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Article(id=1239165056127135873, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1239165048212476136, articleNumber=null, orderNo=null, doi=10.12347/j.ycyk.20250804001, pmid=null, cstr=32406.14.ycyk.20250804001, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1754236800000, receivedDateStr=2025-08-04, revisedDate=1755964800000, revisedDateStr=2025-08-24, acceptedDate=null, acceptedDateStr=null, onlineDate=1773369571954, onlineDateStr=2026-03-13, pubDate=1757865600000, pubDateStr=2025-09-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773369571954, onlineIssueDateStr=2026-03-13, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773369571954, creator=13701087609, updateTime=1773369571954, updator=13701087609, issue=Issue{id=1239165048212476136, tenantId=1146029695717560320, journalId=1238841944844054536, year='2025', volume='46', issue='5', pageStart='1', pageEnd='158', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773369570067, creator=13701087609, updateTime=1773617788336, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1240206151170707811, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1239165048212476136, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1240206151170707812, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1239165048212476136, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=109, endPage=118, ext={EN=ArticleExt(id=1239165056395571337, articleId=1239165056127135873, tenantId=1146029695717560320, journalId=1238841944844054536, language=EN, title=GPS LNAV and CNAV Broadcast Ephemerides Accuracy Comparison and Validation, columnId=1239165052184482030, journalTitle=Journal of Telemetry, Tracking and Command, columnName=Navigation Technology Column, runingTitle=null, highlight=null, articleAbstract=

To systematically evaluate the accuracy of GPS LNAV and CNAV broadcast ephemerides and verify their performance in real-time applications, this study conducted a year-long accuracy assessment for 2024 based on GNSS broadcast and precise ephemerides, complemented by validation through real-time orbit determination (RTOD) experiments using LEO satellites. Broadcast and precise ephemerides from 2024 were used to perform statistical analyses of ephemeris accuracy across different satellite blocks and navigation message types. In addition, reduced-dynamic RTOD experiments were carried out using onboard GPS observations from the GRACE-FO C satellite to assess the impact of different broadcast ephemerides on orbit accuracy. The results show that the accuracy of broadcast ephemerides varies significantly among satellite blocks, with BLOCK IIIA performing the best and BLOCK IIF performing the worst. After the clock source switch on G08 and G10 in 2024, the constellation-averaged SISRE for LNAV and CNAV broadcast ephemerides reached 25.5 cm and 23.8 cm, respectively, representing a substantial improvement compared to the LNAV SISRE of 37.0 cm in 2021. The LEO RTOD experiments further demonstrated that, compared to LNAV, CNAV provides improved accuracy in the along-track, cross-track, radial, and 3D directions, with a maximum reduction in 3D orbit error of 0.8 cm and an average improvement of about 3.2%, thereby confirming the advantage of CNAV in real-time applications. Overall, both the ephemeris accuracy statistics and LEO RTOD results consistently indicate that CNAV broadcast ephemerides outperform LNAV. With the gradual retirement of BLOCK IIR satellites and the continued deployment of BLOCK IIIA satellites, navigation, positioning, and timing services based on CNAV broadcast ephemerides are expected to achieve even higher accuracy, further enhancing their value for real-time positioning and scientific applications.

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为了系统评估GPS（全球定位系统）系统LNAV（遗留导航电文）与CNAV（民用导航电文）广播星历的精度，并验证其在实时应用中的性能，本研究基于2024全年GNSS（全球导航卫星系统）广播与精密星历开展精度对比分析，并结合LEO实时定轨实验进行验证。选取2024年全年GNSS广播星历与精密星历数据，统计分析不同卫星型号和导航电文类型的星历精度。同时，利用GRACE-FO C星（重力恢复与气候实验后续任务C星）的星载GPS观测数据开展缩减动力学实时定轨实验，评估不同广播星历对轨道精度的影响。研究表明：不同卫星型号的广播星历精度存在显著差异，其中BLOCK IIIA（GPS卫星型号）卫星表现最佳，BLOCK IIF最差。2024年G08和G10完成钟源切换后LNAV与CNAV广播星历的全星座SISRE（空间信号测距误差）均值分别为25.5 cm和23.8 cm，较2021年LNAV星历的37.0 cm显著降低。LEO（低地球轨道）实时定轨实验结果显示：相较于LNAV广播星历，采用CNAV广播星历A、C、R及三维方向精度均有提升，三维轨道误差最大提升0.8 cm，轨道精度平均提高约3.2%，进一步验证了CNAV在实时应用中的优势。综合星历精度与LEO实时定轨验证结果，CNAV广播星历整体表现优于LNAV。随着BLOCK IIR卫星逐步退役及BLOCK IIIA卫星的持续部署，预计未来基于CNAV广播星历的导航、定位与授时服务将实现更高精度，进一步增强其在实时定位与科学应用中的价值。

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高翠　1996年生，硕士，助教。

裴炳南　1956年生，教授，博士生导师。

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高翠　1996年生，硕士，助教。

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高翠　1996年生，硕士，助教。

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裴炳南　1956年生，教授，博士生导师。

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裴炳南　1956年生，教授，博士生导师。

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(2024)[2025-01-20]. https://www.navcen.uscg.gov/?Do=constellationStatus&NANU=2024010., articleTitle=Notices Advisory to NAVSTAR Users (NANU) 2024010, refAbstract=null)], funds=[Fund(id=1239265689358365158, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, awardId=2023J011801, language=CN, fundingSource=福建省自然科学基金(2023J011801), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1239265683570225329, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, xref=1., ext=[AuthorCompanyExt(id=1239265683578613938, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, companyId=1239265683570225329, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.Quanzhou University of Information Engineering, Quanzhou 362000, China), AuthorCompanyExt(id=1239265683587002547, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, companyId=1239265683570225329, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1泉州信息工程学院 泉州 362000)]), AuthorCompany(id=1239265683662500024, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, xref=2., ext=[AuthorCompanyExt(id=1239265683675082937, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, companyId=1239265683662500024, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.Fujian Key Laboratory of the Modern Communication and Beidou Positioning Technology in Universities, Quanzhou 362000, China), AuthorCompanyExt(id=1239265683687665851, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, companyId=1239265683662500024, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2现代通信与北斗定位技术福建省高校重点实验室 泉州 362000)])], figs=[ArticleFig(id=1239265685717709147, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=EN, label=Fig. 1, caption=Comparison of LNAV broadcast and precise ephemerides, figureFileSmall=L54Erkd/qOwg0kPDIIQT4Q==, figureFileBig=5NseUEuosYffFvlDAfaLAw==, tableContent=null), ArticleFig(id=1239265687210881375, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=CN, label=图1, caption=LNAV广播星历与精密星历对比结果, figureFileSmall=L54Erkd/qOwg0kPDIIQT4Q==, figureFileBig=5NseUEuosYffFvlDAfaLAw==, tableContent=null), ArticleFig(id=1239265687353487725, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=EN, label=Fig. 2, caption=Comparison of CNAV broadcast and precise ephemerides, figureFileSmall=eIJ6JAqLzQqDHy4/v1Gq9A==, figureFileBig=nMttIKVoJyAIqDzGgAzjGQ==, tableContent=null), ArticleFig(id=1239265687433179507, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=CN, label=图2, caption=CNAV广播星历与精密星历对比结果, figureFileSmall=eIJ6JAqLzQqDHy4/v1Gq9A==, figureFileBig=nMttIKVoJyAIqDzGgAzjGQ==, tableContent=null), ArticleFig(id=1239265687563202937, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=EN, label=Fig. 3, caption=Orbit errors of LNAV, figureFileSmall=Fo8Hr8q1qm6XDX2PoG2e8w==, figureFileBig=eOwqFyp8HTSVFYO2D8IArQ==, tableContent=null), ArticleFig(id=1239265687672254847, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=CN, label=图3, caption=LNAV广播星历轨道误差, figureFileSmall=Fo8Hr8q1qm6XDX2PoG2e8w==, figureFileBig=eOwqFyp8HTSVFYO2D8IArQ==, tableContent=null), ArticleFig(id=1239265687798083977, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=EN, label=Fig. 4, caption=Orbit errors of CNAV, figureFileSmall=fswY7spK5tcBiuorDX+VRw==, figureFileBig=kFK8HYe1a/qMLiG7iNN17g==, tableContent=null), ArticleFig(id=1239265687898747277, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=CN, label=图4, caption=CNAV广播星历轨道误差, figureFileSmall=fswY7spK5tcBiuorDX+VRw==, figureFileBig=kFK8HYe1a/qMLiG7iNN17g==, tableContent=null), ArticleFig(id=1239265688016187795, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=EN, label=Table 1, caption=

PRN and satellite type correspondence

, figureFileSmall=null, figureFileBig=null, tableContent=
BLOCKPRN
IIRG02 G13 G16 G19 G20 G21 G22
IIR-MG05 G07 G12 G15 G17 G29 G31
IIFG03 G06 G08 G09 G10 G24 G25
G26 G27 G30 G32
IIIAG04 G11 G14 G18 G23 G28
), ArticleFig(id=1239265688116851097, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=CN, label=表1, caption=

PRN与卫星型号对应关系

, figureFileSmall=null, figureFileBig=null, tableContent=
BLOCKPRN
IIRG02 G13 G16 G19 G20 G21 G22
IIR-MG05 G07 G12 G15 G17 G29 G31
IIFG03 G06 G08 G09 G10 G24 G25
G26 G27 G30 G32
IIIAG04 G11 G14 G18 G23 G28
), ArticleFig(id=1239265688225903007, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=EN, label=Table 2, caption=

RMS of accuracy indicators for LNAV broadcast ephemerides

, figureFileSmall=null, figureFileBig=null, tableContent=
BLOCKPRN△A/m△C/m△R/m△T/mSISRE(orb) /mSISRE/m
IIRG021.202 (1.177)0.560 (0.574)0.145 (0.143)0.161 (0.155)0.237 (0.234)0.277 (0.271)
G130.979 (1.000)0.559 (0.562)0.120 (0.119)0.217 (0.203)0.199 (0.201)0.284 (0.276)
G160.937 (0.964)0.568 (0.576)0.139 (0.146)0.173 (0.175)0.208 (0.215)0.235 (0.240)
G190.809 (0.783)0.503 (0.523)0.128 (0.125)0.149 (0.150)0.185 (0.182)0.227 (0.225)
G200.798 (0.822)0.554 (0.572)0.115 (0.118)0.172 (0.170)0.179 (0.184)0.245 (0.247)
G210.956 (0.974)0.560 (0.548)0.165 (0.168)0.208 (0.211)0.226 (0.229)0.288 (0.292)
G220.776 (0.776)0.548 (0.551)0.109 (0.112)0.146 (0.147)0.173 (0.175)0.224 (0.224)
mean 0.922 (0.928) 0.550 (0.558) 0.132 (0.133) 0.175 (0.173) 0.201 (0.203) 0.254 (0.254)
IIR-MG050.818 (0.827)0.484 (0.489)0.162 (0.162)0.211 (0.203)0.209 (0.21)0.246 (0.238)
G071.092 (1.143)0.727 (0.716)0.141 (0.139)0.236 (0.225)0.233 (0.236)0.315 (0.309)
G121.073 (1.086)0.545 (0.549)0.146 (0.148)0.163 (0.165)0.224 (0.226)0.241 (0.243)
G150.884 (0.881)0.571 (0.574)0.123 (0.114)0.144 (0.142)0.193 (0.188)0.223 (0.220)
G171.122 (1.106)0.589 (0.566)0.154 (0.151)0.235 (0.214)0.236 (0.232)0.308 (0.289)
G290.845 (0.858)0.426 (0.432)0.134 (0.131)0.224 (0.219)0.189 (0.188)0.273 (0.269)
G310.868 (0.885)0.530 (0.523)0.118 (0.119)0.186 (0.181)0.185 (0.187)0.252 (0.249)
mean 0.957 (0.970) 0.553 (0.550) 0.140 (0.138) 0.200 (0.193) 0.210 (0.210) 0.265 (0.260)
IIFG030.851 (0.867)0.486 (0.489)0.174 (0.169)0.278 (0.266)0.220 (0.218)0.360 (0.347)
G060.853 (0.813)0.455 (0.463)0.186 (0.189)0.126 (0.126)0.229 (0.228)0.269 (0.268)
G080.912 (0.864)0.629 (0.609)0.182 (0.163)0.300 (0.163)0.238 (0.220)0.385 (0.278)
G090.678 (0.666)0.359 (0.348)0.162 (0.146)0.111 (0.111)0.193 (0.179)0.225 (0.214)
G101.031 (0.991)0.735 (0.734)0.186 (0.178)0.272 (0.170)0.257 (0.248)0.376 (0.302)
G240.847 (0.782)0.400 (0.381)0.163 (0.164)0.110 (0.107)0.208 (0.203)0.244 (0.238)
G250.853 (0.805)0.467 (0.453)0.156 (0.164)0.110 (0.108)0.207 (0.208)0.246 (0.247)
G260.826 (0.821)0.553 (0.552)0.188 (0.189)0.150 (0.157)0.232 (0.233)0.272 (0.277)
G271.049 (1.055)0.703 (0.703)0.173 (0.172)0.127 (0.126)0.247 (0.247)0.284 (0.283)
G300.743 (0.743)0.511 (0.489)0.158 (0.160)0.131 (0.125)0.201 (0.202)0.248 (0.246)
G320.834 (0.774)0.501 (0.488)0.166 (0.151)0.103 (0.097)0.214 (0.198)0.237 (0.221)
mean 0.862 (0.835) 0.527 (0.519) 0.172 (0.168) 0.165 (0.142) 0.222 (0.217) 0.286 (0.266)
IIIAG040.918 (0.917)0.540 (0.550)0.130 (0.122)0.101 (0.099)0.199 (0.194)0.211 (0.209)
G110.846 (0.875)0.454 (0.472)0.154 (0.151)0.100 (0.098)0.204 (0.205)0.224 (0.225)
G141.034 (1.045)0.603 (0.578)0.136 (0.142)0.094 (0.093)0.217 (0.220)0.231 (0.233)
G181.049 (1.079)0.748 (0.713)0.164 (0.157)0.098 (0.095)0.244 (0.241)0.258 (0.253)
G230.913 (0.943)0.615 (0.638)0.153 (0.145)0.102 (0.099)0.218 (0.216)0.232 (0.230)
G280.985 (0.960)0.512 (0.522)0.130 (0.135)0.112 (0.114)0.204 (0.205)0.226 (0.227)
mean 0.958 (0.970) 0.579 (0.579) 0.145 (0.142) 0.101 (0.100) 0.214 (0.214) 0.230 (0.230)
Total mean 0.918 (0.912) 0.549 (0.546) 0.151 (0.148) 0.163 (0.152) 0.213 (0.211) 0.263 (0.255)
), ArticleFig(id=1239265688339149223, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=CN, label=表2, caption=

LNAV广播星历精度指标RMS

, figureFileSmall=null, figureFileBig=null, tableContent=
BLOCKPRN△A/m△C/m△R/m△T/mSISRE(orb) /mSISRE/m
IIRG021.202 (1.177)0.560 (0.574)0.145 (0.143)0.161 (0.155)0.237 (0.234)0.277 (0.271)
G130.979 (1.000)0.559 (0.562)0.120 (0.119)0.217 (0.203)0.199 (0.201)0.284 (0.276)
G160.937 (0.964)0.568 (0.576)0.139 (0.146)0.173 (0.175)0.208 (0.215)0.235 (0.240)
G190.809 (0.783)0.503 (0.523)0.128 (0.125)0.149 (0.150)0.185 (0.182)0.227 (0.225)
G200.798 (0.822)0.554 (0.572)0.115 (0.118)0.172 (0.170)0.179 (0.184)0.245 (0.247)
G210.956 (0.974)0.560 (0.548)0.165 (0.168)0.208 (0.211)0.226 (0.229)0.288 (0.292)
G220.776 (0.776)0.548 (0.551)0.109 (0.112)0.146 (0.147)0.173 (0.175)0.224 (0.224)
mean 0.922 (0.928) 0.550 (0.558) 0.132 (0.133) 0.175 (0.173) 0.201 (0.203) 0.254 (0.254)
IIR-MG050.818 (0.827)0.484 (0.489)0.162 (0.162)0.211 (0.203)0.209 (0.21)0.246 (0.238)
G071.092 (1.143)0.727 (0.716)0.141 (0.139)0.236 (0.225)0.233 (0.236)0.315 (0.309)
G121.073 (1.086)0.545 (0.549)0.146 (0.148)0.163 (0.165)0.224 (0.226)0.241 (0.243)
G150.884 (0.881)0.571 (0.574)0.123 (0.114)0.144 (0.142)0.193 (0.188)0.223 (0.220)
G171.122 (1.106)0.589 (0.566)0.154 (0.151)0.235 (0.214)0.236 (0.232)0.308 (0.289)
G290.845 (0.858)0.426 (0.432)0.134 (0.131)0.224 (0.219)0.189 (0.188)0.273 (0.269)
G310.868 (0.885)0.530 (0.523)0.118 (0.119)0.186 (0.181)0.185 (0.187)0.252 (0.249)
mean 0.957 (0.970) 0.553 (0.550) 0.140 (0.138) 0.200 (0.193) 0.210 (0.210) 0.265 (0.260)
IIFG030.851 (0.867)0.486 (0.489)0.174 (0.169)0.278 (0.266)0.220 (0.218)0.360 (0.347)
G060.853 (0.813)0.455 (0.463)0.186 (0.189)0.126 (0.126)0.229 (0.228)0.269 (0.268)
G080.912 (0.864)0.629 (0.609)0.182 (0.163)0.300 (0.163)0.238 (0.220)0.385 (0.278)
G090.678 (0.666)0.359 (0.348)0.162 (0.146)0.111 (0.111)0.193 (0.179)0.225 (0.214)
G101.031 (0.991)0.735 (0.734)0.186 (0.178)0.272 (0.170)0.257 (0.248)0.376 (0.302)
G240.847 (0.782)0.400 (0.381)0.163 (0.164)0.110 (0.107)0.208 (0.203)0.244 (0.238)
G250.853 (0.805)0.467 (0.453)0.156 (0.164)0.110 (0.108)0.207 (0.208)0.246 (0.247)
G260.826 (0.821)0.553 (0.552)0.188 (0.189)0.150 (0.157)0.232 (0.233)0.272 (0.277)
G271.049 (1.055)0.703 (0.703)0.173 (0.172)0.127 (0.126)0.247 (0.247)0.284 (0.283)
G300.743 (0.743)0.511 (0.489)0.158 (0.160)0.131 (0.125)0.201 (0.202)0.248 (0.246)
G320.834 (0.774)0.501 (0.488)0.166 (0.151)0.103 (0.097)0.214 (0.198)0.237 (0.221)
mean 0.862 (0.835) 0.527 (0.519) 0.172 (0.168) 0.165 (0.142) 0.222 (0.217) 0.286 (0.266)
IIIAG040.918 (0.917)0.540 (0.550)0.130 (0.122)0.101 (0.099)0.199 (0.194)0.211 (0.209)
G110.846 (0.875)0.454 (0.472)0.154 (0.151)0.100 (0.098)0.204 (0.205)0.224 (0.225)
G141.034 (1.045)0.603 (0.578)0.136 (0.142)0.094 (0.093)0.217 (0.220)0.231 (0.233)
G181.049 (1.079)0.748 (0.713)0.164 (0.157)0.098 (0.095)0.244 (0.241)0.258 (0.253)
G230.913 (0.943)0.615 (0.638)0.153 (0.145)0.102 (0.099)0.218 (0.216)0.232 (0.230)
G280.985 (0.960)0.512 (0.522)0.130 (0.135)0.112 (0.114)0.204 (0.205)0.226 (0.227)
mean 0.958 (0.970) 0.579 (0.579) 0.145 (0.142) 0.101 (0.100) 0.214 (0.214) 0.230 (0.230)
Total mean 0.918 (0.912) 0.549 (0.546) 0.151 (0.148) 0.163 (0.152) 0.213 (0.211) 0.263 (0.255)
), ArticleFig(id=1239265688444006831, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=EN, label=Table 3, caption=

RMS of accuracy indicators for CNAV broadcast ephemerides

, figureFileSmall=null, figureFileBig=null, tableContent=
BLOCKPRN△A/m△C/m△R/m△T/mSISRE(orb) /mSISRE/m
IIR-MG050.799 (0.811)0.475 (0.486)0.149 (0.150)0.203 (0.195)0.197 (0.199)0.228 (0.222)
G071.025 (1.065)0.710 (0.695)0.122 (0.121)0.218 (0.213)0.214 (0.217)0.289 (0.286)
G121.049 (1.067)0.535 (0.543)0.136 (0.137)0.156 (0.159)0.215 (0.217)0.228 (0.231)
G150.840 (0.836)0.560 (0.562)0.101 (0.094)0.137 (0.135)0.175 (0.171)0.202 (0.200)
G171.042 (1.026)0.559 (0.536)0.136 (0.133)0.225 (0.204)0.215 (0.211)0.285 (0.265)
G290.798 (0.802)0.412 (0.415)0.120 (0.117)0.212 (0.206)0.174 (0.173)0.253 (0.247)
G310.826 (0.844)0.513 (0.506)0.099 (0.100)0.175 (0.170)0.170 (0.171)0.233 (0.230)
mean 0.911 (0.922) 0.538 (0.535) 0.123 (0.122) 0.189 (0.183) 0.194 (0.194) 0.245 (0.240)
IIFG030.809 (0.819)0.481 (0.476)0.161 (0.155)0.259 (0.245)0.207 (0.204)0.335 (0.321)
G060.815 (0.786)0.447 (0.456)0.168 (0.171)0.113 (0.112)0.212 (0.212)0.248 (0.248)
G080.855 (0.804)0.606 (0.586)0.167 (0.146)0.291 (0.154)0.222 (0.202)0.366 (0.257)
G090.652 (0.632)0.354 (0.341)0.152 (0.135)0.101 (0.101)0.183 (0.167)0.212 (0.200)
G100.996 (0.959)0.723 (0.724)0.173 (0.164)0.266 (0.163)0.244 (0.235)0.362 (0.287)
G240.833 (0.751)0.382 (0.358)0.148 (0.148)0.101 (0.098)0.195 (0.187)0.228 (0.220)
G250.829 (0.782)0.461 (0.448)0.140 (0.148)0.095 (0.095)0.193 (0.194)0.226 (0.228)
G260.788 (0.772)0.543 (0.537)0.177 (0.179)0.139 (0.146)0.221 (0.221)0.254 (0.259)
G271.001 (1.010)0.679 (0.679)0.156 (0.154)0.117 (0.115)0.230 (0.230)0.266 (0.264)
G300.704 (0.704)0.503 (0.481)0.146 (0.147)0.124 (0.120)0.189 (0.189)0.234 (0.232)
G320.799 (0.739)0.489 (0.473)0.154 (0.137)0.087 (0.079)0.202 (0.184)0.220 (0.201)
mean 0.826 (0.796) 0.515 (0.505) 0.158 (0.153) 0.154 (0.130) 0.209 (0.202) 0.268 (0.247)
IIIAG040.885 (0.884)0.530 (0.540)0.120 (0.110)0.090 (0.088)0.188 (0.183)0.196 (0.194)
G110.807 (0.834)0.444 (0.461)0.134 (0.131)0.088 (0.086)0.186 (0.187)0.202 (0.203)
G141.001 (1.011)0.593 (0.569)0.125 (0.131)0.080 (0.080)0.207 (0.210)0.215 (0.217)
G181.006 (1.035)0.741 (0.706)0.145 (0.137)0.086 (0.082)0.228 (0.224)0.238 (0.232)
G230.875 (0.904)0.605 (0.627)0.138 (0.129)0.090 (0.087)0.204 (0.202)0.214 (0.211)
G280.952 (0.925)0.501 (0.509)0.119 (0.125)0.101 (0.104)0.193 (0.194)0.212 (0.212)
mean 0.921 (0.932) 0.569 (0.569) 0.130 (0.127) 0.089 (0.088) 0.201 (0.200) 0.213 (0.212)
Total mean 0.874 (0.867) 0.535 (0.530) 0.141 (0.138) 0.148 (0.135) 0.203 (0.199) 0.248 (0.236)
), ArticleFig(id=1239265688536281526, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=CN, label=表3, caption=

CNAV广播星历精度指标RMS

, figureFileSmall=null, figureFileBig=null, tableContent=
BLOCKPRN△A/m△C/m△R/m△T/mSISRE(orb) /mSISRE/m
IIR-MG050.799 (0.811)0.475 (0.486)0.149 (0.150)0.203 (0.195)0.197 (0.199)0.228 (0.222)
G071.025 (1.065)0.710 (0.695)0.122 (0.121)0.218 (0.213)0.214 (0.217)0.289 (0.286)
G121.049 (1.067)0.535 (0.543)0.136 (0.137)0.156 (0.159)0.215 (0.217)0.228 (0.231)
G150.840 (0.836)0.560 (0.562)0.101 (0.094)0.137 (0.135)0.175 (0.171)0.202 (0.200)
G171.042 (1.026)0.559 (0.536)0.136 (0.133)0.225 (0.204)0.215 (0.211)0.285 (0.265)
G290.798 (0.802)0.412 (0.415)0.120 (0.117)0.212 (0.206)0.174 (0.173)0.253 (0.247)
G310.826 (0.844)0.513 (0.506)0.099 (0.100)0.175 (0.170)0.170 (0.171)0.233 (0.230)
mean 0.911 (0.922) 0.538 (0.535) 0.123 (0.122) 0.189 (0.183) 0.194 (0.194) 0.245 (0.240)
IIFG030.809 (0.819)0.481 (0.476)0.161 (0.155)0.259 (0.245)0.207 (0.204)0.335 (0.321)
G060.815 (0.786)0.447 (0.456)0.168 (0.171)0.113 (0.112)0.212 (0.212)0.248 (0.248)
G080.855 (0.804)0.606 (0.586)0.167 (0.146)0.291 (0.154)0.222 (0.202)0.366 (0.257)
G090.652 (0.632)0.354 (0.341)0.152 (0.135)0.101 (0.101)0.183 (0.167)0.212 (0.200)
G100.996 (0.959)0.723 (0.724)0.173 (0.164)0.266 (0.163)0.244 (0.235)0.362 (0.287)
G240.833 (0.751)0.382 (0.358)0.148 (0.148)0.101 (0.098)0.195 (0.187)0.228 (0.220)
G250.829 (0.782)0.461 (0.448)0.140 (0.148)0.095 (0.095)0.193 (0.194)0.226 (0.228)
G260.788 (0.772)0.543 (0.537)0.177 (0.179)0.139 (0.146)0.221 (0.221)0.254 (0.259)
G271.001 (1.010)0.679 (0.679)0.156 (0.154)0.117 (0.115)0.230 (0.230)0.266 (0.264)
G300.704 (0.704)0.503 (0.481)0.146 (0.147)0.124 (0.120)0.189 (0.189)0.234 (0.232)
G320.799 (0.739)0.489 (0.473)0.154 (0.137)0.087 (0.079)0.202 (0.184)0.220 (0.201)
mean 0.826 (0.796) 0.515 (0.505) 0.158 (0.153) 0.154 (0.130) 0.209 (0.202) 0.268 (0.247)
IIIAG040.885 (0.884)0.530 (0.540)0.120 (0.110)0.090 (0.088)0.188 (0.183)0.196 (0.194)
G110.807 (0.834)0.444 (0.461)0.134 (0.131)0.088 (0.086)0.186 (0.187)0.202 (0.203)
G141.001 (1.011)0.593 (0.569)0.125 (0.131)0.080 (0.080)0.207 (0.210)0.215 (0.217)
G181.006 (1.035)0.741 (0.706)0.145 (0.137)0.086 (0.082)0.228 (0.224)0.238 (0.232)
G230.875 (0.904)0.605 (0.627)0.138 (0.129)0.090 (0.087)0.204 (0.202)0.214 (0.211)
G280.952 (0.925)0.501 (0.509)0.119 (0.125)0.101 (0.104)0.193 (0.194)0.212 (0.212)
mean 0.921 (0.932) 0.569 (0.569) 0.130 (0.127) 0.089 (0.088) 0.201 (0.200) 0.213 (0.212)
Total mean 0.874 (0.867) 0.535 (0.530) 0.141 (0.138) 0.148 (0.135) 0.203 (0.199) 0.248 (0.236)
), ArticleFig(id=1239265688645333437, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=EN, label=Table 4, caption=

Orbit determination model configuration

, figureFileSmall=null, figureFileBig=null, tableContent=
模型/参数设置
观测模型L1/L2 P(Y)无电离层组合，30 s采样
GNSS星历LNAV/CNAV
重力场模型EIGEN-6C4 70×70
三体引力解析公式计算日月位置
固体潮k2固体潮模型
大气阻力Harris-Priester静态密度模型，估计阻力系数
太阳光压球模型，估计光压系数
经验加速度一阶高斯马尔可夫过程
估计器扩展卡尔曼滤波
), ArticleFig(id=1239265688754385349, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=CN, label=表4, caption=

定轨模型配置

, figureFileSmall=null, figureFileBig=null, tableContent=
模型/参数设置
观测模型L1/L2 P(Y)无电离层组合，30 s采样
GNSS星历LNAV/CNAV
重力场模型EIGEN-6C4 70×70
三体引力解析公式计算日月位置
固体潮k2固体潮模型
大气阻力Harris-Priester静态密度模型，估计阻力系数
太阳光压球模型，估计光压系数
经验加速度一阶高斯马尔可夫过程
估计器扩展卡尔曼滤波
), ArticleFig(id=1239265688846660043, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=EN, label=Table 5, caption=

Ephemeris determination accuracy statistics

, figureFileSmall=null, figureFileBig=null, tableContent=
年积日星历SISRE/cm
94~100LNAV24.9
CNAV23.1
114~120LNAV25.5
CNAV23.9
), ArticleFig(id=1239265688943129041, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=CN, label=表5, caption=

星历精度统计

, figureFileSmall=null, figureFileBig=null, tableContent=
年积日星历SISRE/cm
94~100LNAV24.9
CNAV23.1
114~120LNAV25.5
CNAV23.9
), ArticleFig(id=1239265689043792344, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=EN, label=Table 6, caption=

Orbit determination accuracy statistics

, figureFileSmall=null, figureFileBig=null, tableContent=
年积日星历A/cmC/cmR/cm3D/cm
94~100LNAV17.49.48.921.6
CNAV16.69.08.620.8
114~120LNAV19.99.014.326.1
CNAV19.28.914.025.4
), ArticleFig(id=1239265689152844251, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165056127135873, language=CN, label=表6, caption=

定轨精度统计

, figureFileSmall=null, figureFileBig=null, tableContent=
年积日星历A/cmC/cmR/cm3D/cm
94~100LNAV17.49.48.921.6
CNAV16.69.08.620.8
114~120LNAV19.99.014.326.1
CNAV19.28.914.025.4
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GPS LNAV与CNAV广播星历精度对比与验证
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高翠 1, 2 , 裴炳南 1, 2
遥测遥控 | 导航技术专栏 2025,46(5): 109-118
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遥测遥控 | 导航技术专栏 2025, 46(5): 109-118
GPS LNAV与CNAV广播星历精度对比与验证
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高翠1, 2, 裴炳南1, 2
作者信息
  • 1泉州信息工程学院 泉州 362000
  • 2现代通信与北斗定位技术福建省高校重点实验室 泉州 362000

    • 高翠　1996年生，硕士，助教。

    裴炳南　1956年生，教授，博士生导师。

GPS LNAV and CNAV Broadcast Ephemerides Accuracy Comparison and Validation
Cui GAO1, 2, Bingnan PEI1, 2
Affiliations
  • 1.Quanzhou University of Information Engineering, Quanzhou 362000, China
  • 2.Fujian Key Laboratory of the Modern Communication and Beidou Positioning Technology in Universities, Quanzhou 362000, China
出版时间: 2025-09-15 doi: 10.12347/j.ycyk.20250804001
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摘要
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为了系统评估GPS（全球定位系统）系统LNAV（遗留导航电文）与CNAV（民用导航电文）广播星历的精度，并验证其在实时应用中的性能，本研究基于2024全年GNSS（全球导航卫星系统）广播与精密星历开展精度对比分析，并结合LEO实时定轨实验进行验证。选取2024年全年GNSS广播星历与精密星历数据，统计分析不同卫星型号和导航电文类型的星历精度。同时，利用GRACE-FO C星（重力恢复与气候实验后续任务C星）的星载GPS观测数据开展缩减动力学实时定轨实验，评估不同广播星历对轨道精度的影响。研究表明：不同卫星型号的广播星历精度存在显著差异，其中BLOCK IIIA（GPS卫星型号）卫星表现最佳，BLOCK IIF最差。2024年G08和G10完成钟源切换后LNAV与CNAV广播星历的全星座SISRE（空间信号测距误差）均值分别为25.5 cm和23.8 cm，较2021年LNAV星历的37.0 cm显著降低。LEO（低地球轨道）实时定轨实验结果显示：相较于LNAV广播星历，采用CNAV广播星历A、C、R及三维方向精度均有提升，三维轨道误差最大提升0.8 cm，轨道精度平均提高约3.2%，进一步验证了CNAV在实时应用中的优势。综合星历精度与LEO实时定轨验证结果，CNAV广播星历整体表现优于LNAV。随着BLOCK IIR卫星逐步退役及BLOCK IIIA卫星的持续部署，预计未来基于CNAV广播星历的导航、定位与授时服务将实现更高精度，进一步增强其在实时定位与科学应用中的价值。

广播星历  /  遗留导航电文  /  民用导航电文  /  空间信号测距误差  /  低轨卫星  /  实时定轨

To systematically evaluate the accuracy of GPS LNAV and CNAV broadcast ephemerides and verify their performance in real-time applications, this study conducted a year-long accuracy assessment for 2024 based on GNSS broadcast and precise ephemerides, complemented by validation through real-time orbit determination (RTOD) experiments using LEO satellites. Broadcast and precise ephemerides from 2024 were used to perform statistical analyses of ephemeris accuracy across different satellite blocks and navigation message types. In addition, reduced-dynamic RTOD experiments were carried out using onboard GPS observations from the GRACE-FO C satellite to assess the impact of different broadcast ephemerides on orbit accuracy. The results show that the accuracy of broadcast ephemerides varies significantly among satellite blocks, with BLOCK IIIA performing the best and BLOCK IIF performing the worst. After the clock source switch on G08 and G10 in 2024, the constellation-averaged SISRE for LNAV and CNAV broadcast ephemerides reached 25.5 cm and 23.8 cm, respectively, representing a substantial improvement compared to the LNAV SISRE of 37.0 cm in 2021. The LEO RTOD experiments further demonstrated that, compared to LNAV, CNAV provides improved accuracy in the along-track, cross-track, radial, and 3D directions, with a maximum reduction in 3D orbit error of 0.8 cm and an average improvement of about 3.2%, thereby confirming the advantage of CNAV in real-time applications. Overall, both the ephemeris accuracy statistics and LEO RTOD results consistently indicate that CNAV broadcast ephemerides outperform LNAV. With the gradual retirement of BLOCK IIR satellites and the continued deployment of BLOCK IIIA satellites, navigation, positioning, and timing services based on CNAV broadcast ephemerides are expected to achieve even higher accuracy, further enhancing their value for real-time positioning and scientific applications.

Broadcast ephemerides  /  LNAV  /  CNAV  /  SISRE  /  LEO  /  Real-time orbit determination
高翠, 裴炳南. GPS LNAV与CNAV广播星历精度对比与验证. 遥测遥控, 2025 , 46 (5) : 109 -118 . DOI: 10.12347/j.ycyk.20250804001
Cui GAO, Bingnan PEI. GPS LNAV and CNAV Broadcast Ephemerides Accuracy Comparison and Validation[J]. Journal of Telemetry, Tracking and Command, 2025 , 46 (5) : 109 -118 . DOI: 10.12347/j.ycyk.20250804001
正文
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0　引言
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全球定位系统(Global Positioning System, GPS)作为最早投入运行并持续服务至今的全球导航卫星系统，在全球范围内提供连续、可靠的定位、导航和授时服务[1]。由于广播星历可实时获取而被广泛应用于上述服务，广播星历所提供的卫星轨道和钟差信息是用户进行导航定位与授时的关键数据，其精度直接影响标准单点定位、精密单点定位和低轨卫星实时定轨等应用的性能[2]。因此，进行广播星历精度评估具有重要的现实意义。
自GPS投入运行以来，通过L1C/A信号播发的遗留导航电文(Legacy Navigation Message，LNAV)一直为导航用户提供广播星历与钟差信息[3]。然而，随着用户对导航精度与灵活性需求的不断增长，2014年GPS系统正式引入了新的民用导航电文(Civil Navigation Message, CNAV)并在Block IIR-M与IIF卫星的L2C与L5上频点播发[4]。与LNAV相比，CNAV包含的内容更为丰富，结构更为合理，卫星位置的计算方法也更为严密，主要体现在：一是新增两个轨道参数(半长轴变化率和平均角速度)，二是增加四个信号间改正参数，用于刻画L1C/A、L2C、L5I5和L5Q5信号与L1P(Y)信号之间的偏差。前者能够为用户提供更加精确的卫星位置，后者使得利用L1C/A与L2C(或L5)新型双频民用信号开展定位成为可能[5]。
已有研究对LNAV精度进行了长期评估。文献[6]基于GPS系统25年间的数据表明，LNAV广播星历精度逐年提升，2019年轨道误差均方根(Root Mean Square, RMS)优于0.3 m，空间信号测距误差(Signal-In-Space Ranging Error, SISRE)的RMS优于0.6 m。随着GPS Block Ⅲ卫星的发射及星历精度提升计划的推进，文献[7]对2021年11-12月的GPS LNAV广播星历评估结果表明：轨道误差的RMS优于0.25 m，SISRE的RMS优于0.37 m，其中Block Ⅲ卫星轨道与钟差精度显著优于其他类型卫星。文献[8]在GPS SISRE评估中充分考虑了2021年3月28日GPS地面运行中心在生成BLOCKⅡ系列导航星历时，其采用的卫星天线模型由制造商模型切换为IGS(国际GNSS服务)模型。实验结果显示BLOCK IIR、IIF和IIIA系列卫星的SISRE分别约为0.50 m、0.46 m和0.34 m，全星座均值为0.44 m。文献[9]进一步分析了2022年7月至2024年2月期间不同类型与代际卫星的精度差异，并探讨了离群卫星对整体统计值的影响机制。关于CNAV精度，2013年6月首次开展的测试显示其SISRE为0.58 m，而LNAV为0.48 m[10,11]。文献[3]对2014年4月至2015年1月的CNAV广播星历性能评估表明，SISRE约为0.6 m，与相同卫星的LNAV基本一致。文献[5]对2016年1月至2018年3月的CNAV/LNAV性能进行评估，结果显示二者性能相当，且CNAV/LNAV SISRE和仅轨道SISRE分别约为0.5 m和0.3 m，较2014-2015年有所提升。
从现有研究可以看出，关于GPS广播星历的精度评估研究，多集中于LNAV，或是针对CNAV的实验数据时间已较为久远。随着GPS系统的持续发展与完善，尤其是精度提升计划的实施及Block Ⅲ系列卫星的入轨，有必要对近年来广播星历的轨道与钟差精度开展系统评估。本文对2024全年GPS系统的LNAV与CNAV广播星历精度进行系统性分析。利用广播星历计算得到的位置与钟差，与事后精密星历提供的相应结果进行差分，从而评估多个精度指标[12−14]。同时，引入LEO实时定轨精度作为独立验证手段，以进一步检验CNAV与LNAV的性能差异。全文结构安排如下：第一部分为引言；第二部分介绍广播星历的评估方法与精度指标；第三部分展示实验结果并进行分析；最后对研究结论进行总结。本研究不仅可为LNAV/CNAV星历在定位、导航与授时中的推广应用提供技术与方法支撑，还能为LNAV/CNAV广播星历的运行性能提供实证数据。
1　精度评估方法与指标
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1.1　实验数据
本文使用的实验数据包括多模GNSS实验以RINEX 4.00(与接收机无关的数据交换格式)存储的多系统混合广播星历数据文件[15]和欧洲定轨中心(Center for Orbit Determination in Europe, CODE)发布的多系统最终事后精密轨道与钟差数据文件[16,17]。数据时间跨度为2024年1月1日至2024年12月31日，共计366天。CODE的精密轨道文件以5 min的时间间隔给出一颗GPS卫星质心在IGS 20参考框架下的三维坐标，CODE的精密轨道文件以30 s的时间间隔给出一颗GPS卫星的钟差值。为了避免插值导致精密产品精度损失，本文以5 min的间隔进行广播星历精度评估。由于精密星历、精密钟差和广播星历可能会存在质量问题，为了避免粗差对广播星历精度评估的影响，本文采取如下质量控制策略：一是剔除广播星历标记为不健康的卫星；二是以10 m作为广播轨道与精密轨道各个方向以及精密钟差与广播钟差之间差异的阈值。
1.2　系统误差处理
1.2.1　参考框架
GPS广播星历给出的卫星位置以WGS84(世界大地坐标系(1984年))作为参考框架[18]，而CODE给出的精密轨道以IGS 20作为参考框架[19]，上述两个参考框架之间的差异最大值在厘米量级，远优于广播轨道精度，因此在进行广播轨道精度评估时不再考虑参考框架之间的差异带来的影响[7,13]。
1.2.2　天线相位中心改正
GPS广播星历给出的卫星位置是卫星天线相位中心的位置，而CODE给出的精密轨道的参考点是卫星质心[20−23]。因此，在进行广播轨道精度评估时需要利用卫星天线的PCO(相位中心偏差)数据，将广播星历的相位中心位置改正到位置质心以消除参考点的不一致性，再进行广播轨道精度评估，可通过以下公式进行相位中心到质心的转换：
式中，、分别表示广播星历计算的卫星质心和天线相位中心位置，As为卫星星体系到地固系的转换矩阵，为星体系下质心到天线相
位中心的位置矢量。
1.2.3　时间尺度
由于广播星历和精密星历钟差产品对于时间尺度的实现存在一定差异，因此在评估广播钟差精度时还需要考虑两种钟差产品时间尺度不同所引起的系统性偏差。该系统性偏差一般大于广播星历钟差的精度，且具有大小随历元变化但对同一系统所有卫星产生相同的影响特点[7,13]。根据上述特点，可采用二次差法获得该系统偏差，并对钟差误差加以改正，该系统偏差改正如下式所示：
式中，、分别表示第i颗卫星的广播钟差和精密钟差，ΔTi为该历元第i颗卫星广播钟差的误差，n为该历元下GPS系统的卫星数目，u为整个系统同一历元下广播星历计算的钟差与精密钟差的差值均值，即系统偏差。
此外，每颗卫星仍然包含一个均值偏差。为了消除这些偏差对钟差评估的影响，采用单颗星一日内广播星历与精密星历钟差之差的均值为基准，将不同历元的钟差与该均值作差，以此来消除该星钟差的系统性偏差[7]。
1.3　精度指标
广播星历的精度评估除了评估广播轨道与广播钟差精度之外，还需要进行轨道误差与钟差误差对测距误差的综合影响即SISRE的评估。广播轨道误差评估时，需要将得到的地固系下的位置误差投影到卫星轨道系的切向(Along-track)、法向(Cross-track)、径向(Radial)方向上，以更加清晰地展示广播轨道的误差特性。
广播星历的SISRE有如下两个指标：一种是仅考虑卫星轨道误差对用户空间测距的贡献，其表达式如下[14]：
式中，ΔA、ΔC、ΔR分别表示广播轨道误差在切向、法向和径向的分量，wR、代表权重因子，其数值取决于GNSS卫星的高度和截止高度角。本研究中使用的权重因子wR和分别为0.98和1/49[14]。
另一种是同时考虑卫星轨道和钟差误差对用户空间测距的贡献，即综合SISRE，其表达式如下[14]：
式中，ΔT表示以m为单位的广播钟差的误差。
2　实验结果与分析
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2.1　LNAV与CNAV广播星历精度评估与分析
在2024年实验评估期间，GPS星座由四种不同类型的卫星组成，分别为：BLOCK IIR、IIR-M、IIF 和 IIIA，且在实验期间所有卫星均保持稳定，未发生更换。各伪随机噪声码(Pseudorandom Noise, PRN)对应的卫星类型整理见表1。首先，利用一年的实验数据，以5 min间隔计算各历元的LNAV与CNAV广播星历的轨道误差与钟差误差，并统计A、C、R三个方向轨道误差、钟差误差、SISRE(orb)和SISRE的RMS。需要说明的是，由于G02、G13、G16、G19-G22为Block IIR型卫星，不能传输CNAV广播星历，因此不对这7颗卫星的CNAV精度进行评估。此外，G01处于非健康状态，也未纳入广播星历精度评估。图1与图2给出了LNAV与CNAV广播星历在各个历元A、C、R三个方向的轨道误差、钟差误差、SISRE(orb)和SISRE时间序列，表2与表3则分别列出了一年期间各精度指标的RMS统计结果，其中每列括号内的数值表示在扣除年积日1-60天数据后的RMS值。
从表2和表3的统计结果来看，无论是LNAV还是CNAV广播星历，轨道误差均呈现出切向误差最大、径向误差最小的特点，其中切向误差均值约为0.9 m，而径向误差仅约0.2 m。这主要归因于广播星历轨道精度受GPS卫星动力学模型误差的主导影响，通常径向动力学模型精度较高，而切向方向的精度相对较低。进一步对比LNAV与CNAV广播星历轨道误差可发现，得益于CNAV新增的两个轨道参数，所有卫星在A、C、R三个方向的误差以及SISRE(orb)均优于LNAV广播星历。具体而言，CNAV广播星历在A方向的精度提升最大，可达8 cm；在C方向最大提升3 cm；在R方向最大提升2 cm。同时，反映轨道误差对测距误差影响的SISRE(orb)最大提升2 cm。上述结果有力地证明了当前CNAV广播星历的轨道精度优于LNAV广播星历。
从图1和图2的钟差误差时间序列可以观察到，无论是LNAV还是CNAV广播星历，G08与G10在年积日1~60天内均表现出钟差误差较大，随后逐渐减小的现象。这主要与GPS卫星所搭载的原子钟型号有关。IIF型卫星除铷原子钟外，还额外配备了铯原子钟[24,25]。在2024年初，航天器编号为G072和G073的两颗卫星使用铯原子钟作为原子频率标准，对应的PRN分别为G08和G10。2024年2月9日，G073率先将其主钟源从铯钟切换为铷钟；随后在2月21/22日午夜前后，G072也完成了同样的切换。虽然这些钟源转换未以官方公告形式发布，但GPS系统通过NAVSTAR(导航星)通告告知用户，并在铷钟启用后的约十天内将两颗卫星标记为不可用[26,27]。本文通过对广播星历钟差精度的评估，验证了这一系列钟源转换的发生。对比G08与G10一年数据及扣除年积日1~60天数据后的精度指标可见：对于LNAV广播星历，钟差误差分别由30.0 cm、27.2 cm降至16.3 cm、17.0 cm，SISRE则由38.5 cm、37.6 cm降至27.8 cm、30.2 cm；对于CNAV广播星历，钟差误差分别由29.1 cm、26.6 cm降至15.4 cm、16.3 cm，SISRE则由36.6 cm、36.2 cm降至25.7 cm、28.7 cm。值得注意的是，相较于钟差精度最高达13.7 cm的提升幅度，SISRE(orb)的改善仅约2 cm。这一结果表明，G08和G10广播星历的精度提升主要归因于钟差精度的改善。
从表2和表3的统计结果可以看出，无论是LNAV还是CNAV广播星历，各型号卫星的钟差精度由高到低依次为：BLOCK IIIA > BLOCK IIF >BLOCK IIR > BLOCK IIR-M。其中，BLOCK IIIA型卫星因搭载了频率更加稳定的铷原子钟，其钟差精度约为最差的BLOCK IIR-M型的两倍。进一步对比LNAV与CNAV广播星历的钟差误差可以发现，所有卫星的CNAV广播星历钟差误差均小于LNAV广播星历，其中CNAV广播星历钟差精度的最大提升可达2 cm。这表明CNAV广播星历不仅在轨道精度上优于LNAV广播星历，在钟差精度上同样具有优势。反映轨道与钟差对测距误差综合影响的SISRE结果也进一步印证了这一结论：所有卫星的CNAV广播星历SISRE均优于LNAV广播星历，其中SISRE精度最大提升可达3 cm。对比一年数据与剔除年积日1~60天数据后的结果可见，BLOCK IIF型卫星的平均钟差误差在LNAV广播星历中由16.5 cm降至14.2 cm，全星座的平均钟差误差则由16.3 cm降至15.2 cm；在CNAV广播星历中，平均钟差误差由15.4 cm降至13.0 cm，全星座的平均钟差误差由14.8 cm降至13.5 cm。钟差精度的整体提升主要得益于G08与G10的钟源切换。
对比不同类型的卫星可以看出：无论是LNAV还是CNAV广播星历，BLOCK IIIA型的轨道、钟差、SISRE精度均优于所有Ⅱ型卫星，主要是由于最新发射的IIIA型卫星配备了频率更加稳定的原子钟，并采用了更为成熟的定轨和预报技术，其他研究文献亦得出了相同的结论[7]。进一步对比LNAV与CNAV广播星历可以看出：不论是全年精度指标还是扣除年积日1~60天后的精度指标，CNAV在轨道、钟差和SISRE精度上不论是全星座均值还是相同卫星类型的均值均优于LNAV，表明当前CNAV广播星历的性能已超越LNAV广播星历，而非早期研究中得出的“CNAV与LNAV精度相当或稍差”的结论。本文最终结果显示，LNAV广播星历的全星座全年SISRE平均值为26.3 cm、扣除年积日1~60天数据后的SISRE平均值为25.5 cm，CNAV广播星历的全星座全年平均值为24.8 cm、扣除年积日1~60天数据后的SISRE平均值为23.6 cm。与2021年LNAV广播星历37.0 cm的SISRE相比[7]，精度已显著提升。这一进步主要得益于GPS系统实施的星载原子钟切换以及缩短导航数据上传平均时间间隔的精度提升计划。
2.2　LEO实时定轨精度验证
在前一小节中，通过将广播星历与精密星历进行对比，系统评估了LNAV与CNAV广播星历的精度。结果表明，CNAV在各项精度指标上均优于LNAV，凸显其在轨道与钟差精度方面的优势。为进一步验证上述结论，本节将以广播星历在LEO实时定轨中的应用为切入点，综合评估CNAV相较于LNAV在LEO实时定轨场景中的性能提升。
本节实验选取GRACE-FO C星2024年4月3日至9日(年积日94~100)和4月23日至29日(年积日114~120)共计两周的星载GPS观测数据，采用缩减动力学方法开展实时定轨，具体模型配置见表4。为评估LNAV与CNAV广播星历对定轨精度的影响，实验中仅更换不同类型的广播星历，其他参数保持一致。需要说明的是，在采用CNAV广播星历进行定轨时，由于BLOCK IIR卫星未提供CNAV广播星历，为保证各历元具备足够的可见卫星数量，BLOCK IIR卫星仍使用LNAV广播星历进行解算。为了验证两周定轨区间内的LNAV与CNAV星历质量是否与61~365天的统计结果保持一致，我们分别统计了94~100和114~120两个时间段内LNAV与CNAV广播星历SISRE的均值，结果如表5所示。对于LNAV，两个时间段的SISRE均值分别为24.9 cm和25.5 cm；对于CNAV，分别为23.1 cm和23.9 cm。与61~365天内LNAV和CNAV的均值(25.5 cm和23.6 cm)相比，二者基本一致。
在LNAV与CNAV广播星历支持下，各历元A、C、R方向的轨道误差如图3和图4所示，实时定轨精度的RMS统计结果见表6。由表6可知，相较于LNAV广播星历，采用CNAV广播星历在两个时间段内及三维方向均实现精度提升，三维轨道误差最大提升0.8 cm，两个时间段精度平均提高约3.2%。通过LEO实时定轨精度验证，进一步证实了CNAV广播星历在性能上的优势。随着BLOCK IIR卫星逐步退役及新一代BLOCK IIIA卫星的部署，预计未来基于CNAV广播星历的导航、定位与授时服务将获得更显著的精度提升。
3　结论
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通过对2024年全年GNSS广播星历与精密星历的系统对比，并结合LEO实时定轨精度验证实验，本研究全面评估了GPS系统中LNAV与CNAV广播星历的精度，主要结论如下：
①无论LNAV还是CNAV广播星历，不同卫星型号之间的精度差异均较为显著，整体表现为BLOCK IIIA最高，IIF最低。具体而言，LNAV广播星历中，BLOCK IIIA卫星全年与扣除年积日1-60数据后的SISRE均值均为23.0 cm，优于IIR的25.4 cm、IIR-M的26.0 cm(26.5 cm)与IIF的28.6 cm(26.6 cm)，全星座均值为26.3 cm(25.5 cm)；CNAV广播星历中，BLOCK IIIA卫星的SISRE均值进一步降低至21.3 cm (21.2 cm)，IIR-M与IIF卫星分别为24.5 cm(24.0 cm)和26.8 cm (24.7 cm)，全星座均值为24.8 cm(23.6 cm)，整体精度优于LNAV。
②与2021年LNAV广播星历37.0 cm的SISRE评估结果相比，G08和G10完成钟源切换以后LNAV与CNAV广播星历的平均SISRE分别降至25.5 cm和23.6 cm，表明GPS系统广播星历精度取得显著进步。这一改进主要得益于星载原子钟的切换和导航数据上传时间间隔的缩短。本研究对广播星历钟差精度的评估，进一步验证了这一系列钟源转换的发生与实际成效。
③LEO实时定轨实验表明：相较于LNAV广播星历，采用CNAV广播星历在两个时间段内A、C、R及三维方向精度均有提升，三维轨道误差最大提升0.8 cm，两个时间段轨道精度平均提高约3.2%，进一步证实了CNAV广播星历在实时应用中的优势。随着BLOCK IIR卫星逐步退役和新一代BLOCK IIIA卫星的持续部署，预计未来基于CNAV广播星历的导航、定位与授时服务将获得更显著的精度提升。
基金
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  • 福建省自然科学基金(2023J011801)
文献
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doi: 10.12347/j.ycyk.20250804001
  • 接收时间：2025-08-04
  • 首发时间：2026-03-13
  • 出版时间：2025-09-15
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  • 收稿日期：2025-08-04
  • 修回日期：2025-08-24
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福建省自然科学基金(2023J011801)
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    1泉州信息工程学院 泉州 362000
    2现代通信与北斗定位技术福建省高校重点实验室 泉州 362000
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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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