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Article(id=1322941044941267184, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322940829001724376, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.05.261, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1717084800000, receivedDateStr=2024-05-31, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793343324169, onlineDateStr=2026-10-30, pubDate=1747238400000, pubDateStr=2025-05-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793343324169, onlineIssueDateStr=2026-10-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793343324169, creator=13701087609, updateTime=1793343324169, updator=13701087609, issue=Issue{id=1322940829001724376, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='5', pageStart='441', pageEnd='550', issueExtLink='null', onlineDate='null', pubDate='1747238400000', pubDateStr='2025-05-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793343272686, creator='13701087609', updateTime=1793343272686, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=494, endPage=499, ext={EN=ArticleExt(id=1322941046677709041, articleId=1322941044941267184, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Reduced Dynamic Precise Orbit Determination and Orbital Extrapolation of LEO Satellites under Different Gravity Field Models, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

This paper analyzes the orbit determination accuracy and orbit extrapolation accuracy under different gravity field models and finds that the accuracy is higher when the gravity field model order is 100 and 150 compared to when it is 50. In the reduced dynamic orbit determination of GRACE-C and GRACE-D, the 3D directional orbit determination accuracy of EGM2008 and Tongji-Grace02k can reach up to 22.6 mm and 24.0 mm, respectively, both of these gravity field models have better orbit determination accuracy than ITG-Grace03.In orbit extrapolation, Tongji-Grace02k has the highest accuracy, capable of reaching the sub-decimeter level, followed by EGM2008, while ITG-Grace03 has the lowest accuracy, both in decimeter level. Optimizing the random impulse parameters can improve the orbit extrapolation accuracy of the three gravity fields, with the optimization effect being more significant when the model order is 100 and 150 compared to when it is 50.

, authors=Zhenyu LUO1, Chunhua JIANG1, 2, 3, Haiyi FAN1, Huizhong ZHU1, authorsList=Zhenyu LUO, Chunhua JIANG, Haiyi FAN, Huizhong ZHU, authorCompany=null, correspAuthors=null, authorNote=

LUO Zhenyu, postgraduate, majors in LEO satellites precise orbit determination and clock bias estimation, E-mail:

, 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=1322941047717896442, articleId=1322941044941267184, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=不同重力场模型下低轨卫星的简化动力学定轨与轨道外推, columnId=1322506169105633839, journalTitle=大地测量与地球动力学, columnName=现代大地测量, runingTitle=null, highlight=null, articleAbstract=

分析在不同重力场模型下的定轨精度与轨道外推精度发现, 重力场模型阶数为100与150时的定轨精度和轨道外推精度均高于50阶重力场模型的结果。在GRACE-C和GRACE-D简化动力学定轨中, EGM2008与Tongji-Grace02k的3D方向定轨精度最高可达22.6 mm和24.0 mm, 这2种重力场模型定轨精度均优于ITG-Grace03。在轨道外推中, Tongji-Grace02k精度最高, 能达到亚dm级别; 其次是EGM2008, ITG-Grace03精度最低, 二者均在dm级。通过优化随机脉冲参数, 可以提升3种重力场的轨道外推精度, 模型阶数为100与150时的优化效果比阶数为50时明显。

, authors=罗振宇1, 蒋春华1, 2, 3, 范海怡1, 祝会忠1, authorsList=罗振宇, 蒋春华, 范海怡, 祝会忠, authorCompany=null, correspAuthors=null, authorNote=

罗振宇, 硕士生, 主要从事低轨(LEO)卫星精密轨道确定和时钟偏差估计研究, E-mail:

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LUO Zhenyu, postgraduate, majors in LEO satellites precise orbit determination and clock bias estimation, E-mail:

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LUO Zhenyu, postgraduate, majors in LEO satellites precise orbit determination and clock bias estimation, E-mail:

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罗振宇, 硕士生, 主要从事低轨(LEO)卫星精密轨道确定和时钟偏差估计研究, E-mail:

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罗振宇, 硕士生, 主要从事低轨(LEO)卫星精密轨道确定和时钟偏差估计研究, E-mail:

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journalId=1281212831689347082, articleId=1322941044941267184, language=EN, label=Tab. 1, caption=

Low earth orbit satellite data calculation strategy

, figureFileSmall=null, figureFileBig=null, tableContent=
类别 参数 策略
观测值处理策略 观测类型 非差无电离层组合观测
采样间隔 10 s
截至高度角 1°
GNSS卫星天线相位改正PCV 采用igs14.atx天线文件改正
LEO卫星天线相位改正PCV 采用模型改正
模糊度参数 浮点解
积分步长 5 s
摄动力模型 低轨卫星姿态 使用姿态文件
地球重力场 EGM2008 Tongji-Grace02k ITG-Grace03
三体摄动 JPL DE405
海洋潮汐 FES2004
相对论效应 IERS2010
固体潮、极潮 IERS2010
大气密度模型 DTM 94
随机脉冲 A、C、R三个方向，每90 min一组
), ArticleFig(id=1322941052545540397, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322941044941267184, language=CN, label=表1, caption=

低轨卫星数据解算策略

, figureFileSmall=null, figureFileBig=null, tableContent=
类别 参数 策略
观测值处理策略 观测类型 非差无电离层组合观测
采样间隔 10 s
截至高度角 1°
GNSS卫星天线相位改正PCV 采用igs14.atx天线文件改正
LEO卫星天线相位改正PCV 采用模型改正
模糊度参数 浮点解
积分步长 5 s
摄动力模型 低轨卫星姿态 使用姿态文件
地球重力场 EGM2008 Tongji-Grace02k ITG-Grace03
三体摄动 JPL DE405
海洋潮汐 FES2004
相对论效应 IERS2010
固体潮、极潮 IERS2010
大气密度模型 DTM 94
随机脉冲 A、C、R三个方向，每90 min一组
), ArticleFig(id=1322941052688146734, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322941044941267184, language=EN, label=Tab. 2, caption=

The orbit deternination accuracy of GRACE-C satellites in the A, C, R and 3D directions using different gravity field models

, figureFileSmall=null, figureFileBig=null, tableContent=
方向 EGM2008/mm Tongji-Grace02k/mm ITG-Grace03/mm
50阶 100阶 150阶 50阶 100阶 150阶 50阶 100阶 150阶
A 105.6 29.8 29.7 96.8 30.6 29.9 96.5 32.3 32.5
C 110.0 15.2 14.9 100.0 14.9 12.3 104.6 15.4 15.3
R 79.6 20.9 20.9 73.6 26.2 26.1 79.6 33.5 33.6
3D 99.3 22.8 22.6 90.9 24.8 24.0 94.3 28.4 28.4
), ArticleFig(id=1322941052755255599, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322941044941267184, language=CN, label=表2, caption=

GRACE-C卫星在使用不同重力场模型时A、C、R及3D方向定轨精度

, figureFileSmall=null, figureFileBig=null, tableContent=
方向 EGM2008/mm Tongji-Grace02k/mm ITG-Grace03/mm
50阶 100阶 150阶 50阶 100阶 150阶 50阶 100阶 150阶
A 105.6 29.8 29.7 96.8 30.6 29.9 96.5 32.3 32.5
C 110.0 15.2 14.9 100.0 14.9 12.3 104.6 15.4 15.3
R 79.6 20.9 20.9 73.6 26.2 26.1 79.6 33.5 33.6
3D 99.3 22.8 22.6 90.9 24.8 24.0 94.3 28.4 28.4
), ArticleFig(id=1322941052839141680, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322941044941267184, language=EN, label=Tab. 3, caption=

The orbit deternination accuracy of GRACE-D satellites in the A, C, R and 3D directions using different gravity field models

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方向 EGM2008/mm Tongji-Grace02k/mm ITG-Grace03/mm
50阶 100阶 150阶 50阶 100阶 150阶 50阶 100阶 150阶
A 93.6 34.3 34.2 96.5 32.3 31.2 97.7 34.5 34.8
C 109.4 19.1 18.9 101.1 16.5 15.5 105.1 17.7 17.5
R 78.7 32.7 32.7 73.8 31.3 30.5 83.1 34.7 34.8
3D 94.8 29.7 29.6 89.1 27.6 26.7 95.9 30.0 30.2
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GRACE-D卫星在使用不同重力场模型时A、C、R及3D方向定轨精度

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C 109.4 19.1 18.9 101.1 16.5 15.5 105.1 17.7 17.5
R 78.7 32.7 32.7 73.8 31.3 30.5 83.1 34.7 34.8
3D 94.8 29.7 29.6 89.1 27.6 26.7 95.9 30.0 30.2
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不同重力场模型下低轨卫星的简化动力学定轨与轨道外推
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罗振宇 1 , 蒋春华 1, 2, 3 , 范海怡 1 , 祝会忠 1
大地测量与地球动力学 | 现代大地测量 2025,45(5): 494-499
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大地测量与地球动力学 |现代大地测量 2025 , 45 (5) : 494 -499
不同重力场模型下低轨卫星的简化动力学定轨与轨道外推
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罗振宇1 , 蒋春华1, 2, 3, 范海怡1, 祝会忠1
作者信息
  • 1 辽宁工程技术大学测绘与地理科学学院, 辽宁省阜新市玉龙路88号, 123000
  • 2 西安测绘研究所地理信息工程国家重点实验室, 西安市雁塔路中段1号, 710054
  • 3 中国科学院精密测量科学与技术创新研究院大地测量与地球动力学国家重点实验室, 武汉市徐东大街340号, 430077
作者简介:

罗振宇, 硕士生, 主要从事低轨(LEO)卫星精密轨道确定和时钟偏差估计研究, E-mail:

Reduced Dynamic Precise Orbit Determination and Orbital Extrapolation of LEO Satellites under Different Gravity Field Models
Zhenyu LUO1 , Chunhua JIANG1, 2, 3, Haiyi FAN1, Huizhong ZHU1
Affiliations
  • 1 School of Geomatics, Liaoning Technical University, 88 Yulong Road, Fuxin 123000, China
  • 2 State Key Laboratory of Geo-Information Engineering, Xi'an Institute of Surveying and Mapping, 1 Mid-Yanta Road, Xi'an 710054, China
  • 3 State Key Laboratory of Geodesy and Earth's Dynamics, Innovation Academy for Precision Measurement Science and Technology, CAS, 340 Xudong Street, Wuhan 430077, China

    • LUO Zhenyu, postgraduate, majors in LEO satellites precise orbit determination and clock bias estimation, E-mail:

出版时间: 2025-05-15 doi: 10.14075/j.jgg.2024.05.261
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摘要
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分析在不同重力场模型下的定轨精度与轨道外推精度发现, 重力场模型阶数为100与150时的定轨精度和轨道外推精度均高于50阶重力场模型的结果。在GRACE-C和GRACE-D简化动力学定轨中, EGM2008与Tongji-Grace02k的3D方向定轨精度最高可达22.6 mm和24.0 mm, 这2种重力场模型定轨精度均优于ITG-Grace03。在轨道外推中, Tongji-Grace02k精度最高, 能达到亚dm级别; 其次是EGM2008, ITG-Grace03精度最低, 二者均在dm级。通过优化随机脉冲参数, 可以提升3种重力场的轨道外推精度, 模型阶数为100与150时的优化效果比阶数为50时明显。

重力场模型  /  低轨卫星  /  简化动力学定轨  /  轨道外推  /  随机脉冲参数

This paper analyzes the orbit determination accuracy and orbit extrapolation accuracy under different gravity field models and finds that the accuracy is higher when the gravity field model order is 100 and 150 compared to when it is 50. In the reduced dynamic orbit determination of GRACE-C and GRACE-D, the 3D directional orbit determination accuracy of EGM2008 and Tongji-Grace02k can reach up to 22.6 mm and 24.0 mm, respectively, both of these gravity field models have better orbit determination accuracy than ITG-Grace03.In orbit extrapolation, Tongji-Grace02k has the highest accuracy, capable of reaching the sub-decimeter level, followed by EGM2008, while ITG-Grace03 has the lowest accuracy, both in decimeter level. Optimizing the random impulse parameters can improve the orbit extrapolation accuracy of the three gravity fields, with the optimization effect being more significant when the model order is 100 and 150 compared to when it is 50.

gravity field model  /  LEO satellites  /  reduced dynamic precise orbit determination  /  orbit extrapolation  /  random pulse parameters
罗振宇, 蒋春华, 范海怡, 祝会忠. 不同重力场模型下低轨卫星的简化动力学定轨与轨道外推. 大地测量与地球动力学, 2025 , 45 (5) : 494 -499 . DOI: 10.14075/j.jgg.2024.05.261
Zhenyu LUO, Chunhua JIANG, Haiyi FAN, Huizhong ZHU. Reduced Dynamic Precise Orbit Determination and Orbital Extrapolation of LEO Satellites under Different Gravity Field Models[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (5) : 494 -499 . DOI: 10.14075/j.jgg.2024.05.261
正文
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低轨(LEO)卫星是指运行高度为500~2 000 km的卫星[1]，近年来，SpaceX、OneWeb、Iridium和Orbcomm等公司发射或计划发射数千颗低地球轨道卫星从而构建低轨增强GNSS(LEO-enhanced GNSS)卫星星座。与GNSS卫星相比，低轨卫星具有更强的信号以及更快的几何变化，将大规模的低轨卫星星座纳入GNSS系统，可降低PDOP(position dilution of precision)，从而实现精密单点定位的瞬间收敛[2-3]，有效提高导航性能。此外在GNSS卫星能见度有限的地区，例如城市峡谷地区，低轨卫星可以在这种深度衰减环境中进行定位[4]。使用低轨卫星进行定位需要获取低轨卫星精确的位置信息，精度最高的方法是使用SLR技术，但SLR对设备需求较高，所以一般使用运动学定轨、动力学定轨及简化动力学定轨获得低轨卫星精确轨道[5-6]。赵齐乐等[7]使用CHAMP星载观测数据进行运动学定轨，能达到cm级精度。李星星等[8]使用FY-3C星载观测BDS/GPS数据进行定轨，双系统融合的低轨卫星定轨精度最高达到1.6 cm。王广哲等[9]通过优化随机脉冲参数与估计天线相位中心，提升低轨卫星简化动力学定轨精度。Zhao等[10]将天平1B卫星的定轨精度提升到mm级别。
对低轨卫星进行动力学定轨时，卫星所受地球引力摄动力会对定轨精度产生较大的影响，其数量级在10-2 m/s2左右[11]。重力场模型是估算地球引力摄动力的主要手段，目前已有学者研究重力场模型对动力学定轨的影响。Wu等[12]和王正涛等[13]研究发现，不同的重力场模型与不同的重力场模型阶次均会对定轨精度产生影响。
本文在不同重力场模型下对GRACE-C与GRACE-D卫星进行简化动力学定轨，重点分析在不同重力场模型下的定轨精度与轨道外推精度，并针对轨道特性优化随机脉冲参数，最后得出结论。
1 低轨卫星轨道解算
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1.1 随机脉冲参数
随机脉冲参数可表达为：
$p_i=a_i \cdot \delta\left(t-t_i\right) \cdot e(t)$
式中，ai为ti时刻的加速度值；e(t)为某一预设方向；δ(t－ti)为狄拉克函数，通过调整狄拉克函数可以改变运动学轨道和动力学轨道的权重，相应的变分方程为：
$\ddot{\boldsymbol{Y}}_{a_i}=\boldsymbol{A} \cdot \boldsymbol{Y}_{a_i}+\delta\left(t-t_i\right) \cdot e(t)$
式中，Yai为初始历元的6个轨道根数偏导数的线性组合；A表示相应的系数阵。
1.2 简化动力学轨道定轨原理
卫星在惯性坐标系下的运动方程表示如下:
$\ddot{\boldsymbol{r}}=-\frac{G M}{R^3} {\boldsymbol{r}}+f\left(t, {\boldsymbol{r}}, \dot{\boldsymbol{r}}, q_1, q_2, \cdots, q_d\right)$
式中，$ \boldsymbol{r}, \dot{\boldsymbol{r}}, \ddot{\boldsymbol{r}}$分别为卫星在惯性坐标系下的位置、速度和加速度向量；G为引力常数；M为地球质量；R为卫星到地心的距离；q1, q2, …, qd为未知的摄动力参数；f(t, $ \dot{\boldsymbol{r}}, \ddot{\boldsymbol{r}}, $, q1, q2, …, qd)为其他摄动力引起的加速度，其中包括地球引力引起的加速度ang：
$\boldsymbol{a}_{\mathrm{ng}}=\left[\begin{array}{lll}\frac{\partial \boldsymbol{r}}{\partial x_e} & \frac{\partial \varphi}{\partial x_e} & \frac{\partial \lambda}{\partial x_e} \\\frac{\partial \boldsymbol{r}}{\partial y_e} & \frac{\partial \varphi}{\partial y_e} & \frac{\partial \lambda}{\partial y_e} \\\frac{\partial \boldsymbol{r}}{\partial z_e} & \frac{\partial \varphi}{\partial z_e} & \frac{\partial \lambda}{\partial z_e}\end{array}\right] \cdot\left[\begin{array}{l}\frac{\partial T}{\partial \boldsymbol{r}} \\\frac{\partial T}{\partial \varphi} \\\frac{\partial T}{\partial \lambda}\end{array}\right]$
式中，(xe，ye，ze)为卫星的地固笛卡尔坐标；λ为卫星的地心纬度；φ为卫星的地心经度；T为扰动引力位(地球引力摄动通常用球谐函数表示)：
$\begin{gathered}T=\frac{G M}{R^2} \sum\limits_{n=2}^{n_{\max }}\left(\frac{b}{R}\right)^n \cdot \\\sum\limits_{m=0}^n\left(C_{n m} \cos (m \lambda)+S_{n m} \sin (m \lambda)\right) \cdot P_{n m}(\cos \varphi)\end{gathered}$
式中，b为地球赤道半径；Pnm为归一化的勒让德多项式；Cnm和Snm表示球谐系数；n和m分别为球谐函数展开式中的阶数和次数。
1.3 定轨策略
在简化动力学定轨中，需要用到低轨卫星的观测数据与GNSS卫星的精密星历作为参考，其中低轨卫星的观测方程可以表示为：
$P_i^s=\rho_i^s+c\left(\mathrm{~d} t_r-\mathrm{d} t^s\right)+M_P^s+\varepsilon_i^s$
$L_i^s=\rho_i^s+c\left(\mathrm{~d} t_r-\mathrm{d} t^s\right)+\lambda_i^s N_i^s+M_L^s+\xi_i^s$
式中，上标s代表卫星号；i表示观测值频段号；P和L分别表示伪距和载波相位观测值；ρis是卫星与测站间的几何距离；c为真空中光速；dtr和dts分别为接收机钟差和卫星钟差；λis为频率f所对应的载波波长；Nis为载波整周模糊度；MPs和MLs分别为伪距和载波相位观测值的其他误差；εis和ξis分别为伪距和载波相位的观测噪声以及其他未模型化误差。由于低轨卫星与GNSS卫星之间的传输不受对流层影响，所以不考虑对流层延迟。解算策略如表1所示。
2 结果分析
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2.1 数据分析
导航卫星轨道和导航卫星钟差数据来源于WUM发布的高精度GNSS产品，GRACE-FO星载GNSS观测数据与姿态数据由Jet Propulsion Laboratory(JPL)提供。由于观测质量会很大程度上影响定轨的结果，所以有必要对观测质量进行分析。
如图1(a)所示(采样间隔为10 min)，GRACE-C与GRACE-D在24 h内都有良好的可见卫星数，全天都能保持6颗卫星以上，其中GRACE-C的平均可见卫星数为9.18，GRACE-D为9.13，GRACE-C略高于GRACE-D。由于都有良好的可见卫星数，求解出的简化动力学轨道可信度较高。
如图1(b)所示，由于2颗低轨卫星的硬件、外观和运行路径极为相似，所以多路径效应相差不大。地面站的多路径效应约为20~60 cm[12]，而低轨卫星的多路径效应在10 cm左右，最大不超过12 cm。对比地面站，低轨卫星所接收到的GNSS信号所受到的干扰较少，多路径效应普遍不如地面站明显。
2.2 定轨精度分析
为了研究不同重力场模型对低轨卫星简化动力学定轨的影响，本文使用3种不同的重力场模型来计算低轨卫星所受到的摄动力，并进行简化动力学定轨。使用2022年第200-210天低轨卫星观测数据、低轨卫星姿态数据及GNSS精密产品进行定轨，定轨弧长为11 d，使用JPL发布的GRACE-FO精密轨道进行检核。结果如表2、3所示。
可以看出，不同的重力场模型与不同的模型阶数都会对简化动力学定轨精度产生影响，在阶数为50时，GRACE-C和GRACE-D使用EGM2008的定轨精度在10 cm左右，ITG-Grace03的定轨精度在94.3~95.9 mm，Tongji-Grace02k精度最高，最高达到89.1 mm。3种重力场模型均可以达到dm级至亚dm级精度。在阶数为100时，3个重力场模型的定轨精度相对50阶都有大幅提升，GRACE-C使用3个模型的定轨精度分别提升77.1%、72.8%和69.9%，GRACE-D分别提升69.2%、69.0%和68.7%，定轨精度在22.8~30.0 mm。EGM2008模型提升最大，可以看出EGM2008的阶数对简化动力学定轨的影响较大。在GRACE-C精密定轨中使用EGM2008模型的精度最高，Tongji-Grace02k次之，ITG-Grace03精度最低，GRACE-D的精度排序为Tongji-Grace02k、EGM2008、ITG-Grace03。分析认为，Tongji-Grace02k的综合定轨精度最高，更适用于低轨卫星简化动力学定轨。阶数为150时，定轨精度趋于稳定，与阶数100相比无太大区别。
2.3 轨道外推精度
不同的重力场模型会影响简化动力学轨道的外推精度，使用简化动力学定轨后的轨道外推2022年第211天第1个小时的轨道，同样使用JPL发布的GRACE-FO精密轨道进行检核，其中GRACE-C与GRACE-D使用不同重力场模型的轨道外推精度如图2、3所示。
由图可见，在50阶时，使用EGM2008模型，GRACE-C和GRACE-D在1 h内的轨道外推精度分别为459.4 mm和355.2 mm；ITG-Grace03的精度分别为701.4 mm和702 mm；Tongji-Grace02k的外推精度最高，分别为227.2 mm和228.8 mm。
在100阶时，得益于高精度定轨所获得的准确轨道，外推精度相比50阶时有一定提升。可以看出，轨道外推精度与简化动力学定轨精度有一定关系。使用EGM2008重力场模型时2颗卫星外推精度平均提升47.3%，Tongji-Grace02k平均提升28.9%，ITG-Grace03平均提升54.9%。使用不同的重力场模型进行轨道外推1 h精度均可以达到dm级至亚dm级。由于没有观测数据对轨道进行约束，随着轨道外推时间的增加，A、C、R方向的误差也在不断增大，其中A方向的误差在长时间外推中明显比其他2个方向的大。
2.4 随机脉冲参数优化
随机脉冲参数对轨道外推的影响与整体的定轨结果密切相关，在3种重力场模型中，无论是在定轨还是预报时，A方向的误差均略大于其他2个方向。通过分析判断，这可能是由于A方向的随机脉冲过于频繁导致的。为了控制A方向在轨道外推中的误差，需要对A方向的随机脉冲参数进行调整。经过多次实验，180 min为一组的A方向随机脉冲参数能够得到较好的优化效果。将优化后的随机脉冲参数应用于轨道外推，并与优化前的外推精度进行对比，其结果如图4所示。
GRACE-C和GRACE-D在3个不同阶数的EGM2008下的轨道外推精度分别提升35.8%、-94.8%、-104.6%和34.5%、77.4%、74.8%，Tongji-Grace02k为-38.8%、11.0%、10.6%和-16.0%、56.9%、29.7%，ITG-Grace03为13.0%、6.6%、5.3%和42.1%、7.0%、6.0%。可以看出，在优化随机脉冲参数后，外推精度在大部分情况下均有不同程度的提升。这是因为过于频繁的随机脉冲会在轨道外推过程中增加误差累积。在GRACE-C和GRACE-D轨道外推中，90 min一组的A方向随机脉冲并不适用，而180 min一组的效果更好。对于100阶和150阶的重力场模型，优化后效果较为显著；而使用50阶重力场模型时，优化后出现反作用的情况较多。对于ITG-Grace03模型，优化随机脉冲参数的效果较为稳定，所有情况下的轨道外推精度均有提升。
3 结语
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本文对比分析在不同重力场模型下对GRACE-FO卫星进行简化动力学定轨和轨道外推的影响，并针对其轨道特性优化随机脉冲参数。同时使用JPL发布的GRACE-FO精密轨道进行检核，得出如下结论：
1) 在50阶重力场模型中，EGM2008的定轨精度最差，精度为dm级，其余2种模型定轨精度在亚dm级。在100阶的重力场模型下简化动力学定轨精度对比50阶的重力场更高，精度在22.8~30.0 mm，其中在GRACE-C与GRACE-D的精密定轨中，EGM2008与Tongji-Grace02k的定轨性能优于ITG-Grace03。使用150阶的重力场模型时的定轨精度与100阶时并无太大区别。
2) 在对GRACE-C和GRACE-D进行轨道外推时，50阶的重力场模型中外推精度最高的是Tongji-Grace02k，其次是EGM2008，最低的是ITG-Grace03。得益于高精度的低轨卫星定轨，使用100阶重力场模型进行轨道外推的精度相比50阶重力场模型有大幅提升，在1 h内轨道预报均能达到dm级至亚dm级。使用EGM2008模型，外推精度最高能达到65.1 mm。随着外推时间的增加，A、C、R三个方向的偏差也在逐渐变大，其中A方向偏差变大的趋势比其他2个方向明显。结果表明，Tongji-Grace02k更适用于对GRACE-C与GRACE-D进行简化动力学定轨与轨道外推。
3) 在优化随机脉冲参数后，使用100阶和150阶重力场模型进行2颗卫星的轨道外推时，A方向偏差得到一定程度的控制，轨道外推精度有明显提升。其中50阶、100阶与150阶的ITG-Grace03均有提升，优化效果较为稳定。
基金
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  • 国家自然科学基金(42030109)
  • 辽宁省高等学校基本科研项目(LJKMZ20220673)
  • 大地测量与地球动力学国家重点实验室开放基金(SKLGED2023-3-2)
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2025年第45卷第5期
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引用本文
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文章信息
doi: 10.14075/j.jgg.2024.05.261
  • 接收时间：2024-05-31
  • 首发时间：2026-10-30
  • 出版时间：2025-05-15
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  • 收稿日期：2024-05-31
基金
National Natural Science Foundation of China(42030109)
国家自然科学基金(42030109)
Basic Scientific Research Projects of Liaoning Higher Education Institutions(LJKMZ20220673)
辽宁省高等学校基本科研项目(LJKMZ20220673)
Open Fund of State Key Laboratory of Geodesy and Earth's Dynamics(SKLGED2023-3-2)
大地测量与地球动力学国家重点实验室开放基金(SKLGED2023-3-2)
作者信息
    1 辽宁工程技术大学测绘与地理科学学院, 辽宁省阜新市玉龙路88号, 123000
    2 西安测绘研究所地理信息工程国家重点实验室, 西安市雁塔路中段1号, 710054
    3 中国科学院精密测量科学与技术创新研究院大地测量与地球动力学国家重点实验室, 武汉市徐东大街340号, 430077
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https://castjournals.cast.org.cn/joweb/ddcl/CN/10.14075/j.jgg.2024.05.261
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2种不同金属材料的力学参数
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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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