg.2025.06.198
正文
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全球导航卫星系统(GNSS)广泛应用于变形监测[1]、精密工程测量、交通导航等领域，但在森林、山地、城市峡谷等复杂环境下，GNSS信号易受到遮挡、多路径效应和电磁波干扰等因素的影响，导致解算精度下降，甚至无法正常解算。在实际应用中，通常基于经验判断GNSS在不同观测环境下是否可用以及能否达到预期精度，缺乏定量判断标准。因此，量化评估GNSS观测环境的复杂程度及对定位精度的影响具有重要的实际意义。温亚鑫[2]提出GNSS观测环境复杂度的概念，用于描述监测环境的复杂程度，并利用GNSS观测数据质量及综合评价方法定量评估环境复杂度，为GNSS变形监测的适用性提供了判断依据。
GNSS观测数据质量指标主要包括数据完整率、周跳比、多路径误差、载噪比等[3]，这些指标能够反映GNSS数据质量，也可间接反映观测环境的复杂度。现有研究主要是利用这些指标综合评估观测数据质量，采用的评价方法可分为线性加权法[4-5]和非线性综合法两类。其中，线性加权法是将各指标赋权后相加得到综合评估结果，朱璇等[4]对各指标进行经验赋权后线性相加，以评估连续运行参考站的数据质量；非线性综合法则考虑指标间的交互作用或非线性关系，通常使用多准则决策法[6]实现，常见方法主要有灰色关联分析法[7]、逼近理想解排序法(TOPSIS)[8]、多准则妥协解排序法(VIKOR)[9-10]和组合距离评估法(CODAS)[11]等。两类方法都必须先确定各项指标的权重，权重确定方法主要有经验法[4]、变异系数法[5]、熵权法[12]、指标相关权重法(CRITIC)[13]、层次分析法[14]等。由于单一赋权策略易使评估结果出现偏差，可综合多种赋权方法确定指标权重[8]。
温亚鑫[2]评估GNSS观测环境复杂度时，采用经验定权和VIKOR法，该方法组合曼哈顿距离和切比雪夫距离，但存在曼哈顿距离全局空间衡量能力不足和切比雪夫距离对异常值较为敏感的问题，且完全依赖主观权重，评估结果的准确性与稳定性未得到大量数据的验证。为更准确地评估GNSS观测环境复杂度，本文基于数据完整率、周跳比、多路径误差、载噪比和位置精度因子(PDOP)等数据质量指标，提出一种基于主客观赋权的CODAS环境复杂度评估方法。该方法综合CRITIC方法和经验定权对指标进行赋权，并组合欧氏距离、曼哈顿距离和切比雪夫距离，实现全局误差、线性偏差累积与极端偏差控制的协同融合，能够弥补单一距离度量的不足。
为验证该方法的准确性，基于不同赋权策略，分别采用CODAS、TOPSIS以及VIKOR方法对120个监测站的观测环境复杂度进行评估，并以各监测站精密单点定位(PPP)动态解算精度与复杂度评估结果的一致性作为衡量评估方法有效性的标准。采用Spearman相关系数[11]分析各方法评估结果与解算精度之间的相关性，同时调整VIKOR和CODAS方法参数，探究参数变化对评估结果的影响，分析CODAS方法的参数敏感性。
1 环境复杂度CODAS评估方法
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CODAS是一种多准则决策方法，通过结合欧氏距离与曼哈顿距离的双重测度，提升算法对异常值的抗干扰能力和对相似监测站的区分能力。该方法的基本步骤为：1)标准化指标和确定指标权重；2)确定负理想解并计算待评估样本与负理想解的欧氏距离与曼哈顿距离；3)计算差异函数；4)计算综合评估值。
现有的CODAS方法主要应用于排序型决策问题，缺乏可解释的数值输出。为了更好地应用于GNSS测站环境复杂度评估，本文对现有的CODAS方法进行优化：1)根据各项数据质量指标能达到的最优和最劣情况，指定正理想解与负理想解，并对综合评估值进行标准化，以实现测站环境复杂度的定量化评估；2)引入欧氏距离、曼哈顿距离与切比雪夫距离的加权组合形式，以兼顾整体误差、累积偏差与最小偏差的影响。基于上述改进，构建适用于GNSS监测场景的环境复杂度评估方法，具体流程如图 1所示。
1.1 指标标准化
不同评价指标的量纲和数值尺度存在差异，需要对各项指标进行标准化。参考Dai等[10]提出的数据质量评估方法，结合实际GNSS观测环境中各项指标的常见取值范围，基于经验制定各项指标的标准化规则：
$\begin{aligned}& S(I)= \begin{cases}0 & I \geqslant 90 \\(90-I) / 50 & 40<I<90 \\1 & I \leqslant 40\end{cases} \\& S(R)= \begin{cases}0 & R \geqslant 1000 \\(1000-R) / 900 & 100<R<1000 \\1 & R \leqslant 100\end{cases} \\& S(\mathrm{MP})= \begin{cases}0 & \mathrm{MP} \leqslant 10 \\(\mathrm{MP}-10) / 90 & 10<\mathrm{MP}<100 \\1 & \mathrm{MP} \geqslant 100\end{cases} \\& S(\mathrm{SNR})= \begin{cases}0 & \mathrm{SNR} \geqslant 50 \\(50-\mathrm{SNR}) / 30 & 20<\mathrm{SNR}<50 \\1 & \mathrm{SNR} \leqslant 20\end{cases} \\& S(\mathrm{PDOP})= \begin{cases}0 & P \leqslant 0.8 \\(P-0.8) / 3.2 & 0.8<P<4 \\1 & P \geqslant 4\end{cases}\end{aligned}$
式中，S(I)、S(R)、S(MP)、S(SNR)、S(PDOP)分别表示数据完整率、周跳比、伪距多路径、载噪比和PDOP的评分量化规则，其中伪距多路径单位为cm，载噪比单位为dB·Hz。由于不同观测环境下的GNSS信号质量差异显著[15]，为确保各评价指标能反映实际观测环境的多样性，需覆盖较大的取值范围。
为实现以百分制形式定量评估环境复杂度，根据经验设定标准化后各项指标的最优最劣情况，即正负理想解：
$\begin{gathered}\mathrm{PIS}: S(I)^*=S(R)^*=S(\mathrm{MP})^*= \\S(\mathrm{SNR})^*=S(\mathrm{PDOP})^*=0 \\\mathrm{NIS}: S(I)^{-}=S(R)^{-}=S(\mathrm{MP})^{-}= \\S(\mathrm{SNR})^{-}=S(\mathrm{PDOP})^{-}=1\end{gathered}$
1.2 评价指标赋权
本文采用CRITIC法计算客观权重，结合经验定权，通过线性加权融合实现主客观综合赋权，具体步骤为：
1) 经验赋权。经验赋权方法依赖领域专家的知识与经验，直接设定各项指标的权重。本文在潘玥等[8]和Dai等[10]的基础上，结合实际GNSS定位精度对数据完整性和卫星几何分布的依赖性，赋予数据完整率和PDOP较高的权重。
2) CRITIC法计算客观权重。相较于仅依赖数据变异度的熵权法，CRITIC法在权重分配中同时考虑了指标的变异性和相关性。本文利用n个测站和2个理想解计算各项指标的客观权重，指标标准化后的数据矩阵X可表示为：
$\boldsymbol{X}=\left[\begin{array}{cccc}x_{11} & x_{12} & \cdots & x_{1 m} \\x_{21} & x_{22} & \cdots & x_{2 m} \\\vdots & \vdots & \vdots & \vdots \\x_{n 1} & x_{n 2} & \cdots & x_{n m} \\x_{b 1} & x_{b 2} & \cdots & x_{b m} \\x_{w 1} & x_{w 2} & \cdots & x_{w m}\end{array}\right]$
式中，xnm为第n个测站的第m项指标标准化后的指标值；xb1, …, xbm 为正理想解的各项指标值；xw1, …, xwm 为负理想解的各项指标值。
计算各项指标的标准差σj，确定数据变异度，表达式为：
$\sigma_j=\sqrt{\frac{1}{n-1} \sum\limits_{i=1}^{n+2}\left(x_{i j}-\bar{x}_j\right)^2}, j=1, 2, \cdots, m$
式中，$\bar{x}_j$为第j项指标标准化后的均值。
计算两个指标的相关系数rjk：
$\begin{gathered}r_{j k}=\frac{\sum\limits_{i=1}^{n+2}\left(x_{i j}-\bar{x}_j\right)\left(x_{i k}-\bar{x}_k\right)}{\sqrt{\sum\limits_{i=1}^{n+2}\left(x_{i j}-\bar{x}_j\right)^2} \sqrt{\sum\limits_{i=1}^{n+2}\left(x_{i k}-\bar{x}_k\right)^2}}, \\j=1, 2, \cdots, m ; k=1, 2, \cdots, m\end{gathered}$
计算冲突度Rj，表达式为：
$R_j=\sum\limits_{k=1}^m\left(1-r_{j k}\right)$
如果两个指标的相关系数接近1，说明信息重叠部分较大，冲突性较小，其中一个指标可能会被另一个指标线性表征，因此其权重也就越低。
计算信息承载量Cj和客观权重$W_j^{\text {obj }} $。信息承载量可用于衡量指标的重要性，对信息承载量进行标准化，求出各指标的客观权重：
$C_j=\sigma_j \times R_j, j=1, 2, \cdots, m $
$W_j^{\mathrm{obj}}=\frac{C_j}{\sum\limits_{j=1}^m C_j}, j=1, 2, \cdots, m$
客观定权结果的科学性与适用性依赖于参与权重计算的测站数量和其代表性，应采用尽可能多、分布广泛的测站进行客观赋权，获得全局统一的客观权重。客观权重一经确定，在后续评估中均作为固定输入，不再随参与评估的测站数量变化而调整。
3) 综合主客观赋权。为兼顾数据驱动与专家经验的优势，采用加权融合策略确定最终的指标权重：
$W_j=\alpha \cdot W_j^{\mathrm{obj}}+(1-\alpha) W_j^{\mathrm{sub}}$
式中，α为主客观权重的平衡因子；$W_j^{\text {obj }}、W_j^{\text {sub }}、W_j$分别为第j个指标的客观权重、主观权重和最终权重。
1.3 测站环境复杂度计算
监测站i与负理想解的欧氏距离Ei、曼哈顿距离Ti和切比雪夫距离Li可表示为：
$E_i=\sqrt{\sum\limits_{j=1}^m W_j\left(x_{i j}-S_j^{-}\right)^2}$
$T_i=\sum\limits_{j=1}^m W_j\left|x_{i j}-S_j^{-}\right|$
$L_i=\max\limits _{j=1}^m\left(W_j \cdot\left(x_{i j}-S_j^{-}\right)\right)$
监测站i的综合评估值为：
$h_i=v \cdot\left(E_i+T_i\right)+(1-v) \cdot L_i$
式中，v为折衷系数，用于权衡测站的整体表现与最优表现，取值范围为0~1。
将式(13)进行标准化，得到监测站i的环境复杂度：
$H_i=100 \times \frac{h_{\max }-h_i}{h_{\max }-h_{\min }}$
式中，hmax、hmin分别为正、负理想解的综合评估值。
2 实验与分析
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为比较分析GNSS观测环境复杂度评估方法的准确性和稳定性，设计以下两组实验：
1) 准确性分析。基于不同赋权策略，分别采用TOPSIS、VIKOR以及CODAS方法对120个监测站的观测环境复杂度进行评估，通过分析各方法评估结果与解算精度之间的相关性，验证评估结果的准确性。2)参数敏感性分析。为探究评估结果是否依赖折衷系数的设定，对CODAS和VIKOR方法的折衷系数进行调整，评估不同参数下评估结果的稳定性。
2.1 实验数据与指标权重确定
实验选取我国福建、湖南和江西等地区的120个不同观测环境的GNSS监测站连续1 d的观测数据，采样间隔为30 s。所选监测站均配置相同型号的接收机(北云T1系列)和天线(BY500)，以保证数据的一致性和可比性。使用GNSS ANUBIS[16]软件，提取各监测站GPS+BDS双系统的数据质量指标。采用熵权法、CRITIC法和综合主客观赋权法对指标进行权重计算，结果如表 1所示。综合主客观权重按式(9)进行计算，其中α=0.4。
2.2 准确性分析
GNSS定位精度与观测环境密切相关，为验证环境复杂度评估的准确性，将PPP动态解算精度与复杂度评估结果的相关性作为准确性的判断依据，相关性越高说明复杂度评估越准确。对各监测站观测数据进行GPS+BDS双频PPP动态解算，将所得三维方向上的均方根误差(RMSE)和平均误差(ME)作为监测站环境复杂度评估的依据。
2.2.1 实验设计
设计6种不同方案对GNSS监测站的环境复杂度进行计算，具体方案如下：方案1，熵权法+CODAS(折衷系数v=0.5)；方案2，CRITIC+CODAS(折衷系数v=0.5)；方案3，经验赋权+CODAS(折衷系数v=0.5)；方案4，CRITIC+经验赋权+TOPSIS；方案5，CRITIC+经验赋权+VIKOR(折衷系数v=0.5)；方案6，CRITIC+经验赋权+CODAS(折衷系数v=0.5)。
2.2.2 结果分析
为评估不同方案评估结果的准确性，计算各方案的评估结果与RMSE和ME的Spearman相关系数，结果如图 2所示。
由图 2可知，方案1评估结果与RMSE和ME的Spearman相关系数最低，分别为0.407和0.473；方案2采用CRITIC方法进行指标赋权后，评估结果有所优化，相关系数提升至0.592和0.630。结合表 1可知，熵权法对周跳比赋予过高的权重，对数据完整率和PDOP赋权过低，与实际GNSS定位精度对数据完整性和卫星几何分布的依赖性不符。CRITIC方法考虑了各项指标的相关性，可平衡各指标的权重，但其对PDOP赋权仍然较低，仅依靠CRITIC方法进行指标赋权，无法满足环境复杂度评估的精度需求。方案3基于经验赋权CODAS方法的评估性能得到很大提升，评估结果与RMSE和ME的相关系数分别为0.890和0.873。CODAS方法采用综合主客观赋权后，评估结果最准确，能够弥补单一赋权方法的缺点。
方案4~6采用综合主客观赋权法进行指标赋权，TOPSIS和VIKOR方法的评估性能相近，CODAS方法评估结果与RMSE和ME的相关系数分别为0.897和0.924，评估结果与解算精度的匹配度最佳。
为进一步验证所提方法的准确性，从120个监测站中选取8个测站，数据质量指标如表 2所示。采用综合主客观赋权的TOPSIS、VIKOR和CODAS三种方法对8个监测站的环境复杂度进行评估，评估结果与RMSE如图 3所示。可以看出，TOPSIS和VIKOR方法对JC066监测站的评估结果偏离实际解算精度，原因为标准化后JC066测站的周跳比显著偏小，说明这2种方法的评估结果容易受到个别指标的过度影响。而CODAS方法能够有效缓解个别指标主导评估结果的现象，其评估结果与RMSE变化趋势完全一致。实验结果表明，综合主客观赋权CODAS方法的评估结果与解算精度的相关性更高，可为监测站环境复杂度评估提供有力支持。
2.3 参数敏感性分析
为探究评估结果在不同折衷系数下的稳定性，分析折衷系数v对CODAS和VIKOR方法评估结果的影响。
2.3.1 实验设计
CODAS和VIKOR方法中折衷系数v一般为0~1，为全面评估参数变化对2种方法评估结果的影响，在表 1的综合主客观权重下，设置9个0~1之间的参数，分析在不同参数设定下评估结果的变化情况。
2.3.2 结果分析
对2种方法不同参数下的评估结果与解算精度进行Spearman相关分析，结果如图 4所示。可以看出，CODAS和VIKOR方法在不同折衷系数下的评估结果与RMSE的相关系数的标准差分别为0.013 29和0.013 94，与ME的相关系数的标准差分别为0.025 71和0.025 70。2种方法在整体相关性波动上差异较小，当折衷系数接近0和1时，评估结果的相关性波动增大，表明2种方法对极端折衷系数设定较为敏感。当折衷系数接近0.5时，评估结果相对稳定，且准确性较高。
为进一步验证CODAS方法在监测站环境复杂度评估中的稳定性，从120个监测站中选取10个测站，数据质量指标及RMSE如表 3所示。
调整CODAS和VIKOR方法的折衷系数v，得到10个监测站的评估结果的标准差及其排序变化情况，结果如表 4、图 5和图 6所示。VIKOR方法在折衷系数变化过程中，10个监测站中有7个监测站的排序结果发生变化，部分测站变化频繁，尤其是JC063测站评估结果排序发生4次变化，且存在某项突出指标的JC082和JC093测站的评估结果表现出较大波动，其标准差均超过5.2。相比之下，CODAS方法只有5个监测站的评估结果排序发生变化，大部分测站只发生1次变化，仅有周跳比突出的JC029测站发生3次变化。此外，采用CODAS方法时10个测站评估值的标准差均值为1.434，明显低于VIKOR方法的2.315。表明CODAS方法使用3种距离的组合后，评估结果的稳定性得到提升。
3 结语
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本文针对当前GNSS观测环境复杂度难以量化评估的问题，提出一种基于主客观赋权的CODAS方法，并对120个监测站的观测环境复杂度进行评估，得到以下结论：
1) CRITIC方法的赋权结果稍优于熵权法，但仍无法满足评估精度需求；综合主客观赋权可较好地结合主观赋权和客观赋权的优势，能够提升评估精度。
2) 基于主客观赋权的CODAS方法评估环境复杂度的准确性优于TOPSIS和VIKOR方法，并且该方法的参数敏感性低于VIKOR方法。
总体而言，综合主客观赋权CODAS的GNSS观测环境复杂度评估方法，可为复杂环境下GNSS高精度定位适用性判断、监测站选址优化、数据质量评估及地质灾害监测等应用提供理论与技术支撑。未来研究可进一步结合机器学习和视觉等技术，优化评估模型，增强复杂环境下GNSS观测环境的智能评估能力。
基金
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  • 国家自然科学基金(42474059)
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2026年第46卷第4期
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doi: 10.14075/j.jgg.2025.06.198
  • 接收时间：2025-06-12
  • 首发时间：2026-10-29
  • 出版时间：2026-04-15
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  • 收稿日期：2025-06-12
基金
国家自然科学基金(42474059)
作者信息
    1 中南大学地球科学与信息物理学院, 长沙, 410083
    2 空天信息大学(筹)导航与物联网学院, 济南, 250299

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戴吾蛟, 教授, 主要从事GNSS导航定位研究, E-mail:
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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
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