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Article(id=1322940604509978874, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322940449979244751, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.04.176, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1713024000000, receivedDateStr=2024-04-14, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793343219163, onlineDateStr=2026-10-30, pubDate=1741968000000, pubDateStr=2025-03-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793343219163, onlineIssueDateStr=2026-10-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793343219163, creator=13701087609, updateTime=1793343219163, updator=13701087609, issue=Issue{id=1322940449979244751, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='3', pageStart='221', pageEnd='330', issueExtLink='null', onlineDate='null', pubDate='1741968000000', pubDateStr='2025-03-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793343182320, creator='13701087609', updateTime=1793343182320, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=290, endPage=296, ext={EN=ArticleExt(id=1322940605713744123, articleId=1322940604509978874, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Applicability Analysis of ECOM Solar Radiation Pressure Models in Precise Orbit Determination, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

The solar pressure perturbation, as the largest non-conservative force experienced by in-orbit navigation satellites, is an important error source for precise orbit determination. Currently, most solar radiation pressure models are established for global positioning system(GPS) satellites, and there is relatively little adaptability analysis of solar radiation pressure models for precise orbit determination accuracy of Beidou-3(BDS-3) satellites. We use observation data from the multi-GNSS experiment(MGEX) to conduct orbit determination experiments based on five solar radiation pressure models, including ECOM1-9, ECOM1-7, ECOM1-5, ECOM2, ECOMC. The results show that the applicability of solar radiation pressure model varies for satellites developed by different manufacturers. For satellites developed by China Academy of Space Technology(CAST), the ECOMC model exhibits optimal applicability in radial, tangential, and normal directions. For satellites developed by Shanghai Engineering Center for Microsatellites(SECM), the radial, tangential, and normal directions have the best accuracy for ECOM1-5, ECOMC, and ECOMC models, respectively. For 3D entirety, the ECOMC model is recommended for orbit determination of both CAST and SECM satellites. From the 24-hour prediction results, for CAST type satellites, the accuracy of ECOM1-9, ECOM1-7, ECOM1-5, ECOM2, and ECOMC models is 23.3 cm, 20.6 cm, 17.2 cm, 21.8 cm, and 10.4 cm, respectively. For SECM type satellites, the accuracy is 25.7 cm, 19.1 cm, 15.9 cm, 12.9 cm, and 11.9 cm, respectively.

, authors=Binghong SONG1, Jianhua YANG1, authorsList=Binghong SONG, Jianhua YANG, authorCompany=null, correspAuthors=null, authorNote=

SONG Binghong, senior engineer, majors in GNSS data processing and its applications, E-mail:

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太阳光压摄动作为在轨导航卫星受到的最大非保守力，是卫星精密定轨的重要误差源，而目前多数光压模型是针对全球定位系统(GPS)卫星而建立的，对北斗三号(BDS-3)卫星精密定轨的适用性分析较少。本文借助MGEX观测数据对5种欧洲定轨中心拓展轨道模型(ECOM1-9、ECOM1-7、ECOM1-5、ECOM2、ECOMC)太阳光压模型进行定轨实验。结果表明，不同厂商研制的卫星对光压模型的适用性不同，对中国空间技术研究院(CAST)研制的卫星而言，ECOMC模型在径向、切向和法向均表现出最优适用性；对上海微小卫星工程中心(SECM)研制的卫星而言，径向、切向和法向分别为ECOM1-5、ECOMC、ECOMC模型精度最佳；对三维整体而言，CAST卫星和SECM卫星定轨均推荐采用ECOMC模型；从24 h预测结果来看，对于CAST卫星，ECOM1-9、ECOM1-7、ECOM1-5、ECOM2、ECOMC模型24 h预测精度分别为23.3 cm、20.6 cm、17.2 cm、21.8 cm、10.4 cm，对于SECM卫星，各模型预测精度分别为25.7 cm、19.1 cm、15.9 cm、12.9 cm、11.9 cm。

, authors=宋秉红1, 杨建华1, authorsList=宋秉红, 杨建华, authorCompany=null, correspAuthors=null, authorNote=

宋秉红，高级工程师，主要研究方向为GNSS数据处理与应用，E-mail：

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SONG Binghong, senior engineer, majors in GNSS data processing and its applications, E-mail:

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SONG Binghong, senior engineer, majors in GNSS data processing and its applications, E-mail:

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宋秉红，高级工程师，主要研究方向为GNSS数据处理与应用，E-mail：

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宋秉红，高级工程师，主要研究方向为GNSS数据处理与应用，E-mail：

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Remote Sensing, 2022, 14 (16), articleTitle=Impacts of Arc Length and ECOM Solar Radiation Pressure Models on BDS-3 Orbit Prediction, refAbstract=null), Reference(id=1322940691323683156, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, doi=null, pmid=null, pmcid=null, year=2017, volume=34, issue=4, pageStart=347, pageEnd=352, url=null, language=null, rfNumber=10, rfOrder=14, authorNames=彭汉兵, 杨元喜, 王刚, journalName=测绘科学技术学报, refType=null, unstructuredReference=彭汉兵, 杨元喜, 王刚. 不同经验太阳光压模型对于北斗卫星定轨的适用性分析[J]. 测绘科学技术学报, 2017, 34 (4): 347- 352, articleTitle=不同经验太阳光压模型对于北斗卫星定轨的适用性分析, refAbstract=null), Reference(id=1322940693416640853, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, doi=null, pmid=null, pmcid=null, year=2017, volume=34, issue=4, pageStart=347, pageEnd=352, url=null, language=null, rfNumber=10, rfOrder=15, authorNames=Peng Hanbing, Yang Yuanxi, Wang Gang, journalName=null, refType=null, unstructuredReference= Peng Hanbing , Yang Yuanxi , Wang Gang . 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Journal of Geomatics Science and Technology, 2017, 34 (4): 347- 352, articleTitle=null, refAbstract=null), Reference(id=1322940694607823190, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, doi=null, pmid=null, pmcid=null, year=2019, volume=48, issue=2, pageStart=169, pageEnd=175, url=null, language=null, rfNumber=11, rfOrder=16, authorNames=陈秋丽, 杨慧, 陈忠贵, journalName=测绘学报, refType=null, unstructuredReference=陈秋丽, 杨慧, 陈忠贵, 等. 北斗卫星太阳光压解析模型建立及应用[J]. 测绘学报, 2019, 48 (2): 169- 175, articleTitle=北斗卫星太阳光压解析模型建立及应用, refAbstract=null), Reference(id=1322940696361042264, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, doi=null, pmid=null, pmcid=null, year=2019, volume=48, issue=2, pageStart=169, pageEnd=175, url=null, language=null, rfNumber=11, rfOrder=17, authorNames=Chen Qiuli, Yang Hui, Chen Zhonggui, journalName=null, refType=null, unstructuredReference= Chen Qiuli , Yang Hui , Chen Zhonggui , et al. Solar Radiation Pressure Modeling and Application of BDS Satellite[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48 (2): 169- 175, articleTitle=null, refAbstract=null), Reference(id=1322940697543835993, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, doi=null, pmid=null, pmcid=null, year=2019, volume=11, issue=24, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=12, rfOrder=18, authorNames=Liu Y, Liu Y X, Tian Z W, journalName=Remote Sensing, refType=null, unstructuredReference= Liu Y , Liu Y X , Tian Z W , et al. Impact of ECOM Solar Radiation Pressure Models on Multi-GNSS Ultra-Rapid Orbit Determination[J]. Remote Sensing, 2019, 11 (24), articleTitle=Impact of ECOM Solar Radiation Pressure Models on Multi-GNSS Ultra-Rapid Orbit Determination, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1322940623363375368, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, xref=null, ext=[AuthorCompanyExt(id=1322940624634249482, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, companyId=1322940623363375368, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1 Lanzhou Urban Construction Design and Research Institute Co Ltd, 875 East-Nanbinhe Road, Lanzhou 730050, China), AuthorCompanyExt(id=1322940624978182411, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, companyId=1322940623363375368, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1 兰州城市建设设计研究院有限公司, 兰州市南滨河东路875号, 730050)])], figs=[ArticleFig(id=1322940643894493472, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=EN, label=Fig. 1, caption=Visualization results of RMS values of orbit determination residuals for different solar radiation pressure models of CAST satellites, figureFileSmall=vSk2GuMvu98ezDIXH8TUDg==, figureFileBig=Q3aIH3A7ho8Q32Zhd+wZhw==, tableContent=null), ArticleFig(id=1322940645098258721, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=CN, label=图1, caption=CAST卫星不同光压模型定轨残差RMS值可视化结果, figureFileSmall=vSk2GuMvu98ezDIXH8TUDg==, figureFileBig=Q3aIH3A7ho8Q32Zhd+wZhw==, tableContent=null), ArticleFig(id=1322940649309339939, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=EN, label=Fig. 2, caption=RMS values of orbit determination residuals for CAST satellite(PRN C19) with different arc lengths, figureFileSmall=2KiKmXhw+qPSAQeXrgeCJQ==, figureFileBig=gVZRiWZR+xqy+6q3Jl783Q==, tableContent=null), ArticleFig(id=1322940649808462116, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=CN, label=图2, caption=CAST卫星(PRN C19)不同轨道弧长定轨残差RMS值, figureFileSmall=2KiKmXhw+qPSAQeXrgeCJQ==, figureFileBig=gVZRiWZR+xqy+6q3Jl783Q==, tableContent=null), ArticleFig(id=1322940650563436837, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=EN, label=Fig. 3, caption=Visualization results of RMS values of orbit determination residuals for different solar radiation pressure models of SECM satellites, figureFileSmall=nkgkldWuevyvHZzeBAwkdg==, figureFileBig=DYAoY2czqLAzE211s0vDWA==, tableContent=null), ArticleFig(id=1322940651821728038, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=CN, label=图3, caption=SECM卫星不同光压模型定轨残差RMS值可视化结果, figureFileSmall=nkgkldWuevyvHZzeBAwkdg==, figureFileBig=DYAoY2czqLAzE211s0vDWA==, tableContent=null), ArticleFig(id=1322940653486866727, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=EN, label=Fig. 4, caption=RMS values of orbit determination residuals for SECM satellite(PRN C25) with different orbital arc lengths, figureFileSmall=CYvmMVn+vgyN8gJHx34Pjw==, figureFileBig=nSI753tAVgFttbZYiO/XtA==, tableContent=null), ArticleFig(id=1322940653952434472, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=CN, label=图4, caption=SECM卫星(PRN C25)不同轨道弧长定轨残差RMS值, figureFileSmall=CYvmMVn+vgyN8gJHx34Pjw==, figureFileBig=nSI753tAVgFttbZYiO/XtA==, tableContent=null), ArticleFig(id=1322940655164588329, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=EN, label=Fig. 5, caption=3D residual RMS values of different solar radiation pressure models, figureFileSmall=hUhbYnfcuGSoTyWc5oW7xQ==, figureFileBig=jaeZX83lfunXCmkYWWMU8Q==, tableContent=null), ArticleFig(id=1322940656074752298, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=CN, label=图5, caption=不同光压模型3D残差RMS值, figureFileSmall=hUhbYnfcuGSoTyWc5oW7xQ==, figureFileBig=jaeZX83lfunXCmkYWWMU8Q==, tableContent=null), ArticleFig(id=1322940658129961259, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=EN, label=Tab. 1, caption=

Basic parameters of Beidou satellites

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面板 外尺寸参数/m 光学参数
BDS-2 BDS-3 CAST BDS-3 SECM BDS-2 BDS-3 CAST BDS-3 SECM
α β α β α β
+X 3.78 2.86 1.25 0.35 0.65 0.35 0.65 0.20 0.80
-X 3.78 2.86 1.25 0.35 0.65 0.92 0.08 0.20 0.80
+Y 4.40 3.63 3.13 0.14 0.86 0.14 0.86 0.20 0.80
-Y 4.40 3.63 3.13 0.14 0.86 0.14 0.86 0.20 0.80
+Z 3.44 2.18 2.59 0.35 0.65 0.92 0.08 0.20 0.80
-Z 3.44 2.18 2.59 0.35 0.65 0.92 0.08 0.20 0.80
太阳帆板 11.35×2 10.22×2 5.40×2 0.72 0.28 0.92 0.08 0.92 0.08
), ArticleFig(id=1322940658629083438, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=CN, label=表1, caption=

北斗卫星基本参数

, figureFileSmall=null, figureFileBig=null, tableContent=
面板 外尺寸参数/m 光学参数
BDS-2 BDS-3 CAST BDS-3 SECM BDS-2 BDS-3 CAST BDS-3 SECM
α β α β α β
+X 3.78 2.86 1.25 0.35 0.65 0.35 0.65 0.20 0.80
-X 3.78 2.86 1.25 0.35 0.65 0.92 0.08 0.20 0.80
+Y 4.40 3.63 3.13 0.14 0.86 0.14 0.86 0.20 0.80
-Y 4.40 3.63 3.13 0.14 0.86 0.14 0.86 0.20 0.80
+Z 3.44 2.18 2.59 0.35 0.65 0.92 0.08 0.20 0.80
-Z 3.44 2.18 2.59 0.35 0.65 0.92 0.08 0.20 0.80
太阳帆板 11.35×2 10.22×2 5.40×2 0.72 0.28 0.92 0.08 0.92 0.08
), ArticleFig(id=1322940659421806895, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=EN, label=Tab. 2, caption=

Processing strategy for orbit determination parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
参数 处理策略
截止高度角 10°
观测值 双频无电离层组合
轨道弧长 24 h
初始轨道参数 广播星历
固体潮、海潮、极移 IERS2010
相对论效应 IERS2010
模糊度 参数估计
对流层延迟 Saastamoinen+GMF
重力场 EGM2008模型
天线发射功率 130 W
N体引力 JPL DE405模型
大气阻力 忽略不计
地球返照辐射 忽略不计
太阳光压模型 ECOM1-9、ECOM1-7、ECOM1-5、ECOM2、ECOMC
), ArticleFig(id=1322940661049196848, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=CN, label=表2, caption=

定轨参数处理策略

, figureFileSmall=null, figureFileBig=null, tableContent=
参数 处理策略
截止高度角 10°
观测值 双频无电离层组合
轨道弧长 24 h
初始轨道参数 广播星历
固体潮、海潮、极移 IERS2010
相对论效应 IERS2010
模糊度 参数估计
对流层延迟 Saastamoinen+GMF
重力场 EGM2008模型
天线发射功率 130 W
N体引力 JPL DE405模型
大气阻力 忽略不计
地球返照辐射 忽略不计
太阳光压模型 ECOM1-9、ECOM1-7、ECOM1-5、ECOM2、ECOMC
), ArticleFig(id=1322940662362014001, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=EN, label=Tab. 3, caption=

RMS values of orbit determination residuals for different solar radiation pressure models of CAST satellites

, figureFileSmall=null, figureFileBig=null, tableContent=
PRN ECOM1-9模型 ECOM1-7模型 ECOM1-5模型 ECOM2模型 ECOMC模型
RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS
C19 12.5 8.5 9.0 17.6 9.6 9.0 8.2 15.5 7.4 8.7 7.5 13.7 4.5 16.6 15.2 23.0 4.2 6.5 5.5 9.5
C20 10.2 10.2 8.5 16.7 9.5 10.8 8.0 16.5 7.2 10.2 7.2 14.4 5.2 15.5 15.2 22.3 4.1 5.8 5.7 9.1
C21 9.6 11.0 9.5 17.4 8.8 10.5 8.0 15.9 6.5 10.3 7.2 14.1 4.6 17.0 17.5 24.8 4.4 6.1 5.2 9.1
C22 10.3 9.5 9.2 16.8 9.2 9.6 8.3 15.7 7.4 9.8 7.6 14.4 4.6 15.6 14.8 22.0 4.2 6.2 5.4 9.2
C23 13.6 9.2 12.0 20.3 11.5 9.0 8.8 17.0 8.6 8.8 6.0 13.7 6.4 9.5 6.7 13.3 5.5 5.9 4.8 9.4
C24 8.9 12.0 10.4 18.2 8.5 11.5 8.2 16.5 7.0 11.0 6.2 14.4 5.1 13.2 13.6 19.6 4.4 5.8 5.2 8.9
C32 11.1 10.8 9.6 18.2 9.0 10.5 7.6 15.8 6.5 10.0 6.5 13.6 5.5 11.4 12.0 17.4 5.0 6.2 5.0 9.4
C33 16.2 11.2 9.6 21.9 12.4 9.6 8.8 18.0 8.7 9.4 7.1 14.6 6.4 10.7 10.4 16.2 5.8 5.5 4.6 9.2
C36 10.2 10.5 9.1 17.2 9.3 9.5 8.0 15.5 8.2 9.2 7.3 14.3 5.6 8.8 9.9 14.4 4.3 6.0 5.6 9.3
C37 10.3 9.0 9.5 16.7 9.0 8.5 8.6 15.1 7.7 8.6 7.3 13.7 5.6 11.8 12.1 17.8 4.5 5.8 4.4 8.6
C41 12.2 9.6 9.4 18.1 12.0 8.8 8.5 17.1 8.9 8.5 6.8 14.1 6.6 12.0 13.6 19.3 5.8 6.1 5.8 10.2
C42 11.6 10.1 10.0 18.3 10.4 9.5 9.1 16.8 8.8 9.0 6.5 14.2 6.5 9.5 10.0 15.2 5.5 6.2 5.4 9.9
C45 10.0 10.5 9.5 17.3 9.1 10.0 7.7 15.6 7.4 9.6 6.2 13.6 5.6 8.5 9.2 13.7 5.2 6.5 5.2 9.8
C46 9.8 8.9 9.8 16.5 8.4 8.5 8.2 14.5 6.5 8.4 7.0 12.7 6.0 13.2 11.7 18.6 5.2 6.3 4.9 9.5
), ArticleFig(id=1322940663582556466, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=CN, label=表3, caption=

CAST卫星不同光压模型定轨残差RMS值

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PRN ECOM1-9模型 ECOM1-7模型 ECOM1-5模型 ECOM2模型 ECOMC模型
RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS
C19 12.5 8.5 9.0 17.6 9.6 9.0 8.2 15.5 7.4 8.7 7.5 13.7 4.5 16.6 15.2 23.0 4.2 6.5 5.5 9.5
C20 10.2 10.2 8.5 16.7 9.5 10.8 8.0 16.5 7.2 10.2 7.2 14.4 5.2 15.5 15.2 22.3 4.1 5.8 5.7 9.1
C21 9.6 11.0 9.5 17.4 8.8 10.5 8.0 15.9 6.5 10.3 7.2 14.1 4.6 17.0 17.5 24.8 4.4 6.1 5.2 9.1
C22 10.3 9.5 9.2 16.8 9.2 9.6 8.3 15.7 7.4 9.8 7.6 14.4 4.6 15.6 14.8 22.0 4.2 6.2 5.4 9.2
C23 13.6 9.2 12.0 20.3 11.5 9.0 8.8 17.0 8.6 8.8 6.0 13.7 6.4 9.5 6.7 13.3 5.5 5.9 4.8 9.4
C24 8.9 12.0 10.4 18.2 8.5 11.5 8.2 16.5 7.0 11.0 6.2 14.4 5.1 13.2 13.6 19.6 4.4 5.8 5.2 8.9
C32 11.1 10.8 9.6 18.2 9.0 10.5 7.6 15.8 6.5 10.0 6.5 13.6 5.5 11.4 12.0 17.4 5.0 6.2 5.0 9.4
C33 16.2 11.2 9.6 21.9 12.4 9.6 8.8 18.0 8.7 9.4 7.1 14.6 6.4 10.7 10.4 16.2 5.8 5.5 4.6 9.2
C36 10.2 10.5 9.1 17.2 9.3 9.5 8.0 15.5 8.2 9.2 7.3 14.3 5.6 8.8 9.9 14.4 4.3 6.0 5.6 9.3
C37 10.3 9.0 9.5 16.7 9.0 8.5 8.6 15.1 7.7 8.6 7.3 13.7 5.6 11.8 12.1 17.8 4.5 5.8 4.4 8.6
C41 12.2 9.6 9.4 18.1 12.0 8.8 8.5 17.1 8.9 8.5 6.8 14.1 6.6 12.0 13.6 19.3 5.8 6.1 5.8 10.2
C42 11.6 10.1 10.0 18.3 10.4 9.5 9.1 16.8 8.8 9.0 6.5 14.2 6.5 9.5 10.0 15.2 5.5 6.2 5.4 9.9
C45 10.0 10.5 9.5 17.3 9.1 10.0 7.7 15.6 7.4 9.6 6.2 13.6 5.6 8.5 9.2 13.7 5.2 6.5 5.2 9.8
C46 9.8 8.9 9.8 16.5 8.4 8.5 8.2 14.5 6.5 8.4 7.0 12.7 6.0 13.2 11.7 18.6 5.2 6.3 4.9 9.5
), ArticleFig(id=1322940664438194484, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=EN, label=Tab. 4, caption=

RMS values of orbit determination residuals for CAST satellite(PRN C19) with different arc lengths

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类别 ECOM1-9模型 ECOM1-7模型 ECOM1-5模型 ECOM2模型 ECOMC模型
6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h
RRMS 14.4 13.6 12.5 11.1 10.4 9.6 8.9 8.4 7.4 5.7 5.2 4.5 5.8 5.1 4.2
ARMS 9.9 9.2 8.5 10.8 9.9 9.0 9.9 9.5 8.7 20.3 18.6 16.6 7.8 7.3 6.5
CRMS 10.6 9.8 9.0 9.7 8.9 8.2 8.8 8.2 7.5 19.4 17.5 15.2 7.8 6.6 5.5
3DRMS 20.4 19.1 17.6 18.3 16.9 15.5 16.0 15.1 13.7 28.7 26.1 23.0 12.5 11.1 9.5
), ArticleFig(id=1322940664878596405, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=CN, label=表4, caption=

CAST卫星(PRN C19)不同轨道弧长定轨残差RMS值

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类别 ECOM1-9模型 ECOM1-7模型 ECOM1-5模型 ECOM2模型 ECOMC模型
6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h
RRMS 14.4 13.6 12.5 11.1 10.4 9.6 8.9 8.4 7.4 5.7 5.2 4.5 5.8 5.1 4.2
ARMS 9.9 9.2 8.5 10.8 9.9 9.0 9.9 9.5 8.7 20.3 18.6 16.6 7.8 7.3 6.5
CRMS 10.6 9.8 9.0 9.7 8.9 8.2 8.8 8.2 7.5 19.4 17.5 15.2 7.8 6.6 5.5
3DRMS 20.4 19.1 17.6 18.3 16.9 15.5 16.0 15.1 13.7 28.7 26.1 23.0 12.5 11.1 9.5
), ArticleFig(id=1322940666984137014, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=EN, label=Tab. 5, caption=

RMS values of orbit determination residuals for different solar radiation pressure models of SECM satellites

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PRN ECOM1-9模型 ECOM1-7模型 ECOM1-5模型 ECOM2模型 ECOMC模型
RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS
C25 9.1 13.6 10.8 19.6 8.2 12.2 9.8 17.7 5.5 8.8 9.2 13.9 6.0 6.9 5.2 10.5 5.8 6.4 4.5 9.7
C26 8.8 13.0 10.2 18.7 7.0 12.5 9.6 17.2 5.2 8.5 9.0 13.4 5.5 7.2 5.6 10.7 5.5 6.9 4.2 9.8
C27 6.5 13.5 9.6 17.8 5.5 9.9 9.0 14.5 6.0 9.4 8.5 14.0 5.9 6.6 5.5 10.4 6.4 7.2 4.4 10.6
C28 18.8 23.5 20.4 36.4 6.5 9.5 9.5 14.9 5.8 9.8 9.2 14.6 6.6 6.8 6.4 11.4 6.6 7.0 4.2 10.5
C29 7.5 11.1 9.5 16.4 6.8 10.4 8.4 15.0 5.5 10.6 7.7 14.2 6.2 7.0 5.5 10.8 6.0 6.1 5.1 10.0
C30 8.2 14.4 10.3 19.5 7.9 13.6 8.4 17.8 6.2 10.8 8.0 14.8 6.8 7.5 6.5 12.0 7.2 6.5 5.2 11.0
C34 8.8 12.6 10.6 18.7 7.5 10.0 9.3 15.6 5.3 8.0 9.0 13.2 6.6 6.5 5.5 10.8 6.5 6.6 4.8 10.4
C35 8.0 12.9 9.9 18.1 6.6 12.5 8.5 16.5 5.5 8.9 8.2 13.3 6.9 6.8 5.2 11.0 6.5 7.4 4.6 10.9
C43 7.9 16.1 13.0 22.1 6.4 12.0 10.2 17.0 5.2 11.0 9.0 15.1 6.5 6.9 7.0 11.8 6.2 5.9 5.5 10.2
C44 8.4 10.5 12.2 18.2 7.0 12.4 10.4 17.6 5.6 8.6 9.3 13.8 7.2 7.4 6.6 12.3 6.9 6.3 5.0 10.6
), ArticleFig(id=1322940667776860471, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=CN, label=表5, caption=

SECM卫星不同光压模型定轨残差RMS值

, figureFileSmall=null, figureFileBig=null, tableContent=
PRN ECOM1-9模型 ECOM1-7模型 ECOM1-5模型 ECOM2模型 ECOMC模型
RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS
C25 9.1 13.6 10.8 19.6 8.2 12.2 9.8 17.7 5.5 8.8 9.2 13.9 6.0 6.9 5.2 10.5 5.8 6.4 4.5 9.7
C26 8.8 13.0 10.2 18.7 7.0 12.5 9.6 17.2 5.2 8.5 9.0 13.4 5.5 7.2 5.6 10.7 5.5 6.9 4.2 9.8
C27 6.5 13.5 9.6 17.8 5.5 9.9 9.0 14.5 6.0 9.4 8.5 14.0 5.9 6.6 5.5 10.4 6.4 7.2 4.4 10.6
C28 18.8 23.5 20.4 36.4 6.5 9.5 9.5 14.9 5.8 9.8 9.2 14.6 6.6 6.8 6.4 11.4 6.6 7.0 4.2 10.5
C29 7.5 11.1 9.5 16.4 6.8 10.4 8.4 15.0 5.5 10.6 7.7 14.2 6.2 7.0 5.5 10.8 6.0 6.1 5.1 10.0
C30 8.2 14.4 10.3 19.5 7.9 13.6 8.4 17.8 6.2 10.8 8.0 14.8 6.8 7.5 6.5 12.0 7.2 6.5 5.2 11.0
C34 8.8 12.6 10.6 18.7 7.5 10.0 9.3 15.6 5.3 8.0 9.0 13.2 6.6 6.5 5.5 10.8 6.5 6.6 4.8 10.4
C35 8.0 12.9 9.9 18.1 6.6 12.5 8.5 16.5 5.5 8.9 8.2 13.3 6.9 6.8 5.2 11.0 6.5 7.4 4.6 10.9
C43 7.9 16.1 13.0 22.1 6.4 12.0 10.2 17.0 5.2 11.0 9.0 15.1 6.5 6.9 7.0 11.8 6.2 5.9 5.5 10.2
C44 8.4 10.5 12.2 18.2 7.0 12.4 10.4 17.6 5.6 8.6 9.3 13.8 7.2 7.4 6.6 12.3 6.9 6.3 5.0 10.6
), ArticleFig(id=1322940668619915577, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=EN, label=Tab. 6, caption=

RMS values of orbit determination residuals for SECM satellite(PRN 25) with different orbital arc lengths

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类别 ECOM1-9模型 ECOM1-7模型 ECOM1-5模型 ECOM2模型 ECOMC模型
6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h
RRMS 11.2 10.5 9.1 10.5 9.6 8.2 6.9 6.4 5.5 7.5 6.8 6.0 7.0 6.3 5.8
ARMS 15.6 14.4 13.6 14.7 13.4 12.2 10.2 9.5 8.8 8.8 7.6 6.9 8.2 7.5 6.4
CRMS 12.2 11.6 10.8 12.5 11.2 9.8 11.1 10.3 9.2 8.1 6.9 5.2 6.6 5.4 4.5
3DRMS 22.8 21.3 19.6 22.0 19.9 17.7 16.6 15.4 13.9 14.1 12.3 10.5 12.6 11.2 9.7
), ArticleFig(id=1322940669098066234, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=CN, label=表6, caption=

SECM卫星(PRN 25)不同轨道弧长定轨残差RMS值

, figureFileSmall=null, figureFileBig=null, tableContent=
类别 ECOM1-9模型 ECOM1-7模型 ECOM1-5模型 ECOM2模型 ECOMC模型
6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h 6 h 12 h 24 h
RRMS 11.2 10.5 9.1 10.5 9.6 8.2 6.9 6.4 5.5 7.5 6.8 6.0 7.0 6.3 5.8
ARMS 15.6 14.4 13.6 14.7 13.4 12.2 10.2 9.5 8.8 8.8 7.6 6.9 8.2 7.5 6.4
CRMS 12.2 11.6 10.8 12.5 11.2 9.8 11.1 10.3 9.2 8.1 6.9 5.2 6.6 5.4 4.5
3DRMS 22.8 21.3 19.6 22.0 19.9 17.7 16.6 15.4 13.9 14.1 12.3 10.5 12.6 11.2 9.7
), ArticleFig(id=1322940671555928379, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=EN, label=Tab. 7, caption=

RMS values of BDS-3 satellite orbit prediction

, figureFileSmall=null, figureFileBig=null, tableContent=
卫星类型 ECOM1-9模型 ECOM1-7模型 ECOM1-5模型 ECOM2模型 ECOMC模型
RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS
CAST 15.5 13.0 11.5 23.3 12.2 11.6 11.8 20.6 9.4 10.6 9.8 17.2 7.3 14.4 14.6 21.8 5.5 6.2 6.2 10.4
SECM 13.8 16.9 13.5 25.7 8.4 13.3 10.8 19.1 6.6 10.4 10.1 15.9 7.9 7.5 7.0 12.9 7.6 6.4 6.5 11.9
), ArticleFig(id=1322940672440926526, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322940604509978874, language=CN, label=表7, caption=

BDS-3卫星轨道预测RMS值

, figureFileSmall=null, figureFileBig=null, tableContent=
卫星类型 ECOM1-9模型 ECOM1-7模型 ECOM1-5模型 ECOM2模型 ECOMC模型
RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS RRMS ARMS CRMS 3DRMS
CAST 15.5 13.0 11.5 23.3 12.2 11.6 11.8 20.6 9.4 10.6 9.8 17.2 7.3 14.4 14.6 21.8 5.5 6.2 6.2 10.4
SECM 13.8 16.9 13.5 25.7 8.4 13.3 10.8 19.1 6.6 10.4 10.1 15.9 7.9 7.5 7.0 12.9 7.6 6.4 6.5 11.9
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ECOM系列光压模型在精密定轨中的适用性分析
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宋秉红 1 , 杨建华 1
大地测量与地球动力学 | 现代大地测量 2025,45(3): 290-296
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大地测量与地球动力学 |现代大地测量 2025 , 45 (3) : 290 -296
ECOM系列光压模型在精密定轨中的适用性分析
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宋秉红，高级工程师，主要研究方向为GNSS数据处理与应用，E-mail：

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宋秉红1 , 杨建华1
作者信息
  • 1 兰州城市建设设计研究院有限公司, 兰州市南滨河东路875号, 730050
作者简介:

宋秉红，高级工程师，主要研究方向为GNSS数据处理与应用，E-mail：

Applicability Analysis of ECOM Solar Radiation Pressure Models in Precise Orbit Determination
Binghong SONG1 , Jianhua YANG1
Affiliations
  • 1 Lanzhou Urban Construction Design and Research Institute Co Ltd, 875 East-Nanbinhe Road, Lanzhou 730050, China

    • SONG Binghong, senior engineer, majors in GNSS data processing and its applications, E-mail:

出版时间: 2025-03-15 doi: 10.14075/j.jgg.2024.04.176
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摘要
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太阳光压摄动作为在轨导航卫星受到的最大非保守力，是卫星精密定轨的重要误差源，而目前多数光压模型是针对全球定位系统(GPS)卫星而建立的，对北斗三号(BDS-3)卫星精密定轨的适用性分析较少。本文借助MGEX观测数据对5种欧洲定轨中心拓展轨道模型(ECOM1-9、ECOM1-7、ECOM1-5、ECOM2、ECOMC)太阳光压模型进行定轨实验。结果表明，不同厂商研制的卫星对光压模型的适用性不同，对中国空间技术研究院(CAST)研制的卫星而言，ECOMC模型在径向、切向和法向均表现出最优适用性；对上海微小卫星工程中心(SECM)研制的卫星而言，径向、切向和法向分别为ECOM1-5、ECOMC、ECOMC模型精度最佳；对三维整体而言，CAST卫星和SECM卫星定轨均推荐采用ECOMC模型；从24 h预测结果来看，对于CAST卫星，ECOM1-9、ECOM1-7、ECOM1-5、ECOM2、ECOMC模型24 h预测精度分别为23.3 cm、20.6 cm、17.2 cm、21.8 cm、10.4 cm，对于SECM卫星，各模型预测精度分别为25.7 cm、19.1 cm、15.9 cm、12.9 cm、11.9 cm。

全球卫星导航系统  /  太阳光压  /  几何结构  /  定轨参数

The solar pressure perturbation, as the largest non-conservative force experienced by in-orbit navigation satellites, is an important error source for precise orbit determination. Currently, most solar radiation pressure models are established for global positioning system(GPS) satellites, and there is relatively little adaptability analysis of solar radiation pressure models for precise orbit determination accuracy of Beidou-3(BDS-3) satellites. We use observation data from the multi-GNSS experiment(MGEX) to conduct orbit determination experiments based on five solar radiation pressure models, including ECOM1-9, ECOM1-7, ECOM1-5, ECOM2, ECOMC. The results show that the applicability of solar radiation pressure model varies for satellites developed by different manufacturers. For satellites developed by China Academy of Space Technology(CAST), the ECOMC model exhibits optimal applicability in radial, tangential, and normal directions. For satellites developed by Shanghai Engineering Center for Microsatellites(SECM), the radial, tangential, and normal directions have the best accuracy for ECOM1-5, ECOMC, and ECOMC models, respectively. For 3D entirety, the ECOMC model is recommended for orbit determination of both CAST and SECM satellites. From the 24-hour prediction results, for CAST type satellites, the accuracy of ECOM1-9, ECOM1-7, ECOM1-5, ECOM2, and ECOMC models is 23.3 cm, 20.6 cm, 17.2 cm, 21.8 cm, and 10.4 cm, respectively. For SECM type satellites, the accuracy is 25.7 cm, 19.1 cm, 15.9 cm, 12.9 cm, and 11.9 cm, respectively.

GNSS  /  solar radiation pressure  /  geometric structure  /  orbit determination parameters
宋秉红, 杨建华. ECOM系列光压模型在精密定轨中的适用性分析. 大地测量与地球动力学, 2025 , 45 (3) : 290 -296 . DOI: 10.14075/j.jgg.2024.04.176
Binghong SONG, Jianhua YANG. Applicability Analysis of ECOM Solar Radiation Pressure Models in Precise Orbit Determination[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (3) : 290 -296 . DOI: 10.14075/j.jgg.2024.04.176
正文
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北斗卫星导航系统(BDS)可为用户提供定位、导航和授时等服务，而北斗卫星轨道的确定是其提供服务的前提条件[1-2]。太阳辐射压(solar radiation pressure，SRP)摄动是由太阳辐射的光子连续“撞击”卫星表面所产生的力的作用，BDS卫星在轨所受的非引力摄动主要来源于太阳光压[3]。光压模型通过分析太阳光对卫星的影响，可以实现高精度的卫星轨道测量，因此太阳光压模型误差是卫星动力学模型误差的主要误差源[4-5]。
20世纪60年代起，国内外学者就对太阳光压进行相应研究，根据模型建立原理可分为经验型光压模型、半经验型光压模型和分析型光压模型[6-9]，其中多数光压模型是针对全球定位系统(GPS)卫星而建立的，而BDS卫星光压模型研究进展相对滞后。彭汉兵等[10]利用观测值残差、轨道内外符合精度以及外推精度对不同经验太阳光压模型在BDS-2卫星定轨中的适用性进行分析，确定BDS-2卫星定轨的最优ECOM模型；陈秋丽等[11]通过分析光压辐射的物理机制和北斗卫星物理、光学参数构建光压摄动综合解析模型，可实现dm级的精密定轨。建立光压模型需要长期在轨数据支撑，与其他全球卫星导航系统相比，BDS建立较晚，其精密轨道产品积累较少，ECOM系列模型由于简单高效的表达形式，目前仍广泛应用于BDS定轨中，同时现阶段研究成果表明各种模型各有优缺点，且在不同卫星导航系统间适用性不同。基于此，本文围绕ECOM1模型(9参数、7参数和5参数)、ECOM2模型、ECOMC模型对BDS-3 MEO卫星定轨适用性进行系统分析，旨在提高BDS-3 MEO卫星定轨精度，并为模型优化提供参考依据。
1 ECOM系列光压模型
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ECOM1-9模型可表示为：
$\left\{\begin{array}{l}a_D=D_0+D_c \cos u+D_s \sin u \\ a_Y=Y_0+Y_c \cos u+Y_s \sin u \\ a_B=B_0+B_c \cos u+B_s \sin u\end{array}\right.$
式中，D0、Y0、B0表示常数项；Dc、Ds、Yc、Ys、Bc、Bs表示周期项；u表示人造卫星相对于惯性系升交点的角度。欧洲定轨中心(CODE)对Dc、Ds、Yc、Ys四项参数进行优化，提出ECOM1-5模型。
部分学者进一步研究发现，ECOM1模型定轨过程中会产生系统性误差，进而提出改进的ECOM2光压模型，其数学表达式为：
$\left\{\begin{array}{l}a_D=D_0+\sum\limits_{i=1}^{n_D}\left(D_{2 i, c} \cos (2 i \Delta u)+\right. \\ \left.\quad D_{2 i, s} \sin (2 i \Delta u)\right) \\ a_Y=Y_0 \\ a_B=B_0+\sum\limits_{i=1}^{n_B}\left(B_{2 i-1, c} \cos ((2 i-1) \Delta u)+\right. \\ \left.\quad B_{2 i-1, s} \sin ((2 i-1) \Delta u)\right)\end{array}\right.$
式中，nD和nB分别为D方向和B方向上的周期项数目；Δu为卫星相对于太阳的轨道角。
对ECOM1和ECOM2模型数据进行收集再处理，得到ECOMC光压模型，该模型兼顾ECOM1和ECOM2模型的特点，但未知参数多、参数间相关性强[12]，其数学表达式为：
$\left\{\begin{array}{l}a_D=D_0+D_{1 c} \cos (\Delta u)+D_{1 s} \sin (\Delta u)+ \\ \quad D_{2 c} \cos (2 \Delta u)+D_{2 s} \sin (2 \Delta u)+ \\ \quad D_{4 c} \cos (4 \Delta u)+D_{4 s} \sin (4 \Delta u) \\ a_Y=Y_0+Y_{1 c} \cos (\Delta u)+Y_{1 s} \sin (\Delta u) \\ a_B=B_{1 c} \cos (\Delta u)+B_{1 s} \sin (\Delta u)\end{array}\right.$
式中，各自变量含义同式(1)、(2)。
2 基本参数与定轨策略
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2.1 BDS卫星基本参数
BDS-2和BDS-3卫星基本参数信息存在明显区别，同时考虑到由中国空间技术研究院(China Academy of Space Technology，CAST)和上海微小卫星工程中心(Shanghai Engineering Center for Microsatellites，SECM)供应的BDS-3卫星在卫星本体和太阳帆板面积上差异明显，因此本文将BDS-3卫星适用性分析划分为SECM和CAST两种类型，详细参数如表1所示。
由表1可知，BDS-2卫星在空间几何结构上接近正方体，而BDS-3卫星接近长方体；在光学参数上，BDS-2和BDS-3卫星在X、Y、Z面板和太阳帆板方面均存在差异，因此BDS-2和BDS-3卫星的太阳光压摄动加速度截然不同。
2.2 定轨策略
本文借助MGEX(multi-GNSS experiment)观测数据，分别采用5种太阳光压模型(ECOM1-9、ECOM1-7、ECOM1-5、ECOM2、ECOMC)进行定轨实验。使用控制变量法进行对照实验，实验过程中仅太阳光压模型不同，其余参数完全一致。定轨过程中截止高度角设置为10°，观测值采用双频无电离层组合模式，轨道弧长设置为24 h，固体潮、海潮、极移和相对论效应均采用IERS2010模型进行改正，对流层延迟使用Saastamoinen模型+全球映射函数(global mapping function，GMF)进行改正，重力场使用EGM2008模型进行改正，天线发射功率设置为130 W，N体(太阳、月亮和其他近地行星)引力采用JPL实验室公布的JPL DE405模型进行改正，定轨过程中不考虑大气阻力和地球返照辐射的影响，同时在实验过程中不考虑地影期和非地影期对定轨结果的影响，具体处理策略见表2。精度评估使用武汉大学事后精密星历产品作为真值，通过估计精度和预测精度分析不同太阳光压模型在BDS卫星定位中的适用性。
3 案例分析
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为研究不同光压模型对BDS-3卫星定轨精度的影响，使用2022年年积日190-197的MGEX观测数据，按照§2.2定轨策略进行定轨实验。将拟合结果与武汉大学事后精密星历产品进行对比，分析径向(radial)、切向(along)、法向(cross)和三维方向(3D)残差。
3.1 CAST卫星适用性分析
CAST卫星径向、切向、法向和3D方向残差的均方根(root mean square，RMS)统计结果见表3(单位cm，RRMS、ARMS、CRMS、3DRMS分别表示径向、切向、法向和三维方向残差的RMS值)，可视化结果如图1所示。
由表3和图1可知，使用不同光压模型时，CAST卫星定轨结果存在差异。从径向上看，不同光压模型定轨精度从高至低为ECOMC、ECOM2、ECOM1-5、ECOM1-7、ECOM1-9模型；从切向上看，不同光压模型定轨精度从高至低为ECOMC、ECOM1-5、ECOM1-7、ECOM1-9、ECOM2模型；从法向上看，不同光压模型定轨精度从高至低为ECOMC、ECOM1-5、ECOM1-7、ECOM1-9、ECOM2模型，不同光压模型的定轨结果在法向与切向上的适用性表现较为一致；从三维整体来看，不同光压模型定轨精度从高至低为ECOMC、ECOM1-5、ECOM1-7、ECOM1-9、ECOM2模型。ECOMC模型定轨精度在径向、切向和法向上均最高，可以达到cm级；ECOM2模型定轨精度在径向上仅次于ECOMC模型，而在切向和法向上定轨精度最差，表明ECOMC模型对CAST卫星定轨的适用性较好，而ECOM2模型适用性较差，其原因可能为ECOMC模型兼顾了ECOM1和ECOM2模型的特点，未知参数较多，可吸收更多的未建模误差，使得ECOMC模型对CAST卫星的适用性最强。
为进一步评估不同轨道弧长对CAST卫星精密定轨的影响，分别采用6 h、12 h和24 h轨道弧长进行精密定轨实验，表4(单位cm)为CAST卫星(PRN C19)在径向、切向、法向和3D方向残差的RMS值，可视化结果如图2所示。
由表4和图2可知，使用同一光压模型不同轨道弧长时，CAST卫星定轨结果存在差异。采用同一轨道弧长进行定轨，不同光压模型定轨结果与表3完全一致。整体来看，采用同一光压模型时，24 h轨道弧长定轨结果在径向、切向和法向上均表现最佳，6 h轨道弧长定轨结果在径向、切向和法向上均表现最差，原因可能为长轨道弧长可提供更加稳定的轨道数据，降低定轨误差。采用24 h轨道弧长定轨较12 h轨道弧长定轨精度平均提升10.40%，较6 h轨道弧长定轨精度平均提升17.43%。
3.2 SECM卫星适用性分析
SECM卫星在径向、切向、法向和3D方向残差的RMS值统计结果见表5(单位cm)，可视化结果如图3所示。
由表5和图3可知，使用不同光压模型时，SECM卫星定轨结果存在差异，该结果与CAST卫星表现一致，进一步证实了不同光压模型对BDS-3卫星定轨适用性不同。从径向上看，不同光压模型定轨精度从高至低为ECOM1-5、ECOM2、ECOMC、ECOM1-7、ECOM1-9模型；从切向上看，不同光压模型定轨精度从高至低为ECOMC、ECOM2、ECOM1-5、ECOM1-7、ECOM1-9模型；从法向上看，不同光压模型定轨精度从高至低为ECOMC、ECOM2、ECOM1-5、ECOM1-7、ECOM1-9模型；从三维整体来看，不同光压模型定轨精度从高至低为ECOMC、ECOM2、ECOM1-5、ECOM1-7、ECOM1-9模型。对SECM卫星而言，不同光压模型的定轨结果在法向与切向上的适用性表现较为一致，均为ECOMC模型定轨精度最高，ECOM1-9模型定轨精度最低，而在径向上ECOM1-5模型定轨精度最高，可以达到cm级。因此，SECM卫星定轨在三维整体上推荐使用ECOMC模型。
为进一步评估不同轨道弧长对SECM卫星精密定轨的影响，分别采用6 h、12 h和24 h轨道弧长进行精密定轨实验，表6(单位cm)为SECM卫星(PRN C25)在径向、切向、法向和3D方向残差的RMS值，可视化结果如图4所示。
由表6和图4可知，使用同一光压模型不同轨道弧长时，SECM卫星定轨结果存在差异。采用同一轨道弧长进行定轨，不同光压模型定轨结果与表5完全一致。整体来看，采用同一光压模型时，24 h轨道弧长定轨结果在径向、切向和法向上均表现最佳，6 h轨道弧长定轨结果在径向、切向和法向上均表现最差，其结果与CAST卫星表现一致。采用24 h轨道弧长定轨较12 h轨道弧长定轨精度平均提升11.32%，较6 h轨道弧长定轨精度平均提升19.64%。
3.3 预测精度评估
为进一步评估5种光压模型对BDS-3卫星定轨的适用性，对CAST和SECM卫星24 h预测整时刻轨道结果的径向、切向、法向和三维方向RMS均值进行统计，结果如表7(单位cm)所示，三维整体RMS值可视化结果如图5所示。
由表7和图5可知，对CAST卫星而言，ECOMC模型在径向、切向和法向预测精度最高；对SECM卫星而言，ECOM1-5模型在径向预测精度最高，ECOMC模型在切向和法向预测精度最高，该结果与§3.1和§3.2适用性分析结论相同。从整体来看，对CAST卫星而言，使用ECOM1-9、ECOM1-7、ECOM1-5、ECOM2、ECOMC模型24 h预测精度分别为23.3 cm、20.6 cm、17.2 cm、21.8 cm、10.4 cm；对SECM卫星而言，各模型24 h预测精度分别为25.7 cm、19.1 cm、15.9 cm、12.9 cm、11.9 cm。对三维整体而言，CAST和SECM卫星定轨均推荐采用ECOMC模型，该模型在BDS-3 MEO卫星定轨中具有最优适用性，其原因可能为ECOMC模型兼顾了ECOM1和ECOM2模型的优点。
4 结语
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本文基于MGEX观测数据，采用5种太阳光压模型(ECOM1-9、ECOM1-7、ECOM1-5、ECOM2、ECOMC)进行BDS-3 MEO卫星定轨实验，得到以下结论：
1) 对三维整体而言，不同光压模型对不同类型BDS-3 MEO卫星定轨结果存在差异，ECOMC模型在BDS-3 MEO卫星定轨中具有最优适用性，CAST和SECM卫星定轨均推荐采用ECOMC模型。
2) 对于CAST卫星，使用ECOM1-9、ECOM1-7、ECOM1-5、ECOM2、ECOMC模型24 h预测精度分别为23.3 cm、20.6 cm、17.2 cm、21.8 cm、10.4 cm；对于SECM卫星，各模型24 h预测精度分别为25.7 cm、19.1 cm、15.9 cm、12.9 cm、11.9 cm。

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doi: 10.14075/j.jgg.2024.04.176
  • 接收时间：2024-04-14
  • 首发时间：2026-10-30
  • 出版时间：2025-03-15
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  • 收稿日期：2024-04-14
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    1 兰州城市建设设计研究院有限公司, 兰州市南滨河东路875号, 730050
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2种不同金属材料的力学参数
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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
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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
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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