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Article(id=1322916878783492978, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322916858604696290, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2025.08.266, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1754323200000, receivedDateStr=2025-08-05, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793337562508, onlineDateStr=2026-10-30, pubDate=1786723200000, pubDateStr=2026-08-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793337562508, onlineIssueDateStr=2026-10-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793337562508, creator=13701087609, updateTime=1793337562508, updator=13701087609, issue=Issue{id=1322916858604696290, tenantId=1146029695717560320, journalId=1281212831689347082, year='2026', volume='46', issue='8', pageStart='913', pageEnd='1038', issueExtLink='null', onlineDate='null', pubDate='1786723200000', pubDateStr='2026-08-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793337557698, creator='13701087609', updateTime=1793337557698, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=971, endPage=978, ext={EN=ArticleExt(id=1322916878968042355, articleId=1322916878783492978, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Marine Long Baseline GNSS Positioning Based on Distance-Constrained Robust Kalman Filter, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Aiming at the significant multipath effect of GNSS at sea and the decline in observation data quality caused by various environmental factors, the performance of traditional Kalman filter algorithm is often significantly affected under such complex conditions. To improve the positioning accuracy in dynamic marine environment, we propose a robust Kalman filter baseline differential positioning model based on the IGGⅢ weighting function. Considering the marine platform has multiple receivers, distance constraint conditions are introduced to correct the filter solution, and the influence of constraint conditions on positioning results is analyzed. The model is verified through real measurement data. The results show that in long baseline differential positioning, the robust Kalman filter can effectively suppress gross error interference, and the positioning accuracy is significantly better than that of the traditional extended Kalman filter algorithm. After introducing distance constraints, the accuracy of positioning solution is further improved, verifying the effectiveness and practicality of this method in complex marine environments.

, authors=Yinze LAN1, Anmin ZENG1, 2, 3, *, Jia FANG1, authorsList=Yinze LAN, Anmin ZENG, Jia FANG, authorCompany=null, correspAuthors=Anmin ZENG, 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=1322916881648202618, articleId=1322916878783492978, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=基于距离约束抗差卡尔曼滤波的海上长基线GNSS定位, columnId=1281909276545356011, journalTitle=大地测量与地球动力学, columnName=大地测量学, runingTitle=null, highlight=null, articleAbstract=

针对海上GNSS多路径效应显著以及各类环境因素导致观测数据质量下降的问题，传统卡尔曼滤波算法在此类复杂条件下的滤波性能常受到显著影响。为提高在海洋动态环境下的定位精度，设计一种基于IGGⅢ权函数的抗差卡尔曼滤波基线差分定位模型，考虑到海上平台具有多台接收机，引入距离约束条件对滤波解进行修正，并分析约束条件对定位结果的影响。通过实测数据对模型进行验证，结果表明，在长基线差分定位中，抗差卡尔曼滤波能有效抑制粗差干扰，定位精度明显优于传统扩展卡尔曼滤波算法；引入距离约束后，定位解精度进一步提升，验证了该方法在复杂海洋环境下的有效性与实用性。

, authors=兰尹泽1, 曾安敏1, 2, 3, *, 方甲1, authorsList=兰尹泽, 曾安敏, 方甲, authorCompany=null, correspAuthors=曾安敏, authorNote=

兰尹泽，硕士生，主要从事海洋环境下的GNSS长基线动态定位研究，E-mail：

, correspAuthorsNote=
曾安敏, 博士, 研究员, 主要从事大地测量学与测量工程研究, 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=tshCpGrtLf0+ZQmZAzlmLQ==, magXml=y8+pNsK19gnpcH1Fw80XrQ==, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=cLPZfJsN6Q+vgs8nDCy+1g==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=YnUsIuuf372ttZEgmcBgZA==, mapNumber=null, fund=null)}, authors=[Author(id=1322916882323485573, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, orderNo=0, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=lanyinze2023@163.com, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1322916882419954567, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, authorId=1322916882323485573, language=EN, stringName=Yinze LAN, firstName=Yinze, middleName=null, lastName=LAN, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=1, address=1 School of Geological Engineering and Geomatics, Chang'an University, Xi'an 710054, China, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1322916882499646344, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, authorId=1322916882323485573, language=CN, stringName=兰尹泽, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=1, address=1 长安大学地质工程与测绘学院, 西安, 710054, bio={"content":"

兰尹泽，硕士生，主要从事海洋环境下的GNSS长基线动态定位研究，E-mail：

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兰尹泽，硕士生，主要从事海洋环境下的GNSS长基线动态定位研究，E-mail：

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tableContent=null), ArticleFig(id=1322916885922198436, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, language=CN, label=图3, caption=不同方案海上长基线差分定位偏差, figureFileSmall=hbRy6Gkq9tSZOmtR1FYCcQ==, figureFileBig=MUkLgsctHDjelz2XGsAtnw==, tableContent=null), ArticleFig(id=1322916885993501605, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, language=EN, label=Tab. 1, caption=

Quality check of GNSS data at each station

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测站 系统 数据可用率 多路径效应 周跳比
历元总数/个 实际历元数/个 占比/% MP1/cm MP2/cm MP7/cm 观测值个数/ 周跳个数 CSR
S0349 GPS 116 40 116 40 100.00 32.8 32.7 7 142.9
BDS 116 40 116 40 100.00 33.3 31.6
HCN1 GPS 116 40 116 39 99.99 30.4 37.2 47 21.3
BDS 116 40 116 40 100.00 20.0 21.4
S4165 GPS 116 40 116 31 99.92 67.9 69.5 6 166.7
BDS 116 40 116 40 100.00 66.4 63.1
S4159 GPS 172 80 172 80 100.00 28.8 24.5 10 100.0
BDS 172 80 172 80 100.00 19.1 14.1
S0306 GPS 172 80 172 80 100.00 20.2 19.6 648 6 0.2
BDS 172 80 172 80 100.00 18.6 12.2
), ArticleFig(id=1322916886081581990, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, language=CN, label=表1, caption=

各测站GNSS数据质量检核

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测站 系统 数据可用率 多路径效应 周跳比
历元总数/个 实际历元数/个 占比/% MP1/cm MP2/cm MP7/cm 观测值个数/ 周跳个数 CSR
S0349 GPS 116 40 116 40 100.00 32.8 32.7 7 142.9
BDS 116 40 116 40 100.00 33.3 31.6
HCN1 GPS 116 40 116 39 99.99 30.4 37.2 47 21.3
BDS 116 40 116 40 100.00 20.0 21.4
S4165 GPS 116 40 116 31 99.92 67.9 69.5 6 166.7
BDS 116 40 116 40 100.00 66.4 63.1
S4159 GPS 172 80 172 80 100.00 28.8 24.5 10 100.0
BDS 172 80 172 80 100.00 19.1 14.1
S0306 GPS 172 80 172 80 100.00 20.2 19.6 648 6 0.2
BDS 172 80 172 80 100.00 18.6 12.2
), ArticleFig(id=1322916886169662375, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, language=EN, label=Tab. 2, caption=

Statistics of positioning results for different schemes

, figureFileSmall=null, figureFileBig=null, tableContent=
方案 E方向 N方向 U方向
STD/m RMSE/m STD/m RMSE/m STD/m RMSE/m
EKF 0.044 0.066 0.016 0.020 0.050 0.360
RKF 0.037 0.047 0.015 0.019 0.045 0.338
), ArticleFig(id=1322916886245159848, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, language=CN, label=表2, caption=

不同方案定位结果统计

, figureFileSmall=null, figureFileBig=null, tableContent=
方案 E方向 N方向 U方向
STD/m RMSE/m STD/m RMSE/m STD/m RMSE/m
EKF 0.044 0.066 0.016 0.020 0.050 0.360
RKF 0.037 0.047 0.015 0.019 0.045 0.338
), ArticleFig(id=1322916886320657321, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, language=EN, label=Tab. 3, caption=

Statistics of RMS sequences for different schemes

, figureFileSmall=null, figureFileBig=null, tableContent=
方案 最小值/m 最大值/m 均值/m STD/m
EKF 0.1 6.2 0.37 0.36
RKF 0.1 5.6 0.32 0.21
), ArticleFig(id=1322916886404543402, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, language=CN, label=表3, caption=

不同方案RMS序列统计

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方案 最小值/m 最大值/m 均值/m STD/m
EKF 0.1 6.2 0.37 0.36
RKF 0.1 5.6 0.32 0.21
), ArticleFig(id=1322916886467457963, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, language=EN, label=Tab. 4, caption=

Baselines information

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名称 测站 长度/km
BL1 S0306-S0349 441.718~450.904
BL2 S0306-HCN1 441.736~450.922
BL3 S0306-S4165 441.723~450.912
BL4 HCN1-S0349 0.022 495
BL5 HCN1-S4165 0.013 171
BL6 S0349-S4165 0.023 192
), ArticleFig(id=1322916886534566828, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, language=CN, label=表4, caption=

基线信息

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名称 测站 长度/km
BL1 S0306-S0349 441.718~450.904
BL2 S0306-HCN1 441.736~450.922
BL3 S0306-S4165 441.723~450.912
BL4 HCN1-S0349 0.022 495
BL5 HCN1-S4165 0.013 171
BL6 S0349-S4165 0.023 192
), ArticleFig(id=1322916886601675693, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, language=EN, label=Tab. 5, caption=

Solution strategies for long baseline differential positioning

, figureFileSmall=null, figureFileBig=null, tableContent=
参数 设置
采样间隔 5 s
频率选择 GPS: L1+L2；BDS-2: B1I+B2I；BDS-3: B1I
截止高度角 15°
卫星星历 广播星历
动力学模型 常速度模型
电离层改正 参数估计
对流层改正 Saastamoinen模型+参数估计
整周模糊度 参数估计
天线改正 igs14_2247.atx
), ArticleFig(id=1322916886668784558, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, language=CN, label=表5, caption=

长基线差分定位解算策略

, figureFileSmall=null, figureFileBig=null, tableContent=
参数 设置
采样间隔 5 s
频率选择 GPS: L1+L2；BDS-2: B1I+B2I；BDS-3: B1I
截止高度角 15°
卫星星历 广播星历
动力学模型 常速度模型
电离层改正 参数估计
对流层改正 Saastamoinen模型+参数估计
整周模糊度 参数估计
天线改正 igs14_2247.atx
), ArticleFig(id=1322916886735893423, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, language=EN, label=Tab. 6, caption=

Statistics of distance errors between antennas for each scheme

, figureFileSmall=null, figureFileBig=null, tableContent=
方案 STD/m RMSE/m
EKF 0.225 0.229
RKF 0.200 0.206
距离约束RKF 0.187 0.201
), ArticleFig(id=1322916886803002288, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916878783492978, language=CN, label=表6, caption=

各方案天线间距离偏差统计

, figureFileSmall=null, figureFileBig=null, tableContent=
方案 STD/m RMSE/m
EKF 0.225 0.229
RKF 0.200 0.206
距离约束RKF 0.187 0.201
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基于距离约束抗差卡尔曼滤波的海上长基线GNSS定位
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兰尹泽 1 , 曾安敏 1, 2, 3, * , 方甲 1
大地测量与地球动力学 | 大地测量学 2026,46(8): 971-978
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大地测量与地球动力学 |大地测量学 2026 , 46 (8) : 971 -978
基于距离约束抗差卡尔曼滤波的海上长基线GNSS定位
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兰尹泽1 , 曾安敏1, 2, 3, * , 方甲1
作者信息
  • 1 长安大学地质工程与测绘学院, 西安, 710054
  • 2 西安测绘研究所, 西安, 710054
  • 3 空间基准全国重点实验室, 西安, 710054
通讯作者:
曾安敏, 博士, 研究员, 主要从事大地测量学与测量工程研究, E-mail:
作者简介:

兰尹泽，硕士生，主要从事海洋环境下的GNSS长基线动态定位研究，E-mail：

Marine Long Baseline GNSS Positioning Based on Distance-Constrained Robust Kalman Filter
Yinze LAN1 , Anmin ZENG1, 2, 3, * , Jia FANG1
Affiliations
  • 1 School of Geological Engineering and Geomatics, Chang'an University, Xi'an 710054, China
  • 2 Xi'an Institute of Surveying and Mapping, Xi'an 710054, China
  • 3 State Key Laboratory of Spatial Datum, Xi'an 710054, China
出版时间: 2026-08-15 doi: 10.14075/j.jgg.2025.08.266
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摘要
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针对海上GNSS多路径效应显著以及各类环境因素导致观测数据质量下降的问题，传统卡尔曼滤波算法在此类复杂条件下的滤波性能常受到显著影响。为提高在海洋动态环境下的定位精度，设计一种基于IGGⅢ权函数的抗差卡尔曼滤波基线差分定位模型，考虑到海上平台具有多台接收机，引入距离约束条件对滤波解进行修正，并分析约束条件对定位结果的影响。通过实测数据对模型进行验证，结果表明，在长基线差分定位中，抗差卡尔曼滤波能有效抑制粗差干扰，定位精度明显优于传统扩展卡尔曼滤波算法；引入距离约束后，定位解精度进一步提升，验证了该方法在复杂海洋环境下的有效性与实用性。

差分定位  /  粗差  /  抗差卡尔曼滤波  /  长基线  /  距离约束

Aiming at the significant multipath effect of GNSS at sea and the decline in observation data quality caused by various environmental factors, the performance of traditional Kalman filter algorithm is often significantly affected under such complex conditions. To improve the positioning accuracy in dynamic marine environment, we propose a robust Kalman filter baseline differential positioning model based on the IGGⅢ weighting function. Considering the marine platform has multiple receivers, distance constraint conditions are introduced to correct the filter solution, and the influence of constraint conditions on positioning results is analyzed. The model is verified through real measurement data. The results show that in long baseline differential positioning, the robust Kalman filter can effectively suppress gross error interference, and the positioning accuracy is significantly better than that of the traditional extended Kalman filter algorithm. After introducing distance constraints, the accuracy of positioning solution is further improved, verifying the effectiveness and practicality of this method in complex marine environments.

differential positioning  /  gross error  /  robust Kalman filter  /  long baseline  /  distance constraint
兰尹泽, 曾安敏, 方甲. 基于距离约束抗差卡尔曼滤波的海上长基线GNSS定位. 大地测量与地球动力学, 2026 , 46 (8) : 971 -978 . DOI: 10.14075/j.jgg.2025.08.266
Yinze LAN, Anmin ZENG, Jia FANG. Marine Long Baseline GNSS Positioning Based on Distance-Constrained Robust Kalman Filter[J]. Journal of Geodesy and Geodynamics, 2026 , 46 (8) : 971 -978 . DOI: 10.14075/j.jgg.2025.08.266
正文
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全球导航卫星系统(GNSS)已广泛应用于现代定位与导航，其中差分定位技术是目前海洋定位中应用最为广泛的方法。差分定位精度与基线距离密切相关，通常仅在距离小于20 km的短基线时能够保持厘米级精度；而在长基线情况下，定位精度将显著下降，可能降至分米级甚至米级。
针对长基线差分定位解算，国内外学者已开展大量研究工作。Kubo等[1]和李玉星等[2]将双差对流层和双差电离层作为参数进行估计，在41 km和超过100 km基线时均达到厘米级定位精度；Liu等[3]提出一种基于BDS-3与Galileo组合系统的超宽巷长基线实时动态差分(real-time kinematic, RTK)定位方法，实现了长基线瞬时分米级定位精度；Xu等[4]基于数值天气预报(numerical weather prediction, NWP)模型对对流层延迟进行约束，提出一种面向中长基线的BDS/GPS组合RTK定位方法，实现了水平方向优于3 cm、垂直方向优于5 cm的定位精度；Wang等[5]利用浮点模糊度的二次形式对其偏差进行建模，提出一种针对长基线固定解中未建模误差的补偿策略，实测的2条长基线固定解误差平均改善率可达41.42%~92.86%，3个方向的均方根误差(RMSE)平均改善率可达39.11%~65.71%；吕震等[6]对BDS-3与Galileo四频宽巷组合方式进行优选，并在超过500 km长基线条件下完成单系统、双系统与三系统的相对定位解算，结果表明, 双系统和三系统的相对定位精度均可达到10-9 m量级；蔡巍等[7]提出一种基于三频组合观测值的RTK卡尔曼滤波定位方法，宽巷模糊度可实现单历元固定，静态固定率约100%，动态情况下固定率约65%，实时平面位置精度达到厘米级。然而，上述研究主要集中于陆地环境及静态条件下，对于海洋环境中动态长基线差分定位问题的研究仍相对有限，亟须进一步探索与验证。
海洋环境复杂多变导致观测噪声增大，并产生显著的多路径效应，进而影响定位性能[8-11]。为应对该问题，本文设计一种削弱观测异常噪声的IGGⅢ权函数的抗差卡尔曼滤波基线差分定位模型。此外，考虑到海上载体通常搭载多个GNSS天线，各天线之间的几何关系已知，可作为约束条件引入定位解算过程中，以提升系统的整体精度与稳定性[12-16]。因此，本文充分利用多个GNSS天线的几何关系，推导引入距离约束条件的抗差滤波解算方法，以提高动态环境下的定位精度和可靠性。最后，基于海边和海上实测数据对上述方法开展实验分析。
1 抗差卡尔曼滤波基线差分定位模型
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1.1 长基线差分定位观测模型
GNSS数据处理中的相对定位通常采用差分技术。通过对同一卫星的双接收机观测进行单差处理，可有效消除与卫星有关的误差，包括卫星钟差和卫星端硬件延迟；进一步对2颗卫星的单差结果进行双差处理，则可同步消除接收机钟差和接收机端硬件延迟，从而构建更稳健、精简的观测模型。在短基线条件下，电离层与对流层延迟等误差具有较强的空间相关性，能在双差处理中被进一步削弱，使得双差模型在高精度定位中表现优异。然而在海洋等长基线环境中，接收机间距离增大，误差空间相关性下降，尤其是大气延迟等系统误差难以被完全抵消，从而影响定位精度。尽管可通过误差建模、多频组合等方法抑制部分误差，但残差项仍难以忽略，需在观测模型中估计多个未知参数，包括测站三维坐标、载波相位模糊度、电离层延迟及天顶对流层延迟等。原始观测方程可表示为：
$\left\{\begin{array}{l}P_{\mathrm{r}, i}^{\mathrm{s}}= \rho_{\mathrm{r}}^{\mathrm{s}}+c\left(\mathrm{~d} t_{\mathrm{r}}-\mathrm{d} t^{\mathrm{s}}\right)+T_{\mathrm{r}}^{\mathrm{s}}+I_{\mathrm{r}, i}^{\mathrm{s}}+ \\ \quad\quad\;\;\; c\left(b_{\mathrm{r}, i}-b_i^{\mathrm{s}}\right)+\delta_{P, \mathrm{r}}^{\mathrm{s}}+\varepsilon_P \\\lambda_i \varphi_{\mathrm{r}, i}^{\mathrm{s}}= \rho_{\mathrm{r}}^{\mathrm{s}}+c\left(\mathrm{~d} t_{\mathrm{r}}-\mathrm{d} t^{\mathrm{s}}\right)+T_{\mathrm{r}}^{\mathrm{s}}-I_{\mathrm{r}, i}^{\mathrm{s}}+ \\ \quad\quad\quad\;\; c\left(B_{\mathrm{r}, i}-B_i^{\mathrm{s}}\right)+\lambda_i N_{\mathrm{r}, i}^{\mathrm{s}}+\delta_{\varphi, \mathrm{r}}^{\mathrm{s}}+\varepsilon_{\varphi}\end{array}\right.$
对上述观测方程进行双差之后，多数误差可被消除或削弱，长基线双差观测模型可表示为：
$\left\{\begin{array}{l}\Delta \nabla P_{\mathrm{qf}, i}^{\mathrm{ad}}= \Delta \nabla \rho_{\mathrm{qf}}^{\mathrm{ad}}+\Delta \nabla I_{\mathrm{qf}, i}^{\mathrm{ad}}+\Delta \nabla T_{\mathrm{qf}}^{\mathrm{ad}}+ \\ \quad\quad\quad\quad\quad\Delta \nabla \varepsilon_P \\\lambda_i \Delta \nabla \varphi_{\mathrm{qf}, i}^{\mathrm{ad}}= \Delta \nabla \rho_{\mathrm{qf}}^{\mathrm{ad}}-\Delta \nabla I_{\mathrm{qf}, i}^{\mathrm{ad}}+\Delta \nabla T_{\mathrm{qf}}^{\mathrm{ad}}+ \\ \quad\quad\quad\quad\quad\quad\lambda_i \Delta \nabla N_{\mathrm{qf}, i}^{\mathrm{ad}}+\Delta \nabla \varepsilon_{\varphi}\end{array}\right.$
式中，a、d表示被观测的2颗卫星；下标q、f分别表示基站与流动站；▽Δ表示双差算符；P和φ分别表示伪距与载波相位观测量；下标i表示所用的频率；c表示真空中光速；λi表示该频率下的载波波长；ρ表示站星间几何距离；I和T分别表示电离层倾斜延迟与对流层倾斜延迟；dtr和dts分别表示接收机钟差和卫星钟差；br, i和bis分别表示该频率下接收机端和卫星端的伪距硬件时延；Br, i和Bis分别表示该频率下接收机端和卫星端的相位硬件时延；N表示整周模糊度项；δP和δφ分别表示伪距及载波的相位中心偏差、潮汐效应和相对论效应等系统误差，可通过相应模型进行改正；εP和εφ分别表示伪距与载波相位观测值的观测噪声项。
1.2 抗差卡尔曼滤波模型
对于双频观测，传统扩展卡尔曼滤波(extended Kalman filter, EKF)模型采用以下状态方程和双差观测方程：
$\left\{\begin{array}{l}\hat{\boldsymbol{x}}_k=\boldsymbol{F}_{k . k-1} \hat{\boldsymbol{x}}_{k-1}+\boldsymbol{w}_{k-1} \\\boldsymbol{z}_k=\boldsymbol{H}_k \hat{\boldsymbol{x}}_k+\boldsymbol{v}_k\end{array}\right.$
式中，$ \hat{\boldsymbol{x}}_k$表示状态向量；Fk.k－1表示状态转移矩阵；wk－1表示过程噪声；Hk、vk、zk分别表示k时刻的设计矩阵、新息向量和观测向量。在长基线差分定位中，状态参数包括流动站三维坐标与速度、单差电离层延迟、对流层延迟及模糊度参数，可表示为：
$\boldsymbol{x}=\left(\boldsymbol{p}_{\mathrm{f}}^{\mathrm{T}}, \boldsymbol{v}_{\mathrm{f}}^{\mathrm{T}}, Z_{\mathrm{f}}, Z_{\mathrm{q}}, \Delta \boldsymbol{I}^{\mathrm{T}}, \Delta \boldsymbol{N}_1^{\mathrm{T}}, \Delta \boldsymbol{N}_2^{\mathrm{T}}\right)^{\mathrm{T}}$
式中，pf为流动站坐标参数；vf为流动站速度参数；Zf、Zq分别为流动站和基准站的天顶对流层参数；ΔI为L1频率下的单差垂直电离层延迟；ΔN1和ΔN2分别为第1个频率和第2个频率的单差模糊度参数。
状态转移矩阵与设计矩阵形式如下：
$\boldsymbol{F}=\left(\begin{array}{ccccc}\boldsymbol{I}_{3 \times 3} & \tau_{\mathrm{f}} \boldsymbol{I}_{3 \times 3} & & & \\& \boldsymbol{I}_{3 \times 3} & & & \\& & \boldsymbol{I}_{2 \times 2} & & \\& & & \boldsymbol{I}_{m \times m} & \\& & & & \boldsymbol{I}_{(2 m-2) \times(2 m-2)}\end{array}\right)$
$\boldsymbol{H}(x)=\left(\begin{array}{cccccc}-\boldsymbol{D} \boldsymbol{E} & \boldsymbol{0} & \boldsymbol{D} \boldsymbol{M}_{T, \mathrm{f}} & \boldsymbol{D} \boldsymbol{M}_{T, \mathrm{q}} & -\gamma_1 \boldsymbol{D} \boldsymbol{M}_I & \lambda_1 \boldsymbol{D} &{}\\-\boldsymbol{D} \boldsymbol{E} & \boldsymbol{0} & \boldsymbol{D} \boldsymbol{M}_{T, \mathrm{f}} & \boldsymbol{D} \boldsymbol{M}_{T, \mathrm{q}} & -\gamma_2 \boldsymbol{D} \boldsymbol{M}_I & {}&\lambda_2 \boldsymbol{D} \\-\boldsymbol{D} \boldsymbol{E} & \boldsymbol{0} & \boldsymbol{D} \boldsymbol{M}_{T, \mathrm{f}} & \boldsymbol{D} \boldsymbol{M}_{T, \mathrm{q}} & \gamma_1 \boldsymbol{D} \boldsymbol{M}_I & \\-\boldsymbol{D} \boldsymbol{E} & \boldsymbol{0} & \boldsymbol{D} \boldsymbol{M}_{T, \mathrm{f}} & \boldsymbol{D} \boldsymbol{M}_{T, \mathrm{q}} & \gamma_2 \boldsymbol{D} \boldsymbol{M}_I &\end{array}\right)$
式中，I表示单位矩阵；τf表示采样间隔；m表示共视卫星数；D表示单差矩阵；E表示流动站至各共视卫星的方向余弦向量；MT, f、MT, q分别表示流动站和基站的对流层投影函数矩阵；MI表示电离层投影函数向量；λ1、λ2表示对应频率波长；γk=λk2/λ12。
双差观测噪声与过程噪声协方差均可表示为分块矩阵：
$\begin{aligned}\boldsymbol{R}= & \operatorname{diag}\left(\boldsymbol{D} \boldsymbol{R}_{\varphi, 1} \boldsymbol{D}^{\mathrm{T}}, \boldsymbol{D} \boldsymbol{R}_{\varphi, 2} \boldsymbol{D}^{\mathrm{T}}, \right. \\& \left.\boldsymbol{D} \boldsymbol{R}_{P, 1} \boldsymbol{D}^{\mathrm{T}}, \boldsymbol{D} \boldsymbol{R}_{P, 2} \boldsymbol{D}^{\mathrm{T}}\right)\end{aligned}$
$\boldsymbol{Q}=\operatorname{diag}\left(\boldsymbol{Q}_\nu, \boldsymbol{Q}_T, \boldsymbol{Q}_I\right)$
式中，Rφ, i、RP, i分别表示第i个频率下的载波相位与伪距观测噪声协方差矩阵，可通过卫星高度角模型进行计算；Qν、QT、QI分别表示速度、对流层延迟和电离层延迟参数的过程噪声矩阵。
抗差卡尔曼滤波(robust Kalman filter, RKF)基于IGGⅢ模型[17]修正观测噪声协方差，表达式为：
$\lambda_{i i}=\left\{\begin{array}{l}1, \left|\widetilde{v}_{k, i}\right| \leqslant k_0 \\\frac{k_0}{\widetilde{v}_{k, i}} \times\left(\frac{k_1-\widetilde{v}_{k, i}}{k_1-k_0}\right)^2, k_0 \leqslant\left|\widetilde{v}_{k, i}\right| \leqslant k_1 \\10^{-10}, \left|\widetilde{v}_{k, i}\right| \geqslant k_1\end{array}\right.$
式中，k0和k1表示相应的阈值，k0一般取1.0~2.5，k1一般取3.0~8.5；$ \widetilde{v}_{k, i}$表示k时刻第i个观测值的标准化残差：
$\widetilde{v}_{k, i}=\frac{v_{k, i}}{\sqrt{\left(\boldsymbol{H}_k \boldsymbol{P}_{k, k-1} \boldsymbol{H}_k^{\mathrm{T}}+\boldsymbol{R}_k\right)_{i i}}}$
式中，vk, i为k时刻第i个观测值；Hk为设计矩阵；Pk, k－1为状态预测参数的方差协方差矩阵；Rk为双差观测噪声矩阵。由于双差观测间存在相关性，其协方差不再是对角阵，应采用双因子等价协方差矩阵[17]：
$\gamma_{i i}=\frac{1}{\lambda_{i i}}, \gamma_{i j}=\sqrt{\gamma_{i i} \gamma_{j j}}$
$\overline{\boldsymbol{R}}_k=\left[\begin{array}{ccc}\gamma_{11} \sigma_{11}^2 & \cdots & \gamma_{1 n} \sigma_{1 n}^2 \\\vdots & \ddots & \vdots \\\gamma_{n 1} \sigma_{n 1}^2 & \cdots & \gamma_{n n} \sigma_{n n}^2\end{array}\right]$
式中，σij2为观测协方差矩阵中的元素；γij为观测协方差矩阵中相应元素所对应的协方差膨胀因子。
2 距离约束的抗差卡尔曼滤波基线差分定位模型
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海上载体一般安装有多套GNSS天线，其相对位置已通过全站仪等测量手段精确测定，因此天线之间的空间几何关系是已知并保持不变的，可在联合解算时作为先验信息引入。
2.1 天线间基线距离约束
设基站与天线y1和y2分别构成基线BL1与BL2，天线y1与y2之间构成基线BL12，则天线间的已知距离可表示为如下约束条件：
$\begin{gathered}\sqrt{\left(X_1-X_2\right)^2+\left(Y_1-Y_2\right)^2+\left(Z_1-Z_2\right)^2}= \\\left|B L_{12}\right|\end{gathered}$
式中，(Xi, Yi, Zi)表示天线y的坐标, i=1, 2；|BL12|表示基线BL12的长度。
式(13)线性化后可简写为：
$\boldsymbol{B} \hat{\boldsymbol{X}}-\boldsymbol{D}=\boldsymbol{0}$
式中，B为n维状态参数系数矩阵；D为常量矩阵。如果有r个约束条件，则此时B为r×n维，矩阵的秩为r，表示存在r个线性无关的等式约束，D为r×1维常量矩阵。将无约束状态向量投影到约束面上求解，表达式为：
$\left\{\begin{array}{l}\min\limits_{{\widetilde{X}}}(\widetilde{\boldsymbol{X}}-\hat{\boldsymbol{X}})^{\mathrm{T}} \boldsymbol{W}(\widetilde{\boldsymbol{X}}-\hat{\boldsymbol{X}}) \\\boldsymbol{B} \widetilde{\boldsymbol{X}}=\boldsymbol{D}\end{array}\right.$
式中，W为任意对称正定的投影矩阵；$ \widetilde{\boldsymbol{X}}$为经过约束条件修正后的状态估值。上述问题的最优解可写为：
$\widetilde{\boldsymbol{X}}=\hat{\boldsymbol{X}}-\boldsymbol{W}^{-1} \boldsymbol{B}^{\mathrm{T}}\left(\boldsymbol{B} \boldsymbol{W}^{-1} \boldsymbol{B}^{\mathrm{T}}\right)^{-1}(\boldsymbol{B} \hat{\boldsymbol{X}}-\boldsymbol{D})$
取$ \boldsymbol{W}=\boldsymbol{Q}_{\hat{{X}}^0}^{-1}$(抗差滤波更新后状态参数的方差协方差阵)，$ \hat{\boldsymbol{X}}$取RKF解时，上式即为附有约束条件的RKF解[17]：
$\widetilde{\boldsymbol{X}}=\hat{\boldsymbol{X}}^0-\boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\left(\boldsymbol{B} \boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\right)^{-1}\left(\boldsymbol{B} \hat{\boldsymbol{X}}^0-\boldsymbol{D}\right)$
2.2 约束条件的影响分析
进一步分析约束条件对参数解的影响，由式(16)可得：
$\begin{gathered}\widetilde{\boldsymbol{X}}=\left(\boldsymbol{I}-\boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\left(\boldsymbol{B} \boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\right)^{-1} \boldsymbol{B}\right) \hat{\boldsymbol{X}}^0+ \\\boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\left(\boldsymbol{B} \boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\right)^{-1} \boldsymbol{D}\end{gathered}$
则$ \widetilde{\boldsymbol{X}}$的协方差矩阵可表示为：
$\boldsymbol{Q}_{\widetilde{X}}=\boldsymbol{Q}_{\hat{X}^0}-\boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\left(\boldsymbol{B} \boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\right)^{-1} \boldsymbol{B} \boldsymbol{Q}_{\hat{X}^0}$
状态约束对滤波解和残差向量的改正值可写为：
$\Delta \boldsymbol{X}=-\boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\left(\boldsymbol{B} \boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\right)^{-1}\left(\boldsymbol{B} \hat{\boldsymbol{X}}^0-\boldsymbol{D}\right)$
$\Delta \boldsymbol{V}=\boldsymbol{H} \boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\left(\boldsymbol{B} \boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\right)^{-1}\left(\boldsymbol{D}-\boldsymbol{B} \hat{\boldsymbol{X}}^0\right)$
根据上述分析可知：
1) 在参数估计过程中引入附加约束条件，相当于在原始无约束解的基础上施加了先验信息或外部已知条件，从而对参数解进行一定程度的修正。解向量可视为无约束估计值加上由约束条件引起的修正量$ -\boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\left(\boldsymbol{B} \boldsymbol{Q}_{\hat{X}^0} \boldsymbol{B}^{\mathrm{T}}\right)^{-1}\left(\boldsymbol{B} \hat{\boldsymbol{X}}^0-\boldsymbol{D}\right)$。
2) 如果约束向量中的改正值$ \boldsymbol{B} \hat{\boldsymbol{X}}^0-\boldsymbol{D}$很小，意味着当前被估计的初始状态参数向量已经较为精确，与先验约束之间的偏差较小。在这种情况下，约束仅起到微调作用，对最终估值贡献有限。因此，初始值越接近真实值，约束条件的调节作用就越小。
3) 当状态向量的初始值存在较大误差时，即与实际状态存在明显偏离，约束条件将发挥更显著的作用。此时，式(20)中的状态参数修正值以及式(21)中的残差修正项往往也较大，表明通过约束条件对估值进行了较大幅度的修正。由此可见，在初始估值不理想或观测条件复杂的情况下，引入合理的约束条件有助于增强状态参数估值和残差的可靠性和稳定性。
4) 由式(19)可知，在引入约束条件后$ \operatorname{tr}\left(\boldsymbol{Q}_{\widetilde{X}}\right) \leqslant \operatorname{tr}\left(\boldsymbol{Q}_{\hat{X}^0}\right)$，说明加入约束条件后的滤波参数解精度更高，结果更可靠。
3 实验与分析
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本文选取实测的BDS-2/GPS双频和BDS-3单频静态与动态长基线观测数据进行实验分析，2组数据均采集于2023-03-25，采样间隔为5 s。静态实验中，2台接收机分别布设在深圳与海口两地，站间直线距离约500 km；动态实验中，海口站接收机作为基准站，船载平台上的接收机作为流动站进行数据采集。观测当天天气多云转阴，海况较为理想，船体航行稳定，为数据连续采集提供了有利条件。在此次观测中，深圳与海口岸基接收机数据连续性良好，未发生中断。海上流动站由于部分参数配置原因，7:50之前出现短时观测中断，随后恢复并持续采集数据。数据处理阶段卫星截止高度角设置为15°，GPS使用L1+L2频率，BDS-2使用B1I+B2I频率，BDS-3采用B1I频率进行解算。电离层延迟与对流层延迟均作为未知参数进行估计，观测值随机模型采用高度角加权模型，以便更真实地反映观测噪声特性。
3.1 数据质量分析
为客观评估海洋环境对船载GNSS数据的影响程度，并为后续实验提供可靠的数据质量依据，采用G-Nut/Anubis软件对采集的动态观测数据(S0349、HCN1与S4165)和静态观测数据(S4159、S0306)进行质量分析。选取数据可用率、周跳比(CSR)以及多路径效应(MP1/MP2/MP7)作为核心评估指标，具体结果见表 1，评估指标计算公式为[18-19]：
$\mathrm{MP}_k=P_k-L_i-\beta\left(L_i-L_j\right)=P_k+\alpha L_i+\beta L_j$
$\left\{\begin{aligned}\alpha & =-\frac{\left(f_j^2+f_k^2\right) f_i^2}{\left(f_i^2-f_j^2\right) f_k^2} \\\beta & =\frac{\left(f_i^2+f_k^2\right) f_i^2}{\left(f_i^2-f_j^2\right) f_k^2}\end{aligned}\right.$
$\text { CSR }=\frac{1000}{O / \text { Slips }}$
式中，MP为多路径效应；P为伪距观测值；L为相位观测值；f为频率；k、i、j为频率索引；O为观测值总数；Slips为周跳/中断数。
从表 1可以看出，虽然各测站的数据可用率均超过99.9%，整体观测时段较为完整，但在不同观测环境下，数据质量差异显著。两个船载动态测站(S0349、S4165)的周跳比(CSR)普遍偏高，分别达到142.9和166.7，明显高于陆地静态测站S4159，表明在海洋动态环境中，受船体摇晃、天线遮挡及信号中断等因素影响，载波相位观测极易出现周跳。
从多路径效应指标(MP1、MP2、MP7)来看，动态数据均表现出较大的多路径影响。其中，S4165测站GPS系统的MP1与MP2分别为67.9 cm和69.5 cm，而BDS系统的MP2与MP7分别为66.4 cm和63.1 cm；S0349测站GPS与BDS系统也分别达到32.8/32.7 cm与33.3/31.6 cm。从整体上看，BDS系统的多路径效应略低于GPS系统，表现出更好的抗干扰能力，但二者差异不大。
在陆地静态环境中，数据整体质量相对较好，但仍存在差异。S4159测站处于无遮挡环境，虽然多路径效应较小，但周跳比仍达到100.0，表明静态观测信号依然存在一定的不连续性。而S0306测站的CSR仅为0.2，说明该站点信号稳定、周跳极少，数据质量最佳。然而，该测站不同系统的多路径效应仍在10~20 cm之间，表明即使在静态环境下也难以完全消除多路径和噪声影响。
因此，无论是在海洋动态环境还是陆地静态环境下，GNSS观测数据均存在不同程度的异常值与噪声干扰，引入抗差滤波算法抑制异常观测，是保证定位解算结果稳健性和精度的必要手段。
3.2 静态长基线抗差卡尔曼滤波实验分析
由§3.1观测数据质量分析结果可知，深圳站观测数据质量相对较差，这为评估不同滤波策略在观测质量欠佳时的定位表现提供了实验条件。为此，本文选取观测质量较好的海口站S0306作为基准站，深圳站S4159作为流动站，开展静态长基线差分定位实验。实验采用双差后的后验残差均方根(RMS)作为主要评价指标，后验残差可表示滤波更新后的状态估计与观测值之间的差异，表达式为：
$\boldsymbol{v}_k=\boldsymbol{y}_k-\boldsymbol{H}_k \hat{\boldsymbol{x}}_{k \mid k}$
对于第k个历元，后验残差RMSk计算公式为：
$\mathrm{RMS}_k=\sqrt{\frac{1}{m_k} \boldsymbol{v}_k^{\mathrm{T}} \boldsymbol{v}_k}$
式中，mk表示第k个历元的观测值个数。
为定量评估EKF与RKF算法的性能，本文以PRIDE PPP-AR软件解算得到的深圳站静态PPP固定解作为参考值，设计2种实验方案：方案1，采用EKF进行BDS/GPS组合差分定位解算；方案2，采用RKF进行BDS/GPS组合差分定位解算，k0、k1分别取2.5、7.5。
为对比2种方案的定位性能，统计2种方案获得的定位结果在东(E)、北(N)、天(U)3个方向的定位偏差序列，并计算相应的后验残差RMS。定位偏差和RMS序列如图 1和图 2所示，统计结果详见表 2和表 3。
结合图 1、2和表 2、3可知：
1) RKF在E、N、U方向的定位偏差明显小于EKF。RKF能有效抑制观测异常，显著减小定位偏差，使得3个方向的定位结果更加平滑和稳定，整体定位精度得到提升。具体而言，E、N、U方向精度分别提升28.8%、5.0%、6.1%。
2) 相比于EKF，经过抗差处理后，RKF的RMS序列最大值有所减小，有效抑制了极端值的影响。同时，RKF的均值和标准差均低于EKF，改善率分别为13.51%和41.67%。总体而言，RKF在减少误差波动和提升定位结果的稳定性方面明显优于EKF。
3.3 海上长基线距离约束抗差卡尔曼滤波实验分析
为进一步验证该方法在动态场景下的定位性能，并分析距离约束对定位精度的影响。选取海口站S0306作为基准站，船载接收机S0349、HCN1和S4165作为流动站，开展海上长基线动态差分定位实验。其中，测站S0349与S4165使用的接收机类型为南方测绘NET S10，测站HCN1使用的接收机类型为华测P5，测站S0306使用的接收机也为南方测绘品牌接收机，但其具体型号在观测文件中未明确标注。为确保观测数据的连续性及各测站时间同步性，选取2023-03-25 07:50—24:00期间的观测数据进行解算与分析。各基线名称及长度详见表 4，长基线差分定位解算策略见表 5。
考虑到基线BL4与BL5的长度已通过全站仪实现高精度标定，因此将其作为距离约束条件进行定位解算。为开展实验对比，分别设计并实施以下3种解算方案。
方案一：采用EKF对基线BL1和BL3进行长基线差分定位解算，得到S0349和S4165位置。
方案二：采用RKF对基线BL1和BL3进行长基线差分定位解算，k0、k1分别取2.5、7.5，得到S0349和S4165位置。
方案三：在RKF方法基础上，引入BL4基线长度作为约束，联合BL1和BL2解算S0349位置；同时，引入BL5基线长度作为约束，联合BL2和BL3解算S4165位置。
通过对定位解算结果进行反算获取基线BL6长度，并以全站仪标定的精确值作为参考。3种方案的天线间距离偏差如图 3所示，解算结果精度统计见表 6。
由图 3和表 6可知，在海上长基线差分定位中，附加约束RKF和RKF相比于EKF，定位误差波动明显减少，定位结果更加平滑。特别是在引入约束条件对抗差解作进一步修正后，定位精度与结果稳定性均得到进一步提升。具体而言，RKF的标准差(STD)和均方根误差(RMSE)相较于EKF分别降低11.1%和10.0%，附加约束RKF的STD和RMSE较RKF进一步降低6.5%和2.4%。
4 结语
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在海洋等复杂环境中，观测质量易受多种因素干扰，进而显著影响传统卡尔曼滤波的定位性能。针对该问题，本文设计一种基于IGGⅢ权函数的RKF长基线差分定位模型，以有效抑制异常观测对定位结果的影响。在此基础上，引入附加约束条件对滤波解作进一步修正，并系统分析该约束条件对提升定位精度的贡献。结果表明，在长基线差分定位中，观测质量下降会导致定位结果受到显著干扰，而本文所提模型能够通过自适应调整观测协方差矩阵，有效削弱异常观测的影响，从而提高定位精度。此外，引入附加约束条件可进一步增强模型对先验信息的利用能力，使定位结果在精度与稳定性方面均得到进一步提升。
综上所述，本文方法在海洋等复杂动态环境下具有一定实用性。考虑到海洋环境中误差的显著时变性，未来研究可进一步引入动态环境感知机制，结合误差状态建模与异常变化的自主识别方法，进一步提升系统在复杂动态环境中的适应性与定位可靠性。
基金
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  • 国家重点研发计划(2023YFC2908401)
  • 国家重点研发计划(2024YFB3909701)
  • 国家自然科学基金(42374012)
  • 国家自然科学基金(42388102)
文献
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参考文献 引证文献
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2026年第46卷第8期
29
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doi: 10.14075/j.jgg.2025.08.266
  • 接收时间：2025-08-05
  • 首发时间：2026-10-30
  • 出版时间：2026-08-15
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  • 收稿日期：2025-08-05
基金
国家重点研发计划(2023YFC2908401)
国家重点研发计划(2024YFB3909701)
国家自然科学基金(42374012)
国家自然科学基金(42388102)
作者信息
    1 长安大学地质工程与测绘学院, 西安, 710054
    2 西安测绘研究所, 西安, 710054
    3 空间基准全国重点实验室, 西安, 710054

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曾安敏, 博士, 研究员, 主要从事大地测量学与测量工程研究, E-mail:
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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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