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Article(id=1322933587401651170, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322933542426116991, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.03.097, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1709827200000, receivedDateStr=2024-03-08, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793341546154, onlineDateStr=2026-10-30, pubDate=1736870400000, pubDateStr=2025-01-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793341546154, onlineIssueDateStr=2026-10-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793341546154, creator=13701087609, updateTime=1793341546154, updator=13701087609, issue=Issue{id=1322933542426116991, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='1', pageStart='1', pageEnd='110', issueExtLink='null', onlineDate='null', pubDate='1736870400000', pubDateStr='2025-01-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793341535431, creator='13701087609', updateTime=1793341535431, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=72, endPage=79, ext={EN=ArticleExt(id=1322933589058401251, articleId=1322933587401651170, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=On Accuracy of Time-Varying Gravity Field Inversion Based on Optimized Preprocessing Method, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Aiming at the problem of missing data and gross errors in GRACE Level1B observations, we propose an optimization method to complete the missing data of SCA1B. At the same time, we use an optimization strategy to eliminate gross errors for KBR1B and kinematic orbit data, then use these data sets to invert the time-varying gravity field model. In addition, based on synthesized data and real data respectively, we analyze the impact of the error from ACC1B in the Y direction on the inversion results and propose an optimization correction strategy. The optimized completion method can recover the missing data of SCA1B effectively, and fully considers the variational characteristics of the observations throughout the arc. The accuracy of the result derived from ACC1B data after correction using the optimization strategy is 3.7 mm, which is higher than the result derived from the uncorrected data. It can be seen from the results that the overall accuracy of the gravity field model solved by the data processed using the optimization method is like that of the three official centers. However, the detailed signals performance of the results from different institutions in regionals are different. It shows that the optimized data preprocessing strategy is effective and feasible.

, authors=Lun PU1, 2, Wei YOU1, *, Biao YU1, Dongming FAN1, authorsList=Lun PU, Wei YOU, Biao YU, Dongming FAN, authorCompany=null, correspAuthors=Wei YOU, authorNote=

PU Lun, PhD candidate, majors in satellite gravity measurement data processing and application, E-mail:

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针对GRACE Level1B观测数据中存在缺失数据及含有粗差的问题, 提出补全SCA1B缺失数据的优化方法, 同时对KBR1B和运动学轨道数据采用优化策略剔除粗差, 用于时变重力场模型反演。此外, 还分别基于合成数据和实测数据分析ACC1B数据在Y轴方向的误差对反演结果的影响, 并提出优化校正策略。利用优化方法能够有效恢复SCA1B的缺失数据, 且充分考虑了观测数据在整个弧段的变化特征。采用优化策略校正后的ACC1B数据计算结果显示, 其精度比未校正的数据计算结果提高3.7 mm。从结果可知, 由优化方法处理后的数据解算的重力场模型与三大官方机构解算结果相比, 总体精度相当, 但不同机构的解算结果在局部区域的细节信号表现有差异, 表明优化的数据预处理策略有效可行。

, authors=蒲伦1, 2, 游为1, *, 余彪1, 范东明1, authorsList=蒲伦, 游为, 余彪, 范东明, authorCompany=null, correspAuthors=游为, authorNote=

蒲伦, 博士生, 主要研究方向为卫星重力测量数据处理及应用, E-mail:

, correspAuthorsNote=

游为, 博士, 副教授, 主要从事卫星重力测量数据处理及应用研究, E-mail:

YOU Wei, PhD, associate professor, majors in the satellite gravity measurement data processing and application, E-mail:

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PU Lun, PhD candidate, majors in satellite gravity measurement data processing and application, E-mail:

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PU Lun, PhD candidate, majors in satellite gravity measurement data processing and application, E-mail:

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Background force models, observations and strategies of the parameter estimation

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力模型 观测数据及参数估计策略
模型类别 名称 类型/参数 数据/策略
静态重力场 GGM05S(180×180阶次) 星间距离变率 KBR1B RL03(5 s)
N体摄动 JPL DE430行星星历 轨道观测数据 ITSG运动学轨道(10 s)
固体潮汐 IERS 2010协议 非保守力数据 ACC1B RL02+SCA1B RL03
海洋潮汐 FES2014b(100×100阶次) 积分弧段长度 24 h(特殊弧段除外)
固体极潮 IERS 2010协议 初始状态向量 每弧段对位置和速度估计
海洋极潮 IERS 2010(100×100阶次) 加速度计偏差 X、Y、Z三轴按1 h估计
大气潮汐 S1+S2(Bode-Biancale 2006) 加速度计尺度 Bettadpur的推荐值(2009年)
大气与海洋去混频模型 AOD RL07(180×180阶次) 球谐位系数 60×60阶次
), ArticleFig(id=1322940346056966549, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322933587401651170, language=CN, label=表1, caption=

背景力模型、观测数据类型及参数估计策略

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力模型 观测数据及参数估计策略
模型类别 名称 类型/参数 数据/策略
静态重力场 GGM05S(180×180阶次) 星间距离变率 KBR1B RL03(5 s)
N体摄动 JPL DE430行星星历 轨道观测数据 ITSG运动学轨道(10 s)
固体潮汐 IERS 2010协议 非保守力数据 ACC1B RL02+SCA1B RL03
海洋潮汐 FES2014b(100×100阶次) 积分弧段长度 24 h(特殊弧段除外)
固体极潮 IERS 2010协议 初始状态向量 每弧段对位置和速度估计
海洋极潮 IERS 2010(100×100阶次) 加速度计偏差 X、Y、Z三轴按1 h估计
大气潮汐 S1+S2(Bode-Biancale 2006) 加速度计尺度 Bettadpur的推荐值(2009年)
大气与海洋去混频模型 AOD RL07(180×180阶次) 球谐位系数 60×60阶次
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基于优化预处理方法的时变重力场反演精度分析
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蒲伦 1, 2 , 游为 1, * , 余彪 1 , 范东明 1
大地测量与地球动力学 | 地球物理解释 2025,45(1): 72-79
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大地测量与地球动力学 |地球物理解释 2025 , 45 (1) : 72 -79
基于优化预处理方法的时变重力场反演精度分析
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蒲伦1, 2 , 游为1, * , 余彪1, 范东明1
作者信息
  • 1 西南交通大学地球科学与工程学院, 成都市犀安路999号, 611756
  • 2 德国地球科学研究中心全球地质监测与重力场分支机构, 韦斯灵克市克劳德多尼尔街1号, 82234
通讯作者:

游为, 博士, 副教授, 主要从事卫星重力测量数据处理及应用研究, E-mail:

YOU Wei, PhD, associate professor, majors in the satellite gravity measurement data processing and application, E-mail:

作者简介:

蒲伦, 博士生, 主要研究方向为卫星重力测量数据处理及应用, E-mail:

On Accuracy of Time-Varying Gravity Field Inversion Based on Optimized Preprocessing Method
Lun PU1, 2 , Wei YOU1, * , Biao YU1, Dongming FAN1
Affiliations
  • 1 Faculty of Geosciences and Engineering, Southwest Jiaotong University, 999 Xi'an Road, Chengdu 611756, China
  • 2 Global Geomonitoring and Gravity Field, GFZ German Research Centre for Geosciences, 1 Claude-Dornier-Straße, Wessling 82234, Germany

    • PU Lun, PhD candidate, majors in satellite gravity measurement data processing and application, E-mail:

出版时间: 2025-01-15 doi: 10.14075/j.jgg.2024.03.097
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摘要
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针对GRACE Level1B观测数据中存在缺失数据及含有粗差的问题, 提出补全SCA1B缺失数据的优化方法, 同时对KBR1B和运动学轨道数据采用优化策略剔除粗差, 用于时变重力场模型反演。此外, 还分别基于合成数据和实测数据分析ACC1B数据在Y轴方向的误差对反演结果的影响, 并提出优化校正策略。利用优化方法能够有效恢复SCA1B的缺失数据, 且充分考虑了观测数据在整个弧段的变化特征。采用优化策略校正后的ACC1B数据计算结果显示, 其精度比未校正的数据计算结果提高3.7 mm。从结果可知, 由优化方法处理后的数据解算的重力场模型与三大官方机构解算结果相比, 总体精度相当, 但不同机构的解算结果在局部区域的细节信号表现有差异, 表明优化的数据预处理策略有效可行。

GRACE  /  数据预处理  /  时变重力场  /  时间序列分解  /  精度分析

Aiming at the problem of missing data and gross errors in GRACE Level1B observations, we propose an optimization method to complete the missing data of SCA1B. At the same time, we use an optimization strategy to eliminate gross errors for KBR1B and kinematic orbit data, then use these data sets to invert the time-varying gravity field model. In addition, based on synthesized data and real data respectively, we analyze the impact of the error from ACC1B in the Y direction on the inversion results and propose an optimization correction strategy. The optimized completion method can recover the missing data of SCA1B effectively, and fully considers the variational characteristics of the observations throughout the arc. The accuracy of the result derived from ACC1B data after correction using the optimization strategy is 3.7 mm, which is higher than the result derived from the uncorrected data. It can be seen from the results that the overall accuracy of the gravity field model solved by the data processed using the optimization method is like that of the three official centers. However, the detailed signals performance of the results from different institutions in regionals are different. It shows that the optimized data preprocessing strategy is effective and feasible.

GRACE  /  data preprocessing  /  time-varying gravity field  /  time series decomposition  /  accuracy analysis
蒲伦, 游为, 余彪, 范东明. 基于优化预处理方法的时变重力场反演精度分析. 大地测量与地球动力学, 2025 , 45 (1) : 72 -79 . DOI: 10.14075/j.jgg.2024.03.097
Lun PU, Wei YOU, Biao YU, Dongming FAN. On Accuracy of Time-Varying Gravity Field Inversion Based on Optimized Preprocessing Method[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (1) : 72 -79 . DOI: 10.14075/j.jgg.2024.03.097
正文
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重力卫星Level1B观测数据的质量直接决定时变地球重力场反演的精度，在采用GRACE及其后续卫星GRACE Follow-On的观测数据解算重力场之前，需对不同观测数据作预处理[1]。该过程主要涉及观测值中的粗差剔除及缺失数据补全，而不同机构对观测数据的处理策略也不尽相同[2-4]。常用于获取非保守力的加速度计数据ACC1B和星载摄像仪数据SCA1B存在大量间断，且受到不同类型误差的影响，作为观测值参与解算的星间距离测距数据KBR1B和轨道数据(如运动学轨道)中也存在大量的粗差[5]。如何获取高质量的观测数据以实现时变重力场精细建模成为卫星大地测量领域的热点问题[6]。针对观测数据中存在的粗差及缺失数据，本文以2009-04 GRACE数据为例，采用优化的数据预处理方法，分别对观测数据进行预处理，并将其用于时变重力场模型反演。同时分析ACC1B数据在Y方向的误差对解算结果的影响，并针对该项误差的校正提供可选择策略。
1 时变重力场反演基本理论
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1.1 动力学反演方法
基于GRACE卫星观测数据解算时变地球重力场模型满足牛顿运动方程[7]，其表达式如下：
$\begin{gather*}\ddot{\boldsymbol{r}}(t)=\frac{\partial V(\boldsymbol{r}, \boldsymbol{u}, t)}{\partial \boldsymbol{r}}+\boldsymbol{f}(\boldsymbol{r}, \dot{\boldsymbol{r}}, \boldsymbol{p}, t)=\\\boldsymbol{a}(\boldsymbol{r}, \dot{\boldsymbol{r}}, \boldsymbol{u}, \boldsymbol{p}, t)\end{gather*}$
式中，$\ddot{\boldsymbol{r}}$为卫星在历元t的加速度，r和$\dot{\boldsymbol{r}}$分别为卫星的位置和速度向量；a表示卫星单位质量受到的引力∂V(r, u, t)/∂r与其他摄动力f(r, $\dot{\boldsymbol{r}}$, p, t)之和，其中u为球谐位系数，p为其他待估参数。
利用背景力模型积分可得到参考轨道r0，将观测轨道r与参考轨道r0作差，可得到轨道残差Δr并建立轨道观测方程：
$\Delta \boldsymbol{r}=\boldsymbol{r}(t)-\boldsymbol{r}_{0}(t)= \\\boldsymbol{R}(t) \delta \boldsymbol{r}_{0}+\boldsymbol{S}(t) \delta \dot{\boldsymbol{r}}_{0}+\boldsymbol{Y}(t) \delta \boldsymbol{x}$
式中，x=(uT, pT)T表示动力学参数，根据R(t)、S(t)和Y(t)可分别求得状态转移矩阵和参数敏感矩阵，通过微分方程数值积分求解后建立系数矩阵，具体积分求解过程详见文献[8]。
同理，求得星间距离变率KBRR(K band range rate)的参考值之后，将观测值与参考值作差，可得KBRR的观测方程：
$\begin{gather*}\Delta \dot{\boldsymbol{\rho}}=\dot{\boldsymbol{\rho}}-\dot{\boldsymbol{\rho}}_{0}=\frac{\partial \dot{\boldsymbol{p}}_{0}}{\partial \boldsymbol{r}_{\mathrm{A}}} \Delta \boldsymbol{r}_{\mathrm{A}}+ \\\frac{\partial \dot{\boldsymbol{p}}_{0}}{\partial \boldsymbol{r}_{\mathrm{B}}} \Delta \boldsymbol{r}_{\mathrm{B}}+\frac{\partial \dot{\boldsymbol{\rho}}_{0}}{\partial \dot{\boldsymbol{r}}_{\mathrm{A}}} \Delta \dot{\boldsymbol{r}}_{\mathrm{A}}+\frac{\partial \dot{\boldsymbol{\rho}}_{0}}{\partial \dot{\boldsymbol{r}}_{\mathrm{B}}} \Delta \dot{\boldsymbol{r}}_{\mathrm{B}}\end{gather*}$
式中，$\dot{\boldsymbol{\rho}}$和$\dot{\boldsymbol{\rho}}$0分别为观测值和积分值；ΔrA、ΔrB、Δ$\dot{\boldsymbol{\rho}}$ A和Δ$\dot{\boldsymbol{\rho}}$B为卫星积分状态偏差，即式(2)中Δr。
采用式(2)和式(3)求出系数矩阵，再由KBRR和轨道的法方程矩阵叠加得到总的法方程，详见文献[9]。完成法方程叠加后，得到局部参数和全局参数混合法方程如下：
$\left[\begin{array}{ll}\boldsymbol{N}_{11} & \boldsymbol{N}_{12} \\\boldsymbol{N}_{21} & \boldsymbol{N}_{22}\end{array}\right]\left[\begin{array}{l}\boldsymbol{x}_{\mathrm{L}} \\\boldsymbol{x}_{\mathrm{G}}\end{array}\right]=\left[\begin{array}{l}\boldsymbol{b}_{x_{\mathrm{L}}} \\\boldsymbol{b}_{x_{\mathrm{G}}}\end{array}\right]$
式中，xL表示局部参数；xG表示全局参数；N11和N22分别表示局部参数和全局参数对应的法方程子矩阵；N12和N21分别表示两种参数相关的子矩阵；bxL和bxG分别表示局部参数和全局参数对应的法方程右向量。消除局部参数后仅保留全局参数的法方程为：
$\left(\boldsymbol{N}_{22}-\boldsymbol{N}_{21} \boldsymbol{N}_{11}^{-1} \boldsymbol{N}_{12}\right) \boldsymbol{x}_{\mathrm{G}}=\left(\boldsymbol{b}_{x_{\mathrm{G}}}-\boldsymbol{N}_{21} \boldsymbol{N}_{11}^{-1} \boldsymbol{b}_{x_{\mathrm{L}}}\right)$
将式(5)简记为NixG=li，叠加该月n个弧段的法方程及右向量，即可求得全局参数xG。
1.2 背景力模型及解算策略
本文以KBRR和ITSG(格拉茨技术大学大地测量研究所)发布的运动学轨道共同作为观测值进行解算，采用的背景力模型如表1所示。其中，海潮模型FES2014b包含33个主潮波和304个次潮波[10]，大气潮汐模型S1和S2计算到2~8阶，N体摄动主要计算日、月潮汐部分。表1还给出本文使用的观测数据及参数估计策略，加速度计数据首先采用Bettadpur的推荐值(2009年)，基于校正关系式fcorr=bais+scale×fobs完成初始校正；然后将偏差参数作为未知数一起参与解算，并通过迭代校正局部参数。
2 数据预处理方法
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2.1 ACC1B数据预处理优化方法
ACC1B观测数据主要受偏差和尺度误差影响较大，由于考虑到加速度计尺度与球谐系数有一定相关性，本文未将尺度因子作为未知参数一并求解[11]，而是采用了Bettadpur的推荐值(2009年)。在科学参考框架(SRF)下Y轴方向还受到不同尺度及偏差的误差影响，主要表现为Y轴方向的观测值存在部分或整个弧段偏离正常波动范围太大，该误差可能受加速度计点火脉冲或仪器原因等影响，仅采用迭代校正局部参数的方式难以消除。因此，针对该项误差，本文提出如下方法进行校正。首先确定所需校正弧段的区间，完成初始校正，再将该区间的Y轴实测数据进行时间序列分解：
$\begin{equation*}f(t)=A+B \Delta t+C \sin (\omega \Delta t)+D \cos (\omega \Delta t)\end{equation*}$
式中，Δt=t－t0，t0表示计算弧段的起始历元，t为当前历元；A表示残余项，B为线性趋势项，C和D用于计算周期项；ω=2π/T，T为卫星绕地球运行的周期(约为1.5 h，即5 400 s)，为符合实际运行周期，本文结合实测数据将T值取为5 640 s。
由于该项误差表现为观测值出现急剧变化，若仅扣除线性趋势，难以将其校正在预期范围内，故还采用三次项拟合来扣除非线性部分。即采用公式(6)计算出线性趋势项和周期项，将其从观测数据中扣除，得到剩余数据；基于该剩余数据采用三次项最小二乘计算拟合曲线：
$\begin{equation*}g(t)=C_{0}+C_{1} \cdot \Delta t+C_{2} \cdot \Delta t^{2}+C_{3} \cdot \Delta t^{3}\end{equation*}$
式中，C0~C3表示拟合系数。将观测数据分别扣除由式(6)计算出的线性趋势及根据式(7)计算得到的拟合曲线部分(不含常数项)，即可得到校正后的结果。
2.2 SCA1B数据预处理优化方法
对于SCA1B缺失数据处理的主流方法为大于一定数量的缺失则舍弃该弧段，小于缺失阈值则采用插值方法来补全[12]。本文采用如下优化方法补全缺失历元的数据。首先根据式(6)计算该弧段的拟合系数A~D，并根据拟合系数计算得到拟合值f(t)。再将实际观测数据与该拟合结果作差得到Δf(t)，基于该残差序列采取线性插值方法补全缺失部分的数据：
$\begin{gather*}\Delta f_{n}=\frac{1}{N_{g}+1}\left[\left(N_{g}+1-n\right) \cdot \Delta f_{-1}+\right. \\\left.n \cdot \Delta f_{+1}\right], n=1, 2, \cdots, N_{g}\end{gather*}$
式中，Ng为缺失个数。最后将采用式(6)得到的时间序列拟合结果与采用式(8)得到的插值计算结果进行叠加，即得到缺失部分的数据。结合SCA1B数据特征，在式(6)中使用的周期取运行周期的2倍，即T的值取为约3 h(本文结合实测数据将T值取为11 280 s)。
2.3 KBR1B数据预处理优化方法
本文对KBR1B数据采用的粗差探测及剔除策略如下。首先根据观测数据文件提供的信噪比，剔除小于450的KBR1B数据，但此时观测数据中仍然含有大量粗差。对于大的粗差，采用预校正的策略加以探测并剔除。在仅采用GNV1B轨道数据作为观测值解算局部参数时，通过迭代方式得到积分KBRR，并与观测值作差。再将该残差扣除One-CPR(cycle per revolution)影响：
$\begin{align*}k(t)=A+ & B t+C t^{2}+D \sin (\omega t)+E \cos (\omega t)+ \\& F t \sin (\omega t)+G t \cos (\omega t)\end{align*}$
式中，A~G为动力学经验参数；ω=2π/T，T为卫星绕地球运行的周期，其取值同式(6)。
根据式(9)求得7个建模参数后即可得到拟合的KBRR残差序列，将观测KBRR残差序列与拟合残差序列作差可扣除One-CPR的影响。此步骤仅用于KBR1B数据的筛选，在解算时变地球重力场的过程中并未采用动力学经验参数。扣除One-CPR影响后，KBRR残差序列中的粗差更加突显，可快速定位到粗差的位置，更方便对其加以剔除。基于上述步骤筛选的KBR1B数据解算所有参数，并通过迭代校正得到KBRR残差。实际上，此时的残差中还含有部分粗差，不同机构针对该部分粗差的处理策略不尽相同。由于该部分粗差在特定月份或不同区域可能还包含有部分地球物理信号，本文结合实际情况，在此基础上采用3σ(即3倍RMS)对其进行粗差探测，进一步对KBR1B数据进行筛选，以获得更加干净的观测数据，最后再将筛选的KBR1B数据用于时变重力场模型解算。
2.4 运动学轨道数据预处理优化方法
除了将KBRR作为观测数据之外，本文还采用ITSG发布的运动学轨道作为输入数据。该轨道数据存在大量缺失并含有大量粗差，若不对这些粗差进行处理，将无法求得预期结果，甚至会得到错误的解。本文在基于处理KBRR残差的思路上，对运动学轨道数据的粗差探测及数据筛选采用如下策略。首先基于GNV1B轨道数据反演并迭代校正后得到积分轨道，将运动学轨道与积分轨道作差得到轨道残差序列。再对轨道残差序列作处理，该残差序列中含有明显的周期性变化和大粗差。基于公式(9)采用经验参数模型扣除残差序列中的周期变化部分，此时的残差序列将更加突出粗差分布的位置。为减小大粗差对建模效果的影响，本文在使用式(9)之前先剔除大于±4 cm的粗差后再进行建模。然后对已扣除周期项影响的轨道残差序列采用3σ剔除其中粗差。最后基于该残差序列来筛选运动学轨道，得到干净的轨道数据用于时变地球重力场模型解算。
3 结果分析
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首先对非保守力观测数据ACC1B的实测数据进行分析，重点分析存在明显波动误差的ACC1B观测数据对解算结果的影响，以及采用本文方法校正后数据的解算精度。图1分别给出2009-04-30(图1(a))和2010-03-18(图1(c))卫星A在Y轴方向的实测数据(红线)及其采用优化方法校正后的结果(蓝色)。此外，为对比非保守力在Y轴方向的整体趋势，图1(a)和(c)中分别增加了ITSG发布的非保守力模型(绿色)进行比对。值得注意的是，此时本文采用的数据为初始校正后的值，还存在加速度计偏差的影响，该差异在迭代校正后将得以减小，而本文分析的明显波动误差在迭代过程中却难以消除。根据图1(b)和(d)可知，在观测数据中扣除基于时间序列分解得到的线性趋势项和三次项拟合得到的曲线部分之后，校正后的结果与实测数据的整体趋势吻合较好。
为了定量分析ACC1B在Y轴方向存在的明显误差对解算结果的影响及校正后的数据对解算结果的改进效果，本文分别以模拟实验及实测数据进行验证。模拟实验中，分别对2009-04-25-29期间A卫星ACC1B观测数据的Y轴方向加入误差项，该误差项来源于图1(d)中分离出的趋势项(深灰色)及曲线部分(绿色)叠加的结果，此模拟数据是为了验证增加误差项对反演结果的影响。实测数据则采用2009-04-30(后半弧段)和2010-03-18(整个弧段)数据。
由图2后验残差对比结果可知，无论采用合成数据进行解算还是基于有误差的ACC1B实测数据进行解算，其解算结果的轨道后验拟合残差在3个轴向上均表现出不同程度的影响，即Y轴方向含有误差的ACC1B数据使得残差值增大，其中轨道残差在Y轴方向表现最为明显(图2(d)、(e)、(f))，X轴方向次之(图2(a)、(b)、(c))，而Z轴方向几乎不受该误差的影响(图2(g)、(h)、(i))。加入误差之后的数据计算的轨道残差，在Y轴方向的误差增大39.1%、X轴方向增大12.8%、Z轴方向仅变化0.2%。实测数据验证中，采用校正后的数据解算的结果与直接采用观测数据的计算结果进行对比，2009-04-30(后半弧段)和2010-03-18(整个弧段)在Y轴方向的精度分别提高3.7 mm和3.8 mm，X轴方向精度分别提高0.6 mm和2.5 mm。此外，图3还给出2009-04合成数据与真实观测数据在迭代前后的重力场模型解算结果，以EIGEN-6C4为参考模型计算的大地水准面阶方差表示，此处使用的轨道数据为GNV1B。图3进一步验证了ACC1B数据在Y轴方向的累积误差对解算时变重力场的影响，尤其是对中阶次部分的影响最为明显，且该影响仅通过迭代校正处理难以消除，因此有必要对该数据进行校正后再参与重力场解算。合成数据和真实数据的实验结果均表明，有效降低ACC1B数据Y轴方向的误差将有助于解算高精度时变重力场模型。
对SCA1B补全数据方法进行验证。以2009-04-01 A卫星观测数据为例，任意移除其中两段数据(即缺失历元分别位于291 830 300~ 291 833 000和291 841 000~291 842 300之间)作为本次实验的缺失数据，选择某弧段SCA1B数据加以验证的前提是确保其他观测数据可用。SCA1B观测的真实数据、缺失数据和采用本文方法补全恢复后的四方位元素结果如图4所示。
由图4可知，采用本文优化的SCA1B数据处理方法补全缺失数据之后与观测数据吻合较好，尤其是呈现周期变化的拐点位置恢复较好，符合整个弧段整体观测值趋势。经过计算补全值与真实值之间的RMSE可得，四方位元素的误差(无量纲)分别为：0.001 7、0.001 3、0.000 8、0.001 8，且在每个历元对应的四方位元素的平方和均接近于1，该指标进一步表明，其恢复结果符合SCA1B的实测数据特征。值得一提的是，在根据已知观测值补全缺失数据的同时，首先需要确保已知数据的准确性，如果该弧段数据的观测质量良好，则可以采用适宜的补全方法来获得缺失部分的数据；但若该弧段的观测数据本身的质量存在问题，无论采用何种补全方法均会产生虚假信息或不正确的结果，故在采用本文缺失数据补全方法前也需确保SCA1B观测数据无明显异常值。
验证了SCA1B数据补全方法的有效性之后，采用该方法补全所有弧段的缺失数据。值得注意的是，在后续实际解算2009-04的结果时舍弃了30日弧段后半部分的数据，这是由于该部分除了受非保守力ACC1B的影响外，KBR1B观测质量也不佳，GFZ RL06解算结果的KBRR残差也证明此部分数据不佳而未参与解算(此处未展示该KBRR残差数据)。对于本文ACC1B数据的校正方法，在其他观测值可用情况下仍然有助于提高解算结果的精度。基于KBRR数据处理的优化策略，图5提供了本文解算结果的KBRR预拟合残差及后验拟合残差(即pre-fit残差和post-fit残差)对比结果。
由图5可见，无论是KBRR预拟合残差还是后验拟合残差，采用本文处理策略得到的残差精度均满足观测数据的精度要求，且残差值波动在±1 μm/s范围内。选取2009-04 KBRR残差数据的6个弧段绘图并加以分析，计算得到pre-fit残差和post-fit残差的标准差的均值分别为0.29 μm/s和0.22 μm/s。其中，由于04-01观测数据存在明显异常值，SWJTU解的pre-fit残差的标准差为0.30 μm/s，post-fit残差的标准差为0.24 μm/s。此外，在解算处理过程中还另外与GFZ两类残差进行了比对，SWJTU的残差结果呈现明显的优越性。结果表明，对于存在明显粗差的KBR1B观测数据，采用本文处理策略进行解算有助于降低KBR1B观测值中的粗差对模型解算精度的影响。关于KBRR残差的处理策略，不同机构处理策略不尽相同，若扣掉粗差，可能会削弱某些局部区域的地球物理信号；但如果将粗差也参与解算，其误差也会对模型解算精度造成不同程度的影响。通过采用本文处理KBR1B的策略进行对比实验可知，若观测数据存在粗差，将其扣除后解算的结果优于未扣除粗差解算的结果；对于仅含有少量异常值的观测数据，不作扣除对结果无明显影响，同时也可充分利用观测中包含的信号。
除了观测值KBRR的质量对解算结果会产生直接影响外，轨道观测值的选择也直接决定了重力场模型的精度。图6分别展示3种常见粗差情况下所对应弧段的处理过程及其后验拟合残差结果，其中图6(a)、(b)、(c)为含有大量粗差的初始轨道残差(该结果由ITSG的运动学轨道数据与积分轨道作差所得)，由图可知，最大残差达±60 cm；图6(d)、(e)、(f)为扣除明显的周期项之后剩余的部分，可以看出，扣除后突显了粗差分布的位置(此处已扣除大于±4 cm的大粗差部分)；图6(g)、(h)、(i)为基于3倍RMS(即3σ)扣除粗差部分后的结果，后面将基于该数据对初始轨道数据进行筛选；经过解算得到如图6(j)、(k)、(l)所示运动学轨道后验残差结果，其残差基本控制在±2 cm内。结果表明，在相同条件下采用本文处理方法剔除粗差后的轨道数据解算结果显著优于含有粗差的数据解算结果(因采用含有粗差的轨道数据解算的结果偏离参考数据较大，故在此不予展示)。
为对比时变重力场模型精度，分别绘制不同数据对应的大地水准面阶方差，图3为验证观测数据ACC1B误差对解算结果的影响，结果表明，在对ACC1B的Y轴方向的观测数据中加入误差项之后，其反演结果无论是否迭代均不如原观测数据解算的结果好。图7展示本文解算模型(以SWJTU-RL02表示)与三大官方机构解算模型的对比。由图可知，SWJTU-RL02结果整体趋势与3家机构一致，且明显优于SWJTU-RL01的结果，其差异的主要原因在于背景力模型和轨道数据的使用不同。CSR-RL06在中高阶表现最优，而在40~50阶处SWJTU-RL02结果优于GFZ-RL06和JPL-RL06，其中KBRR数据的不同处理策略可能成为导致其差异的原因之一。
此外，图8展示了采用半径为300 km的高斯滤波处理后的时变重力场的空间分布，图中数据均以GGM05S为静态重力场进行计算，同时采用SLR的C20替换并增加1阶项。需注意的是，由于此处未涉及具体区域的地球物理信号的应用研究，故该图中的数据均未扣除GIA的影响。由图可见，SWJTU-RL02模型的结果与3家机构的结果一致性较好。从南北条带误差来看，SWJTU-RL02与CSR-RL06和JPL-RL06的结果更接近，而GFZ-RL06条带更明显；从质量变化细节信号来看，如澳大利亚西北部区域，SWJTU-RL02与CSR-RL06及GFZ-RL06的结果一致性更好，JPL-RL06在此处受条带噪声影响较大。整体解算结果与3家机构结果相当，表明本文使用的处理策略有效可行。
4 结语
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本文采用优化数据预处理方法分别对不同观测数据进行处理，并解算2009-04的时变重力场模型，同时分析加速度计数据误差对结果的影响，得到以下结论：
1) 分析ACC1B数据在Y轴方向含有明显误差的情况下对解算模型的影响，提出针对该项误差校正的优化方法，无论是采用合成数据的模拟实验还是基于真实数据解算的结果，均表明该项误差对重力场解算有明显影响，且采用本文优化方法处理后，解算结果得到明显改善。
2) 针对SCA1B观测数据中存在大量的缺失数据，提出一种基于时间序列分解与插值方法相结合的策略来补全缺失历元的数据。经过实验对比分析可知，该方法能够有效恢复缺失部分的四方位元素，尤其是在拐点处恢复效果表现较优，与实际观测数据趋势较为吻合。基于此方法恢复的数据解算的重力场与实际观测值解算结果吻合较好，验证了该方法的有效性及可行性。
3) 采用优化方法对KBR1B和ITSG运动学轨道数据中含有的粗差进行处理，解算的重力场模型与三大官方机构的结果比较，整体精度相当。与GFZ-RL06的结果对比发现，无论是KBRR残差(仅在解算过程中参与对比)、大地水准面阶方差还是空间分布结果，SWJTU-RL02均表现较好，且对于南北条带噪声的抑制整体上优于GFZ-RL06的结果，与CSR-RL06和JPL-RL06的解算结果吻合较好。
基金
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  • 国家自然科学基金(41974013)
  • 国家自然科学基金(42174014)
  • 国家自然科学基金(42474005)
文献
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参考文献 引证文献
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2025年第45卷第1期
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引用本文
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文章信息
doi: 10.14075/j.jgg.2024.03.097
  • 接收时间：2024-03-08
  • 首发时间：2026-10-30
  • 出版时间：2025-01-15
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  • 收稿日期：2024-03-08
基金
National Natural Science Foundation of China(41974013)
国家自然科学基金(41974013)
National Natural Science Foundation of China(42174014)
国家自然科学基金(42174014)
National Natural Science Foundation of China(42474005)
国家自然科学基金(42474005)
作者信息
    1 西南交通大学地球科学与工程学院, 成都市犀安路999号, 611756
    2 德国地球科学研究中心全球地质监测与重力场分支机构, 韦斯灵克市克劳德多尼尔街1号, 82234

通讯作者:

游为, 博士, 副教授, 主要从事卫星重力测量数据处理及应用研究, E-mail:

YOU Wei, PhD, associate professor, majors in the satellite gravity measurement data processing and application, E-mail:

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https://castjournals.cast.org.cn/joweb/ddcl/CN/10.14075/j.jgg.2024.03.097
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