卫星重力测量解析误差分析法
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摘要
卫星重力测量技术被公认为是探测和研究全球重力场最有效且极具发展潜力的方法之一。自进入21世纪以来，基于卫星跟踪卫星技术的CHAMP和GRACE以及基于卫星重力梯度技术的GOCE重力卫星计划相继成功实施，使得人们得以获取高精度和高分辨率的全球重力场信息，进一步提高了对全球物质分布、物质转移交换和地球内部精细结构等科学问题的认识水平。为了研究卫星重力测量计划中指标参数与科学目标之间的关系和评估各种噪声对恢复重力场精度的影响，传统研究方法一般是将重力观测值作为位置或者时间的函数，在此基础上利用最小二乘法进行相关的误差分析。最小二乘误差分析方法从数值的角度间接地进行评估参数的影响，难以直接评估某些单一参数的影响，而且随着解算模型的分辨率越来越高和阶数越来越大，计算量急剧增长并带来严重的数值不稳定性问题。
为了快速评估和确定卫星重力测量计划有关参数，以及评估不同类型载荷噪声的影响，根据仪器功率谱密度和重力位系数阶方差的定义，建立了卫星重力梯度测量噪声与恢复重力场模型精度的直接对应关系。利用二维傅立叶变换性质、二维采样定理和相应的调制理论，进一步推导出了卫星重力测量结果中所含二维空间信号与观测值的一维时间频率的联系，从而可以解析地评估卫星重力测量中色噪声的影响。利用此关系，首先讨论分析了白噪声模型下卫星重力测量技术中测量噪声、卫星轨道高度及运行时间等参数对重力场恢复精度的影响。接着分析了色噪声对恢复重力场模型精度的影响，结果表明低频的噪声在整个频带上都对恢复重力场位系数有影响。考虑到实际测量噪声为色噪声的情况下，如果不采取滤波措施，低频处的1/f噪声将较大地影响恢复重力场的空间分辨率和精度。但是，在使用滤波器后低频噪声得到抑制的同时，重力场信号每一阶所含有的低频信息也被抑制，可能使得单独使用梯度观测值恢复重力场模型系数时产生失真。
此外，根据高低卫—卫跟踪测量原理并结合线性扰动理论和控制理论，我们建立起了高低卫—卫跟踪测量噪声功率谱与重力场恢复精度之间的解析表达式，并在此基础上分析讨论了高低卫—卫跟踪中GPS定位误差和静电悬浮加速度计测量噪声对所恢复重力场精度的影响。结果表明目前高低卫—卫跟踪得到的地球重力场精度主要受限于GPS的测量精度。
为了获取高精度的月球引力场模型，开展了月球卫星引力梯度测量方案的研究。月球引力梯度测量不仅有利于恢复月球引力场的中短波分量信息，而且还有利于消除探月卫星受到的非保守力的影响，可望利用运行在轨道高度为20km的极圆轨道上、梯度测量水平为30mE/Hz1/2的重力梯度卫星，在半波长为7km的空间分辨率上，确定月球水准面的精度约为20.5cm的月球引力场模型。
相对于传统的研究卫星重力测量误差分析和恢复能力论证的方法，我们提出的方法具有简单和直接等优点，且不需要消耗大量计算资源，特别适合项目建议初期对部分观测量或者载荷指标进行快速评估和确定，也可以对卫星重力测量系统数值模拟仿真中参数选择和优化设计提供指导。
Satellite gravimetry is recognized as one of the most effective and potential techniquefor exploring and researching the Earth‘s gravity field with a global coverage. In thebeginning of the21st century, dedicated gravity field missions like CHAMP, GRACE andGOCE were successfully launched. Based on the high spatial resolution and accuracygravity field information retrieved from the missions, we can have a further understandingof the mass transport, mass anomalies, mass distribution in the Earth system, the finestructure of the Earth, and so on. Currently, the corresponding methods of error analysis,which determine science requirements and mission parameters, are mainly based onleast-squares (LS) theory, and basically divided into two types: the time-wise approachand the space-wise approach. The solution to the equations based on LS has the optimumstatistical properties, but both the time-wise and space-wise approaches address the effectof measurement errors and estimate the resolution of gravity field models mainly from anumerical point of view. It is difficult to directly estimate the effect of the parameters, andthe latest and incoming gravitational models with increasing accuracy and resolutionmakes the computation more difficult since the computation become huge and seriousnumerical instabilities arise when degree/order of models gets higher.
For the reasons mentioned above, it is important to develop a direct and efficientprocedure of error analysis for satellite gravity field determination. Direct relationshipbetween the power spectrum density of satellite gravimetry observations and thecoefficients of the Earth‘s gravity potential is established based on definitions of theinstrument‘s power spectrum density and the Earth‘s gravity field potential, and then theeffect of measurement accuracy, the altitude of the satellite, and the operation duration onrecovering of the Earth‘s gravity field is analyzed by using this method which is based on the assumption that the measurement errors are white. Furthermore, the relationshipbetween the spatial frequencies and the temporal frequencies is concluded based on2-DFourier methods,2-D sample theorem and modulation theory. Thus, it is possible toquantify the effect of color noise in missions. From the results in this study, it is indicatedthat the low frequency noise degrades the gravity field recovery in all degrees and thesignals of gravity information at low frequencies are also filtered out when filters areemployed, so the colored noise must be processed carefully.
The analytical relationship between the measurement error PSD of SST-hl and thecoefficient of the Earth gravity potential is established by using a method based on theprinciples of SST-hl, the linear perturbations theory and control theory. Then we analysisthe effects of GPS and accelerometer measurement errors on the accuracy of the Earthgravity field recovery, which is limited by the accuracy of GPS.
In addition, the lunar satellite gravity gradiometry is also proposed and discussed forimproving the Moon‘s gravity field model. This mode not only is effective in recoveringthe medium and short wavelength gravity field information, but also can reduce the effectof non-gravitational forces in order to improve the recovery accuracy. The missionscenario with a high accuracy of14mGal and the geoid with an accuracy of20.5cm at aspatial resolution of7km is recommended, which is under the conditions of orbit heightof20km and gradiometer accuracy level of30mE/Hz1/2.
The method established in this study is effective and direct compared with the othersbased on the least square approach, and is very useful to design and verify the parametersfor the Earth gravity recovery missions.
为了快速评估和确定卫星重力测量计划有关参数，以及评估不同类型载荷噪声的影响，根据仪器功率谱密度和重力位系数阶方差的定义，建立了卫星重力梯度测量噪声与恢复重力场模型精度的直接对应关系。利用二维傅立叶变换性质、二维采样定理和相应的调制理论，进一步推导出了卫星重力测量结果中所含二维空间信号与观测值的一维时间频率的联系，从而可以解析地评估卫星重力测量中色噪声的影响。利用此关系，首先讨论分析了白噪声模型下卫星重力测量技术中测量噪声、卫星轨道高度及运行时间等参数对重力场恢复精度的影响。接着分析了色噪声对恢复重力场模型精度的影响，结果表明低频的噪声在整个频带上都对恢复重力场位系数有影响。考虑到实际测量噪声为色噪声的情况下，如果不采取滤波措施，低频处的1/f噪声将较大地影响恢复重力场的空间分辨率和精度。但是，在使用滤波器后低频噪声得到抑制的同时，重力场信号每一阶所含有的低频信息也被抑制，可能使得单独使用梯度观测值恢复重力场模型系数时产生失真。
此外，根据高低卫—卫跟踪测量原理并结合线性扰动理论和控制理论，我们建立起了高低卫—卫跟踪测量噪声功率谱与重力场恢复精度之间的解析表达式，并在此基础上分析讨论了高低卫—卫跟踪中GPS定位误差和静电悬浮加速度计测量噪声对所恢复重力场精度的影响。结果表明目前高低卫—卫跟踪得到的地球重力场精度主要受限于GPS的测量精度。
为了获取高精度的月球引力场模型，开展了月球卫星引力梯度测量方案的研究。月球引力梯度测量不仅有利于恢复月球引力场的中短波分量信息，而且还有利于消除探月卫星受到的非保守力的影响，可望利用运行在轨道高度为20km的极圆轨道上、梯度测量水平为30mE/Hz1/2的重力梯度卫星，在半波长为7km的空间分辨率上，确定月球水准面的精度约为20.5cm的月球引力场模型。
相对于传统的研究卫星重力测量误差分析和恢复能力论证的方法，我们提出的方法具有简单和直接等优点，且不需要消耗大量计算资源，特别适合项目建议初期对部分观测量或者载荷指标进行快速评估和确定，也可以对卫星重力测量系统数值模拟仿真中参数选择和优化设计提供指导。
Satellite gravimetry is recognized as one of the most effective and potential techniquefor exploring and researching the Earth‘s gravity field with a global coverage. In thebeginning of the21st century, dedicated gravity field missions like CHAMP, GRACE andGOCE were successfully launched. Based on the high spatial resolution and accuracygravity field information retrieved from the missions, we can have a further understandingof the mass transport, mass anomalies, mass distribution in the Earth system, the finestructure of the Earth, and so on. Currently, the corresponding methods of error analysis,which determine science requirements and mission parameters, are mainly based onleast-squares (LS) theory, and basically divided into two types: the time-wise approachand the space-wise approach. The solution to the equations based on LS has the optimumstatistical properties, but both the time-wise and space-wise approaches address the effectof measurement errors and estimate the resolution of gravity field models mainly from anumerical point of view. It is difficult to directly estimate the effect of the parameters, andthe latest and incoming gravitational models with increasing accuracy and resolutionmakes the computation more difficult since the computation become huge and seriousnumerical instabilities arise when degree/order of models gets higher.
For the reasons mentioned above, it is important to develop a direct and efficientprocedure of error analysis for satellite gravity field determination. Direct relationshipbetween the power spectrum density of satellite gravimetry observations and thecoefficients of the Earth‘s gravity potential is established based on definitions of theinstrument‘s power spectrum density and the Earth‘s gravity field potential, and then theeffect of measurement accuracy, the altitude of the satellite, and the operation duration onrecovering of the Earth‘s gravity field is analyzed by using this method which is based on the assumption that the measurement errors are white. Furthermore, the relationshipbetween the spatial frequencies and the temporal frequencies is concluded based on2-DFourier methods,2-D sample theorem and modulation theory. Thus, it is possible toquantify the effect of color noise in missions. From the results in this study, it is indicatedthat the low frequency noise degrades the gravity field recovery in all degrees and thesignals of gravity information at low frequencies are also filtered out when filters areemployed, so the colored noise must be processed carefully.
The analytical relationship between the measurement error PSD of SST-hl and thecoefficient of the Earth gravity potential is established by using a method based on theprinciples of SST-hl, the linear perturbations theory and control theory. Then we analysisthe effects of GPS and accelerometer measurement errors on the accuracy of the Earthgravity field recovery, which is limited by the accuracy of GPS.
In addition, the lunar satellite gravity gradiometry is also proposed and discussed forimproving the Moon‘s gravity field model. This mode not only is effective in recoveringthe medium and short wavelength gravity field information, but also can reduce the effectof non-gravitational forces in order to improve the recovery accuracy. The missionscenario with a high accuracy of14mGal and the geoid with an accuracy of20.5cm at aspatial resolution of7km is recommended, which is under the conditions of orbit heightof20km and gradiometer accuracy level of30mE/Hz1/2.
The method established in this study is effective and direct compared with the othersbased on the least square approach, and is very useful to design and verify the parametersfor the Earth gravity recovery missions.
引文
[1]许厚泽.重力测量技术及重力学研究进展.地理空间信息,2003,1(3):3－4
[2]许厚泽.我国精化大地水准面工作中若干问题的讨论.地理空间信息,2006,4(5):1－4
[3] Rummel R, Horwath M, Yi W, et al. GOCE, Satellite Gravimetry and Antarctic MassTransports. Surveys in Geophysics,2011,32:643－657
[4]宁津生.跟踪世界发展动态致力地球重力场研究.武汉大学学报信息科学版，2001，26(6)：471474
[5]宁津生.卫星重力探测技术与地球重力场研究.大地测量与地球动力学，2002，22：l5
[6]许厚泽,周旭华,彭碧波.卫星重力测量.地理空间信息,2005,3(1):1－3
[7]许厚泽.卫星重力研究：21世纪大地测量研究的新热点.测绘科学，2001，26(3)：13
[8] Reigber C, Balmino G, Schwintzer P, et al. A high quality global gravity field model fromCHAMP GPS tracking data and accelerometry (EIGEN-1S). Geophysical Research Letters,2002,29(14):371374
[9] Jekeli C. The determination of gravitational potential differences from satellite-to-satellitetracking. Celestial Mechanics and Dynamical Astronomy,1999,75(2):85101
[10] Tapley B D, Bettadqur S. The gravity recovery and climate experiment: mission overviewand early results. Geophysical Research Letters,2004,31: L09607.
[11] European Space Agency. Gravity field and steady-state ocean Circulation ExplorationReports for Mission Selection. The four candidate Earth Explorer Core Missions, SP-1233(1).European Space Agency,1999
[12] Rummel R, Yi W, Stummer C. GOCE gravitational gradiometry. Journal of Geodesy,2011,85:777–790
[13] Hirt C, Gruber T, Featherstone W E. Evaluation of the first GOCE static gravity field modelsusing terrestrial gravity, vertical deflec-tions and EGM2008quasigeoid heights. J Geod,2011,85:723–740
[14] Ilk K H, Flury J, Rummel R et al. Mass transport and mass distribution in the earth system.Proposal for a German Priority Research Program, GeoForschungs Zentrum Potsdam.2004
[15]陈俊勇.现代低轨卫星对地球重力场探测的实践和进展.测绘科学,2002,27(1):8－10
[16] Visser P N A M, van den IJssel J, Koop R, et al. Exploring gravity field determination fromorbit perturbations of the European gravity mission GOCE. Journal of Geodesy,2001,75(2):89－98
[17] Hwang C. Gravity recovery using COSMIC GPS data: application of orbital perturbationtheory. Journal of Geodesy,2001,75(2):117－136
[18] Cheng M K. Gravitational perturbation theory for intersatellite tracking. Journal of Geodesy,2002,76(3):169－185
[19]罗佳.利用卫星跟踪卫星确定地球重力场的理论和方法[博士论文].武汉：武汉大学，2003
[20]陆仲连，吴晓平编著，人造地球卫星与地球重力场.北京：测绘出版社，1994
[21]李建成，宁津生，晁定波等.卫星测高在大地测量学中的应用及进展.测绘科学，2006，31(6)：1923
[22]翟国君，黄谟涛，欧阳永忠等.卫星测高原理及其应用.海洋测绘，2002，22(1)：5762
[23] Wahr J, Wingham D, Bentley C. A method of combining ICESat and GRACE satellite data toconstrain Antarctic mass balance. Journal of Geophysical Research,2000,105(b7):16279－16294
[24] Zhang F P, Huang C, Liao X H, et al. Precision ERS-2orbit determination combiningmultiple tracking techniques. Chinese Science Bulletin,2001,44(20):1756－1760
[25]汪海洪，钟波，王伟，于丹.卫星测高的局限与新技术发展.大地测量与地球动力学，2009，29(1)：9195
[26] Han S-C, Jekeli C, Shum C K. Efficient gravity field recovery using in situ disturbingpotential observables from CHAMP. Geophysical Research Letters,2002,29(16):10.1029/2002GL015180
[27] Howe E, Stenseng L, Tscherning C C. Analysis of one month of CHAMP state vector andaccelerometer data for the recovery of the gravity potential. Advances in Geosciences,2003,1:14
[28]徐天河,杨元喜.基于能量守恒方法恢复CHAMP重力场模型.测绘学报,2005,34(1)：16
[29] Touboul P, Bernard A. Electrostatic accelerometers for the equivalence principle test in space,Advances in Space Research,2003,32,1357
[30] Touboul P, Foulon B, Bernard A. Electrostatic servocontrolled accelerometers for futre spacemissions, Futre Fundamental Physics Missions in Space and Enabling Technologies, ElEscroial, Spain, Apr.5-7,1994
[31] Bernard A and Touboul P. The GRADIO accelerometer design and development status,Workship ESA/NASA on the Solid-Earth Mission ARISTOTELES, Anacapri, Italy, Sep.23-24,1991
[32] Bruinsma S, Tamagnan D, Biancale R. Atmospheric densities derived from CHAMP/STARaccelerometer observations. Planetary and Space Science,2004,52,297
[33]祝竺，张晓敏，周泽兵.利用旋转卫星法开展加速度计在轨检验研究.宇航学报，2010，31(5):13621367
[34] Flury J, Bettadpur S, Tapley B D. Precise accelerometry onboard the grace gravity fieldsatellite mission. Advances in Space Research,2008,42,1414
[35]白彦峥，田蔚，周泽兵等.高精度空间加速度计及其应用.空间科学学报，2010，30(6):601606
[36]周泽兵，白彦峥，祝竺等.卫星重力测量中加速度计在轨参数校准方法研究.中国空间科学技术，2009，6:7480
[37] Touboul P, Foulon B, Willemenota E. Electrostatic space accelerometers for present andfuture missions. Acta Astronautica,1999,45,605
[38] Gerlach Ch, Sneeuw N, Visser, et al. CHAMP gravity field recovery using the energy balanceapproach. Advances in Geosciences,2003,1:7380
[39] Reigber C, Jochmann H, Wünsch J, et al. Earth Gravity Field and Seasonal Variability fromCHAMP. In: Reigber C, Lühr H, Schwintzer P, Wickert J (eds.), Earth Observation withCHAMP-Results from Three Years in Orbit, Springer, Berlin,2004,2530
[40] Mayer-Gürr T, Ilk K H, Eicker A, et al. ITG-CHAMP01: a CHAMP gravity field model fromshort kinematic arcs over a one-year observation period. Journal of Geodesy,2005,78:462480
[41]许厚泽,沈云中.利用CHAMP卫星星历恢复引力位模型的模拟研究.武汉大学学报·信息科学版,2001,26(6):483－486
[42] Visser P N A M, van den IJssel J. Verification of CHAMP accelerometer observations.Advanced Space Reviews,2003,31(8):1905－1910
[43] Klokocnik J, Kostelecky J, Wagner C A, et al. Evaluation of the accuracy of the EIGEN-1Sand-2CHAMP-derived gravity field models by satellite crossover altimetry. Journal ofGeodesy,2005,78(7):405－417
[44] Bruinsma S, Loyer S, Lemoine J M, et al. The impact of accelerometry on CHAMP orbitdetermination. Journal of Geodesy,2003,77(1):86－93
[45] Moore P, Turner J F, Oiang Z. CHAMP orbit determination and gravity field recovery.Advanced Space Reviews,2003,31(8):1897－1903
[46]周旭华,吴斌,彭碧波,许厚泽.利用CHAMP科学轨道数据和星载加速度数据反演地球重力场.武汉大学学报·信息科学版,2006,31(2):172－175
[47] Van Den IJssel J, Visser P N A M. Determination of non-gravitational accelerations fromGPS satellite-to-satellite tracking of CHAMP. Advances in Space Research,2005,36(3):418－423
[48] Thompson B F. Spaceborne accelerometry and temporal gravity analysis from the CHAMPsatellite mission [Dissertation for the Doctoral Degree]. The University of Colorado,2005,1－163
[49] Reigber C, Schwintzer P, Neumayer K H, et al. The CHAMP-only Earth Gravity Field ModelEIGEN-2. Advances in Space Research,2003,31(8):18831888
[50] Reigber C, Jochmann H, Wünsch J, et al.: Earth Gravity Field and Seasonal Variability fromCHAMP. In: Reigber C, Lühr H, Schwintzer P, Wickert J (eds.), Earth Observation withCHAMP-Results from Three Years in Orbit, Springer, Berlin,2005,25-30
[51] Kim J. Simulation study of a low-low satellite-to-satellite tracking mission [PhDDissertation]. Austin: The University of Texas at Austin,2000,1－276
[52] Frommknecht B, Oberndorfer H, Flechtner F, et al. Integrated sensor analysis for GRACE－development and validation. Advances in Geosciences,2003
[53] Frommknecht B. Integrated sensor analysis of the GRACE mission [PhD Dissertation].München: Technische Universit t München,2007
[54] Visser P N A M, van den IJssel J. Aiming at a1-cm orbit for low earth orbiters: reduced-dynamic and kinematic precise orbit determination. Space Science Reviews,2003,108(1):27－36
[55] Cui ch, Lelgemann D. On non-linear low-low SST observation equations for thedetermination of geopotential based on an analytical solution. Journal of Geodesy,2000,74(5):431－440
[56] Rowlands D D, Ray R D, Chinn D S, et al. Short-arc analysis of intersatellite tracking data ina gravity mapping mission. Journal of Geodesy,2002,76(6):307－316
[57] Wagner C, McAdoo D, klokocnik J, et al. Degradation of geopotential recovery from shortrepeat-cycle orbits: application to GRACE monthly fields. Journal of Geodesy,2006,80(2):94－103
[58] Kohlhase A O, Kroes R, D‘Amico S. Interferometric baseline performance estimations formultistatic synthetic aperture radar configurations derived from GRACE GPS observations.Journal of Geodesy,2006,80(1):28－39
[59] Kang Z G, Tapley B, Bettadpur S, et al. Precise orbit determination for the GRACE missionusing only GPS data. Journal of Geodesy,2006,80(2):322－331
[60] Gotzelmann M, Keller W, Reubelt T. Gross error compensation for gravity field analysisbased on kinematic orbit data. Journal of Geodesy,2006,80(4):184－198
[61] Jekeli Ch. The determination of gravitational potential differences from satellite-to-satellitetracking. Celestial Mechanics and Dynamical Astronomy,1999,75:85–101
[62] Reigber C, Schmidt R, Flechtner F et al. An Earth gravity field model complete to degree andorder150from GRACE: EIGEN-GRACE02S, Journal of Geodynamics,2005,39(1):110
[63] GFZ.GRACE gravity model EIGEN-GRACE01S,2003，http://www.gfz-potsdam.de/grace/results/grav/g001EIGEN GRACE01S.pdf
[64] Foerste C, Schmidt R, Stubenvoll R, et al. The GeoForschungsZentrum Potsdam/Groupe deRecherche de Geodesie Spatiale satellite-only and combined gravity field models:EIGEN-GL04S1and EIGEN-GL04C. Journal of Geodesy,2008,82(6):331346
[65] Foerste C, Flechtner F, Schmidt R, et al. EIGEN-GL05C-A new global combinedhigh-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation. GeneralAssembly European Geosciences Union, Geophysical Research Abstracts,10, Vienna,Austria2008
[66] Tapley B, Bettadpur S, Watkins M, et al. The gravity recovery and climate experiment:mission overview and early results. Geophysical Research Letters,2004,31, L09607
[67] Tapley B, Ries J, Bettadpur S, et al. GGM02-An improved Earth gravity field model fromGRACE, Journal of Geodesy,2005,79:467478
[68] Tapley B, Ries J, Bettadpur S, et al. The GGM03mean earth gravity model from GRACE,Eos Trans. AGU,88(52), Fall Meet. Suppl., Abstract G42A-03,2007
[69] Rummel R, Colombo O L. Gravity field determination from satellite gradiometry [R].Bulletin Geodésique.1985,59(3):233246
[70]张传定.卫星重力测量——基础、模型化方法与数据处理算法[博士论文].郑州：中国人民解放军信息工程大学测绘学院.2000.
[71] Visser P N A M, Wakker K F, and Ambrosius B A C. Global gravity field recovery from theARISTOTELES satellite mission. J. Geophys. Res.,1994,99(B2):2841–2851,doi:10.1029/93JB02969
[72] Arabelos D, Tscherning C C. Improvements in height datum transfer expected from theGOCE mission. Journal of Geodesy,2001,75(5):308－312
[73] Kern M, Preimesberger T, Allesch M, et al. Outlier detection algorithms and theirperformance in GOCE gravity field processing. Journal of Geodesy,2005,78(9):509－519
[74] Oberndorfer H, Muller J. GOCE closed-loop simulation. Journal of Geodynamics,2002,33(1):53－63
[75] Pail R, Plank G. GOCE gravity field processing strategy. Studia Geophysica et Geodaetica,2004,48(2):289－309
[76] Marotta A M. Benefits from GOCE within solid Earth geophysics. Space Science Reviews,2003,108(1):95－104
[77] Bouman J, Koop R. Geodetic methods for calibration of GRACE and GOCE. Space ScienceReviews,2003,108(1):409－416
[78] Janák J, Pitonňák M. Comparison and testing of GOCE global gravity models in CentralEurope. Journal ofGeodetic Science,2011,1(4):333－347
[79] Schrama E J O. Error characteristics estimated from CHAMP, GRACE and GOCE derivedgeoids and from satellite altimetry derived mean dynamic topography. Space ScienceReviews,2003,108(1):179－193
[80] Prieto D, Ahmad Z. A drag free control based on model predictive techniques.2005American Control Conference, USA,2005,1527－1532
[81] Canuto E, Martella P. Attitude and drag control: an application to GOCE satellite. SpaceScience Reviews,2003,108(1):357－366
[82] Andreis D, Canuto E S. Drag-free and attitude control for the GOCE satellite. Proceedings ofthe44th IEEE Conference on Decision and Control, and the European Control Conference2005, Spain,4041－4046
[83] Visser P N A M, van den IJssel J. GPS-based precise orbit determination of the very lowEarth-orbiting gravity mission GOCE. Journal of Geodesy,2000,74(7):590－602
[84] Visser P N A M. Gravity field determination with GOCE and GRACE. Advances in SpaceResearch,1999,23(4):771－776
[85] Bock H, J ggi A, Meyer U, et al. GPS-derived orbits for the GOCE satellite. Journal ofGeodesy,2011, DOI10.1007/s00190-011-0484-9
[86] Visser P N A M, Ijssel J van den, Helleputte T Van, et al. Orbit determination for the GOCEsatellite. Advances in Space Research,2009,43:760－768
[87] Arsov K, Pail R. Assessment of two methods for gravity field recovery from GOCEGPS-SST orbit solutions. Advances in Geosciences,2003,1:121－126
[88] Pail R, Goiginger H, Schuh W-D, et al. Combined satellite gravity field model GOCO01Sderived from GOCE and GRACE. Geophysical Research Letters,2010,37, EID L20314
[89] Goiginger H, Hoeck E, Rieser D, et al. The combined satellite-only global gravity fieldmodel GOCO02S, presented at the2011General Assembly of the European GeosciencesUnion,2011, Vienna, Austria
[90] Albertella A, Migliaccio F, Sansó F. GOCE: the earth gravity field by space gradiometry.Celestial Mechanics and Dynamical Astronomy,2002,83:1–15
[91] Bouman J, Fuchs M J. GOCE gravity gradients versus global gravity field models.Geophysical Journal International,2012,189:846–850
[92] Koch K-R, Brockmann J M, Schuh W-D. Optimal regularization for geopotential modelGOCO02S by Monte Carlo methods and multi-scale representation of density anomalies.Journal of Geodesy,2012, DOI10.1007/s00190-012-0546-7
[93] Stummer C, Fecher T, Pail. Alternative method for angular rate determination within theGOCE gradiometer processing. Journal of Geodesy,2011, DOI10.1007/s00190-011-0461-3
[94] Pail R, Goiginger H, Schuh W-D. Combination of GOCE data with complementary gravityfield information. Proc. of4th International GOCE User Workshop,2011
[95] Reed G B (1973) Application of kinemati cal geodesy for determining the shorts wavelengthcomponent of the gravity field by satellite gradiometry, Ohio state University, Dept. ofGeod Science, Rep. No.201, Columbus, Ohio.
[96] Keller W, Sharifi M A. Satellite gradiometry using a satellite pair. Journal of Geodesy,2005,78:544―557
[97] Gruber T, Rummel R, Abrikosov O, van Hees R. GOCE level2product data handbook.GO-MA-HPF-GS-0110,2007, issue3.3
[98] Koop R. Global gravity field modeling using satellite gravity gradiometry, Publications onGeodesy, New series38, Netherlands Geodetic Commission,1993
[99] Hajela D P. Improved procedures for the recovery of5omean gravity anomalies fromATS-6/GEOS-3satellite-to-satellite range-rate observation. Rep276, Department of GeodeticScience, The Ohio State University, Columbus,1974
[100] Colombo O L. Advanced techniques for high-resolution mapping of the gravitational field. In:Theory of satellite geodesy and gravity field determination. Lecture notes in Earth sciences25. Springer, Berlin Heidelberg New York,1989,335–369
[101] Sneeuw N. A semi-analytical approach to gravity field analysis from satellite observations
[PhD Dissertation]. Munich: Technical University of Munich,2000
[102] Rummel R, van Gelderen M, Koop R, et al. Spherical Harmonic Analysis of SatelliteGradiometry. Publications on Geodesy, New Series39, Netherlands Geodetic Commission,1993
[103] Rummel R. Spherical spectral properties of the Earth‘s gravitational potential and its frst andsecond derivatives. In: Lecture Notes in Earth Sciences, Vol.65. Heidelberg: Springer,1997.359–405
[104] Rummel R, Colombo O L. Gravity field determination from satellite gradiometry. Bull Géod,1985,57:233–246
[105] Colombo O L. The global mapping of the gravity field with an orbiting full-tensorgradiometer: an error analysis. IUGG, Vancouver,1987,250–266
[106]高防，月球引力梯度测量与反演研究，课题组内部报告，2012年6月
[107] Visser P, Sneeuw N, Gerlach C. Energy integral method for gravity field determination fromsatellite orbit coordinates. Journal of Geodesy,2003,77:207–216
[108]徐天河.利用CHAMP卫星轨道和加速度计数据推求地球重力场模型[博士论文].郑州:信息工程大学测绘学院,2004
[109] Wagner C A. Direct determination of gravitational harmonics from low-low GRAVSAT data.Journal of Geophysical Research,1983,88(B12):10,309–10,321
[110]周旭华,许厚泽,吴斌等.用GRACE卫星跟踪数据反演地球重力场.地球物理学报,2006,49(3):718–723
[111]宁津生,钟波,罗志才等.基于能量守恒的星间距离变率与地球重力场频谱关系的建立与分析.武汉大学学报,2008,33(3):221–225
[112]沈云中,许厚泽.卫—卫跟踪重力卫星测量模式的模拟与精度分析.大地测量与地球动力学进展.武汉：湖北科学技术出版社,2004,211–218
[113] Schrama E. Gravity field error analysis: application of GPS receivers and gradiometers onlow orbiting platforms. NASA TM-100769, GSFC Greenbelt MD.20771,1990
[114] Tscherning C C. Computation of spherical harmonic coefficients and their error estimatesusing Least Squares Collocation. Journal of Geodesy,2001,75:12–18
[115] Baur O, Austen G, Kusche J. Efficient GOCE satellite gravity field recovery based onleast-squares using QR decomposition. Journal of Geodesy,2008,82(4-5):207–221
[116] Sharifi M A. Satellite to satellite tracking in the space-wise approach [PhD Dissertation].Germany: Geo tisches Institute der Universit t Sttutgart,2006
[117] Hajela D P. Improved procedures for the recovery of5omean gravity anomalies fromATS-6/GEOS-3satellite-to-satellite range-rate observation. Rep276, Department of GeodeticScience, The Ohio State University, Columbus,1974
[118] Rummel R. Geoid height, geoid height differences, and mean gravity anomalies from low–low‘satellite-to-satellite tracking—an error analysis. Rep306, Department of GeodeticScience, The Ohio State University, Columbus,1980
[119] Garcia R V. Local geoid determination from GRACE mis-sion. Rep460, Department ofGeodetic Science, The Ohio State University, Columbus,2002
[120] Han SC, Jekeli C, Shum CK () Static and temporal gravity field recovery using gracepotential difference observables. Adv Geosci,2003,1:19–26
[121] Cesare S. Performance requirements and budgets for the gradiometric mission. TechnicalNote, GO-TN-AI-0027, Issue04, Thales Alenia Space,2008.
[122]祝竺，高精度空间静电重力梯度仪，课题组内部报告，2010年9月
[123] Schuh WD. In-orbit calibration and local gravity field continuation problem. In: ESA-Project(ed): ESA-Project―FromE tv s to mGal+‖, WP1, Final-Report,2002
[124] Drinkwater M R, Haagmans R, Muzi D et al. The GOCE Gravity Mission: ESA's First CoreEarth Explorer, Proceedings of3rd International GOCE User Workshop,6-8November,2006,Frascati, Italy, ESA SP-627, ISBN92-9092-938-3, pp.1-8,2007
[125] Yi W, private communication,2012
[126] W.-D. Schuh, C. Boxhammer, and C. Siemes. Correlations, variances, covariances—fromGOCE signals to GOCE products. In3rdGOCE user work-shop, Frascati,2006. ESA.
[127] Colombo O.L.,1981. Numerical Methods for Harmonic Analysis on the Sphere. TechnicalReport310, Ohio State University, Columbus, Ohio.
[128]蔡林,周泽兵,祝竺等.卫星重力梯度恢复地球重力场的频谱分析.地球物理学报,2012,55(5):1565-1571
[129] Migliaccio F, Reguzzoni M, Sansò F. Space-wise approach to satellite gravity fielddetermination in the presence of colored noise. J Geod,2004,78:304–313
[130]奥本海姆A V.离散时间信号处理.清华大学出版社,2007
[131]冈萨雷斯,伍兹,埃丁斯,等.数字图像处理.电子工业出版社,2005
[132] Sneeuw N. Global spherical harmonic analysis by least‐squares and numerical quadraturemethods in historical perspective. Geophysical Journal International,1994,118(3):707–716.
[133] Sneeuw N, Bun R. Global spherical harmonic computation by two-dimensional Fouriermethods. Journal of Geodesy,1996,70(4):224–232.
[134] Cai L, Zhou Z, Hsu H, Gao F, Zhu Z, Luo J. Analytical error analysis for satellite gravityfield determination based on two-dimensional Fourier method. Journal of Geodesy,2013,87(5):417–426
[135] Krasbutter I, Brockmann J M, Kargoll B, et al. Stochastic model refinements for GOCEgradiometry data, Geotechnologien Status Seminar, Bonn/Germany,2010
[136] Marque J, et al. The ultra sensitive accelerometers of the ESA GOCE mission. In59th IACCongress, Glasgow, Scotland,29September-3October2008
[137] Ditmar P, Kusche J, Klees R. Computation of spheri-cal harmonic coefficients from gravitygradiometry da-ta to be acquired by the GOCE satellite: regularization ssues. J Geod,2003,77:465–477
[138] Schrama E. Gravity Field Error Analysis: Applications of Global Positioning SystemReceivers and Gradiometers on Low Orbiting Platforms. Journal of Goephysical Research,1991,96(B12):20041–20051
[139] Schrama E J O. The role of orbit errors in processing of satellite altimeter data. NertherlandsGeodetic Commission, Publications on Geodesy, New Series, No.33,1989
[140]陈俊勇，宁津生，章传银等.在嫦娥一号探月工程中求定月球重力场.地球物理学报,2005,48(2):275–281
[141] Binder A B. Lunar Prospector: Overview. Science.1998,281:1475–1476
[142] Konopliv A S, Asmar S W, Carranza E, et al. Recent gravity models as a result of the LunarProspector Mission. Icarus.2001,150:1–18
[143] Konopliv A S, Binder A B, Hood L L, et al. Improved gravity field of the Moon from LunarProspector. Science.1998,281:1476–1480
[144] Bills B G, Ferrari A J. A harmonic analysis of lunar gravity. Journal of Geophysical Research.1980,85(B2):1013–1025
[145] Ferrari A J. Lunar gravity: a harmonic analysis. Journal of Geophysical Research.1977,82(20):3065–3084
[146] Konopliv A S, Binder A B, Hood L L, et al. Improved gravity field of the Moon from LunarProspector. Science.1998,281:1476–1480
[147] Liu Q, Kikuchi F, Matsumoto K, et al. Same-beam VLBI observation of SELENE forimproving lunar gravity field model. Radio Science.2010,45(RS2004)
[148] Kikuchi F, Liu Q, Hanada H, et al. Picosecond accuracy VLBI of the two subsatellite ofSELENE(KAGUYA) using multifrequency and same beam methods. Radio Science.2009,44(RS2008)
[149] Hoffman T L. GRAIL: gravity mapping the moon. In: Aerospace Conference2009, IEEE.2009:1–8
[150] Zuber M T, Smith D E, Watkins M M, et al. Gravity field of the Moon from the GravityRecovery and Interior Laboratory (GRAIL) mission. Science,2013,339(6120):668-671.
[151] Zuber M T, Smith D E, Asmar S W, et al. Gravity Recovery and Interior Laboratory (GRAIL):Extended Mission and Endgame Status. LPI Contributions,2013,1719:1777
[152] Goossens S J, Lemoine F G, Sabaka T J, et al. High Degree and Order Gravity Field Modelsof the Moon Derived From GRAIL Primary and Extended Mission Data. LPI Contributions,2013,1719:2382
[153] Zuber M T, Smith D E, Lehman D H, et al. Gravity Recovery and Interior Laboratory(GRAIL): Mapping the lunar interior from crust to core. Space Science Reviews,2013:1-22.
[154] Asmar S W, Konopliv A S, Watkins M M, et al. The scientific measurement system of theGravity Recovery and Interior Laboratory (GRAIL) mission. Space Science Reviews,2012:1-31
[155] Iwata T, Hanada H, Kawano N, et al. Global lunar gravity mapping using SELENEsub-satellites. In: Workshop on Moon Beyond2002,2002
[156] Sneeuw N, Flury J, Rummel R. Science requirements on future missions and simulatedmission scenarios. Earth, Moon, and Planets.2005,94(1-2):113–142
[157] Cai L, Zhou Z, Gao F, Luo J. Lunar gravity gradiometry and requirement analysis. Advancesin Space Research,2013(Accept)
[2]许厚泽.我国精化大地水准面工作中若干问题的讨论.地理空间信息,2006,4(5):1－4
[3] Rummel R, Horwath M, Yi W, et al. GOCE, Satellite Gravimetry and Antarctic MassTransports. Surveys in Geophysics,2011,32:643－657
[4]宁津生.跟踪世界发展动态致力地球重力场研究.武汉大学学报信息科学版，2001，26(6)：471474
[5]宁津生.卫星重力探测技术与地球重力场研究.大地测量与地球动力学，2002，22：l5
[6]许厚泽,周旭华,彭碧波.卫星重力测量.地理空间信息,2005,3(1):1－3
[7]许厚泽.卫星重力研究：21世纪大地测量研究的新热点.测绘科学，2001，26(3)：13
[8] Reigber C, Balmino G, Schwintzer P, et al. A high quality global gravity field model fromCHAMP GPS tracking data and accelerometry (EIGEN-1S). Geophysical Research Letters,2002,29(14):371374
[9] Jekeli C. The determination of gravitational potential differences from satellite-to-satellitetracking. Celestial Mechanics and Dynamical Astronomy,1999,75(2):85101
[10] Tapley B D, Bettadqur S. The gravity recovery and climate experiment: mission overviewand early results. Geophysical Research Letters,2004,31: L09607.
[11] European Space Agency. Gravity field and steady-state ocean Circulation ExplorationReports for Mission Selection. The four candidate Earth Explorer Core Missions, SP-1233(1).European Space Agency,1999
[12] Rummel R, Yi W, Stummer C. GOCE gravitational gradiometry. Journal of Geodesy,2011,85:777–790
[13] Hirt C, Gruber T, Featherstone W E. Evaluation of the first GOCE static gravity field modelsusing terrestrial gravity, vertical deflec-tions and EGM2008quasigeoid heights. J Geod,2011,85:723–740
[14] Ilk K H, Flury J, Rummel R et al. Mass transport and mass distribution in the earth system.Proposal for a German Priority Research Program, GeoForschungs Zentrum Potsdam.2004
[15]陈俊勇.现代低轨卫星对地球重力场探测的实践和进展.测绘科学,2002,27(1):8－10
[16] Visser P N A M, van den IJssel J, Koop R, et al. Exploring gravity field determination fromorbit perturbations of the European gravity mission GOCE. Journal of Geodesy,2001,75(2):89－98
[17] Hwang C. Gravity recovery using COSMIC GPS data: application of orbital perturbationtheory. Journal of Geodesy,2001,75(2):117－136
[18] Cheng M K. Gravitational perturbation theory for intersatellite tracking. Journal of Geodesy,2002,76(3):169－185
[19]罗佳.利用卫星跟踪卫星确定地球重力场的理论和方法[博士论文].武汉：武汉大学，2003
[20]陆仲连，吴晓平编著，人造地球卫星与地球重力场.北京：测绘出版社，1994
[21]李建成，宁津生，晁定波等.卫星测高在大地测量学中的应用及进展.测绘科学，2006，31(6)：1923
[22]翟国君，黄谟涛，欧阳永忠等.卫星测高原理及其应用.海洋测绘，2002，22(1)：5762
[23] Wahr J, Wingham D, Bentley C. A method of combining ICESat and GRACE satellite data toconstrain Antarctic mass balance. Journal of Geophysical Research,2000,105(b7):16279－16294
[24] Zhang F P, Huang C, Liao X H, et al. Precision ERS-2orbit determination combiningmultiple tracking techniques. Chinese Science Bulletin,2001,44(20):1756－1760
[25]汪海洪，钟波，王伟，于丹.卫星测高的局限与新技术发展.大地测量与地球动力学，2009，29(1)：9195
[26] Han S-C, Jekeli C, Shum C K. Efficient gravity field recovery using in situ disturbingpotential observables from CHAMP. Geophysical Research Letters,2002,29(16):10.1029/2002GL015180
[27] Howe E, Stenseng L, Tscherning C C. Analysis of one month of CHAMP state vector andaccelerometer data for the recovery of the gravity potential. Advances in Geosciences,2003,1:14
[28]徐天河,杨元喜.基于能量守恒方法恢复CHAMP重力场模型.测绘学报,2005,34(1)：16
[29] Touboul P, Bernard A. Electrostatic accelerometers for the equivalence principle test in space,Advances in Space Research,2003,32,1357
[30] Touboul P, Foulon B, Bernard A. Electrostatic servocontrolled accelerometers for futre spacemissions, Futre Fundamental Physics Missions in Space and Enabling Technologies, ElEscroial, Spain, Apr.5-7,1994
[31] Bernard A and Touboul P. The GRADIO accelerometer design and development status,Workship ESA/NASA on the Solid-Earth Mission ARISTOTELES, Anacapri, Italy, Sep.23-24,1991
[32] Bruinsma S, Tamagnan D, Biancale R. Atmospheric densities derived from CHAMP/STARaccelerometer observations. Planetary and Space Science,2004,52,297
[33]祝竺，张晓敏，周泽兵.利用旋转卫星法开展加速度计在轨检验研究.宇航学报，2010，31(5):13621367
[34] Flury J, Bettadpur S, Tapley B D. Precise accelerometry onboard the grace gravity fieldsatellite mission. Advances in Space Research,2008,42,1414
[35]白彦峥，田蔚，周泽兵等.高精度空间加速度计及其应用.空间科学学报，2010，30(6):601606
[36]周泽兵，白彦峥，祝竺等.卫星重力测量中加速度计在轨参数校准方法研究.中国空间科学技术，2009，6:7480
[37] Touboul P, Foulon B, Willemenota E. Electrostatic space accelerometers for present andfuture missions. Acta Astronautica,1999,45,605
[38] Gerlach Ch, Sneeuw N, Visser, et al. CHAMP gravity field recovery using the energy balanceapproach. Advances in Geosciences,2003,1:7380
[39] Reigber C, Jochmann H, Wünsch J, et al. Earth Gravity Field and Seasonal Variability fromCHAMP. In: Reigber C, Lühr H, Schwintzer P, Wickert J (eds.), Earth Observation withCHAMP-Results from Three Years in Orbit, Springer, Berlin,2004,2530
[40] Mayer-Gürr T, Ilk K H, Eicker A, et al. ITG-CHAMP01: a CHAMP gravity field model fromshort kinematic arcs over a one-year observation period. Journal of Geodesy,2005,78:462480
[41]许厚泽,沈云中.利用CHAMP卫星星历恢复引力位模型的模拟研究.武汉大学学报·信息科学版,2001,26(6):483－486
[42] Visser P N A M, van den IJssel J. Verification of CHAMP accelerometer observations.Advanced Space Reviews,2003,31(8):1905－1910
[43] Klokocnik J, Kostelecky J, Wagner C A, et al. Evaluation of the accuracy of the EIGEN-1Sand-2CHAMP-derived gravity field models by satellite crossover altimetry. Journal ofGeodesy,2005,78(7):405－417
[44] Bruinsma S, Loyer S, Lemoine J M, et al. The impact of accelerometry on CHAMP orbitdetermination. Journal of Geodesy,2003,77(1):86－93
[45] Moore P, Turner J F, Oiang Z. CHAMP orbit determination and gravity field recovery.Advanced Space Reviews,2003,31(8):1897－1903
[46]周旭华,吴斌,彭碧波,许厚泽.利用CHAMP科学轨道数据和星载加速度数据反演地球重力场.武汉大学学报·信息科学版,2006,31(2):172－175
[47] Van Den IJssel J, Visser P N A M. Determination of non-gravitational accelerations fromGPS satellite-to-satellite tracking of CHAMP. Advances in Space Research,2005,36(3):418－423
[48] Thompson B F. Spaceborne accelerometry and temporal gravity analysis from the CHAMPsatellite mission [Dissertation for the Doctoral Degree]. The University of Colorado,2005,1－163
[49] Reigber C, Schwintzer P, Neumayer K H, et al. The CHAMP-only Earth Gravity Field ModelEIGEN-2. Advances in Space Research,2003,31(8):18831888
[50] Reigber C, Jochmann H, Wünsch J, et al.: Earth Gravity Field and Seasonal Variability fromCHAMP. In: Reigber C, Lühr H, Schwintzer P, Wickert J (eds.), Earth Observation withCHAMP-Results from Three Years in Orbit, Springer, Berlin,2005,25-30
[51] Kim J. Simulation study of a low-low satellite-to-satellite tracking mission [PhDDissertation]. Austin: The University of Texas at Austin,2000,1－276
[52] Frommknecht B, Oberndorfer H, Flechtner F, et al. Integrated sensor analysis for GRACE－development and validation. Advances in Geosciences,2003
[53] Frommknecht B. Integrated sensor analysis of the GRACE mission [PhD Dissertation].München: Technische Universit t München,2007
[54] Visser P N A M, van den IJssel J. Aiming at a1-cm orbit for low earth orbiters: reduced-dynamic and kinematic precise orbit determination. Space Science Reviews,2003,108(1):27－36
[55] Cui ch, Lelgemann D. On non-linear low-low SST observation equations for thedetermination of geopotential based on an analytical solution. Journal of Geodesy,2000,74(5):431－440
[56] Rowlands D D, Ray R D, Chinn D S, et al. Short-arc analysis of intersatellite tracking data ina gravity mapping mission. Journal of Geodesy,2002,76(6):307－316
[57] Wagner C, McAdoo D, klokocnik J, et al. Degradation of geopotential recovery from shortrepeat-cycle orbits: application to GRACE monthly fields. Journal of Geodesy,2006,80(2):94－103
[58] Kohlhase A O, Kroes R, D‘Amico S. Interferometric baseline performance estimations formultistatic synthetic aperture radar configurations derived from GRACE GPS observations.Journal of Geodesy,2006,80(1):28－39
[59] Kang Z G, Tapley B, Bettadpur S, et al. Precise orbit determination for the GRACE missionusing only GPS data. Journal of Geodesy,2006,80(2):322－331
[60] Gotzelmann M, Keller W, Reubelt T. Gross error compensation for gravity field analysisbased on kinematic orbit data. Journal of Geodesy,2006,80(4):184－198
[61] Jekeli Ch. The determination of gravitational potential differences from satellite-to-satellitetracking. Celestial Mechanics and Dynamical Astronomy,1999,75:85–101
[62] Reigber C, Schmidt R, Flechtner F et al. An Earth gravity field model complete to degree andorder150from GRACE: EIGEN-GRACE02S, Journal of Geodynamics,2005,39(1):110
[63] GFZ.GRACE gravity model EIGEN-GRACE01S,2003，http://www.gfz-potsdam.de/grace/results/grav/g001EIGEN GRACE01S.pdf
[64] Foerste C, Schmidt R, Stubenvoll R, et al. The GeoForschungsZentrum Potsdam/Groupe deRecherche de Geodesie Spatiale satellite-only and combined gravity field models:EIGEN-GL04S1and EIGEN-GL04C. Journal of Geodesy,2008,82(6):331346
[65] Foerste C, Flechtner F, Schmidt R, et al. EIGEN-GL05C-A new global combinedhigh-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation. GeneralAssembly European Geosciences Union, Geophysical Research Abstracts,10, Vienna,Austria2008
[66] Tapley B, Bettadpur S, Watkins M, et al. The gravity recovery and climate experiment:mission overview and early results. Geophysical Research Letters,2004,31, L09607
[67] Tapley B, Ries J, Bettadpur S, et al. GGM02-An improved Earth gravity field model fromGRACE, Journal of Geodesy,2005,79:467478
[68] Tapley B, Ries J, Bettadpur S, et al. The GGM03mean earth gravity model from GRACE,Eos Trans. AGU,88(52), Fall Meet. Suppl., Abstract G42A-03,2007
[69] Rummel R, Colombo O L. Gravity field determination from satellite gradiometry [R].Bulletin Geodésique.1985,59(3):233246
[70]张传定.卫星重力测量——基础、模型化方法与数据处理算法[博士论文].郑州：中国人民解放军信息工程大学测绘学院.2000.
[71] Visser P N A M, Wakker K F, and Ambrosius B A C. Global gravity field recovery from theARISTOTELES satellite mission. J. Geophys. Res.,1994,99(B2):2841–2851,doi:10.1029/93JB02969
[72] Arabelos D, Tscherning C C. Improvements in height datum transfer expected from theGOCE mission. Journal of Geodesy,2001,75(5):308－312
[73] Kern M, Preimesberger T, Allesch M, et al. Outlier detection algorithms and theirperformance in GOCE gravity field processing. Journal of Geodesy,2005,78(9):509－519
[74] Oberndorfer H, Muller J. GOCE closed-loop simulation. Journal of Geodynamics,2002,33(1):53－63
[75] Pail R, Plank G. GOCE gravity field processing strategy. Studia Geophysica et Geodaetica,2004,48(2):289－309
[76] Marotta A M. Benefits from GOCE within solid Earth geophysics. Space Science Reviews,2003,108(1):95－104
[77] Bouman J, Koop R. Geodetic methods for calibration of GRACE and GOCE. Space ScienceReviews,2003,108(1):409－416
[78] Janák J, Pitonňák M. Comparison and testing of GOCE global gravity models in CentralEurope. Journal ofGeodetic Science,2011,1(4):333－347
[79] Schrama E J O. Error characteristics estimated from CHAMP, GRACE and GOCE derivedgeoids and from satellite altimetry derived mean dynamic topography. Space ScienceReviews,2003,108(1):179－193
[80] Prieto D, Ahmad Z. A drag free control based on model predictive techniques.2005American Control Conference, USA,2005,1527－1532
[81] Canuto E, Martella P. Attitude and drag control: an application to GOCE satellite. SpaceScience Reviews,2003,108(1):357－366
[82] Andreis D, Canuto E S. Drag-free and attitude control for the GOCE satellite. Proceedings ofthe44th IEEE Conference on Decision and Control, and the European Control Conference2005, Spain,4041－4046
[83] Visser P N A M, van den IJssel J. GPS-based precise orbit determination of the very lowEarth-orbiting gravity mission GOCE. Journal of Geodesy,2000,74(7):590－602
[84] Visser P N A M. Gravity field determination with GOCE and GRACE. Advances in SpaceResearch,1999,23(4):771－776
[85] Bock H, J ggi A, Meyer U, et al. GPS-derived orbits for the GOCE satellite. Journal ofGeodesy,2011, DOI10.1007/s00190-011-0484-9
[86] Visser P N A M, Ijssel J van den, Helleputte T Van, et al. Orbit determination for the GOCEsatellite. Advances in Space Research,2009,43:760－768
[87] Arsov K, Pail R. Assessment of two methods for gravity field recovery from GOCEGPS-SST orbit solutions. Advances in Geosciences,2003,1:121－126
[88] Pail R, Goiginger H, Schuh W-D, et al. Combined satellite gravity field model GOCO01Sderived from GOCE and GRACE. Geophysical Research Letters,2010,37, EID L20314
[89] Goiginger H, Hoeck E, Rieser D, et al. The combined satellite-only global gravity fieldmodel GOCO02S, presented at the2011General Assembly of the European GeosciencesUnion,2011, Vienna, Austria
[90] Albertella A, Migliaccio F, Sansó F. GOCE: the earth gravity field by space gradiometry.Celestial Mechanics and Dynamical Astronomy,2002,83:1–15
[91] Bouman J, Fuchs M J. GOCE gravity gradients versus global gravity field models.Geophysical Journal International,2012,189:846–850
[92] Koch K-R, Brockmann J M, Schuh W-D. Optimal regularization for geopotential modelGOCO02S by Monte Carlo methods and multi-scale representation of density anomalies.Journal of Geodesy,2012, DOI10.1007/s00190-012-0546-7
[93] Stummer C, Fecher T, Pail. Alternative method for angular rate determination within theGOCE gradiometer processing. Journal of Geodesy,2011, DOI10.1007/s00190-011-0461-3
[94] Pail R, Goiginger H, Schuh W-D. Combination of GOCE data with complementary gravityfield information. Proc. of4th International GOCE User Workshop,2011
[95] Reed G B (1973) Application of kinemati cal geodesy for determining the shorts wavelengthcomponent of the gravity field by satellite gradiometry, Ohio state University, Dept. ofGeod Science, Rep. No.201, Columbus, Ohio.
[96] Keller W, Sharifi M A. Satellite gradiometry using a satellite pair. Journal of Geodesy,2005,78:544―557
[97] Gruber T, Rummel R, Abrikosov O, van Hees R. GOCE level2product data handbook.GO-MA-HPF-GS-0110,2007, issue3.3
[98] Koop R. Global gravity field modeling using satellite gravity gradiometry, Publications onGeodesy, New series38, Netherlands Geodetic Commission,1993
[99] Hajela D P. Improved procedures for the recovery of5omean gravity anomalies fromATS-6/GEOS-3satellite-to-satellite range-rate observation. Rep276, Department of GeodeticScience, The Ohio State University, Columbus,1974
[100] Colombo O L. Advanced techniques for high-resolution mapping of the gravitational field. In:Theory of satellite geodesy and gravity field determination. Lecture notes in Earth sciences25. Springer, Berlin Heidelberg New York,1989,335–369
[101] Sneeuw N. A semi-analytical approach to gravity field analysis from satellite observations
[PhD Dissertation]. Munich: Technical University of Munich,2000
[102] Rummel R, van Gelderen M, Koop R, et al. Spherical Harmonic Analysis of SatelliteGradiometry. Publications on Geodesy, New Series39, Netherlands Geodetic Commission,1993
[103] Rummel R. Spherical spectral properties of the Earth‘s gravitational potential and its frst andsecond derivatives. In: Lecture Notes in Earth Sciences, Vol.65. Heidelberg: Springer,1997.359–405
[104] Rummel R, Colombo O L. Gravity field determination from satellite gradiometry. Bull Géod,1985,57:233–246
[105] Colombo O L. The global mapping of the gravity field with an orbiting full-tensorgradiometer: an error analysis. IUGG, Vancouver,1987,250–266
[106]高防，月球引力梯度测量与反演研究，课题组内部报告，2012年6月
[107] Visser P, Sneeuw N, Gerlach C. Energy integral method for gravity field determination fromsatellite orbit coordinates. Journal of Geodesy,2003,77:207–216
[108]徐天河.利用CHAMP卫星轨道和加速度计数据推求地球重力场模型[博士论文].郑州:信息工程大学测绘学院,2004
[109] Wagner C A. Direct determination of gravitational harmonics from low-low GRAVSAT data.Journal of Geophysical Research,1983,88(B12):10,309–10,321
[110]周旭华,许厚泽,吴斌等.用GRACE卫星跟踪数据反演地球重力场.地球物理学报,2006,49(3):718–723
[111]宁津生,钟波,罗志才等.基于能量守恒的星间距离变率与地球重力场频谱关系的建立与分析.武汉大学学报,2008,33(3):221–225
[112]沈云中,许厚泽.卫—卫跟踪重力卫星测量模式的模拟与精度分析.大地测量与地球动力学进展.武汉：湖北科学技术出版社,2004,211–218
[113] Schrama E. Gravity field error analysis: application of GPS receivers and gradiometers onlow orbiting platforms. NASA TM-100769, GSFC Greenbelt MD.20771,1990
[114] Tscherning C C. Computation of spherical harmonic coefficients and their error estimatesusing Least Squares Collocation. Journal of Geodesy,2001,75:12–18
[115] Baur O, Austen G, Kusche J. Efficient GOCE satellite gravity field recovery based onleast-squares using QR decomposition. Journal of Geodesy,2008,82(4-5):207–221
[116] Sharifi M A. Satellite to satellite tracking in the space-wise approach [PhD Dissertation].Germany: Geo tisches Institute der Universit t Sttutgart,2006
[117] Hajela D P. Improved procedures for the recovery of5omean gravity anomalies fromATS-6/GEOS-3satellite-to-satellite range-rate observation. Rep276, Department of GeodeticScience, The Ohio State University, Columbus,1974
[118] Rummel R. Geoid height, geoid height differences, and mean gravity anomalies from low–low‘satellite-to-satellite tracking—an error analysis. Rep306, Department of GeodeticScience, The Ohio State University, Columbus,1980
[119] Garcia R V. Local geoid determination from GRACE mis-sion. Rep460, Department ofGeodetic Science, The Ohio State University, Columbus,2002
[120] Han SC, Jekeli C, Shum CK () Static and temporal gravity field recovery using gracepotential difference observables. Adv Geosci,2003,1:19–26
[121] Cesare S. Performance requirements and budgets for the gradiometric mission. TechnicalNote, GO-TN-AI-0027, Issue04, Thales Alenia Space,2008.
[122]祝竺，高精度空间静电重力梯度仪，课题组内部报告，2010年9月
[123] Schuh WD. In-orbit calibration and local gravity field continuation problem. In: ESA-Project(ed): ESA-Project―FromE tv s to mGal+‖, WP1, Final-Report,2002
[124] Drinkwater M R, Haagmans R, Muzi D et al. The GOCE Gravity Mission: ESA's First CoreEarth Explorer, Proceedings of3rd International GOCE User Workshop,6-8November,2006,Frascati, Italy, ESA SP-627, ISBN92-9092-938-3, pp.1-8,2007
[125] Yi W, private communication,2012
[126] W.-D. Schuh, C. Boxhammer, and C. Siemes. Correlations, variances, covariances—fromGOCE signals to GOCE products. In3rdGOCE user work-shop, Frascati,2006. ESA.
[127] Colombo O.L.,1981. Numerical Methods for Harmonic Analysis on the Sphere. TechnicalReport310, Ohio State University, Columbus, Ohio.
[128]蔡林,周泽兵,祝竺等.卫星重力梯度恢复地球重力场的频谱分析.地球物理学报,2012,55(5):1565-1571
[129] Migliaccio F, Reguzzoni M, Sansò F. Space-wise approach to satellite gravity fielddetermination in the presence of colored noise. J Geod,2004,78:304–313
[130]奥本海姆A V.离散时间信号处理.清华大学出版社,2007
[131]冈萨雷斯,伍兹,埃丁斯,等.数字图像处理.电子工业出版社,2005
[132] Sneeuw N. Global spherical harmonic analysis by least‐squares and numerical quadraturemethods in historical perspective. Geophysical Journal International,1994,118(3):707–716.
[133] Sneeuw N, Bun R. Global spherical harmonic computation by two-dimensional Fouriermethods. Journal of Geodesy,1996,70(4):224–232.
[134] Cai L, Zhou Z, Hsu H, Gao F, Zhu Z, Luo J. Analytical error analysis for satellite gravityfield determination based on two-dimensional Fourier method. Journal of Geodesy,2013,87(5):417–426
[135] Krasbutter I, Brockmann J M, Kargoll B, et al. Stochastic model refinements for GOCEgradiometry data, Geotechnologien Status Seminar, Bonn/Germany,2010
[136] Marque J, et al. The ultra sensitive accelerometers of the ESA GOCE mission. In59th IACCongress, Glasgow, Scotland,29September-3October2008
[137] Ditmar P, Kusche J, Klees R. Computation of spheri-cal harmonic coefficients from gravitygradiometry da-ta to be acquired by the GOCE satellite: regularization ssues. J Geod,2003,77:465–477
[138] Schrama E. Gravity Field Error Analysis: Applications of Global Positioning SystemReceivers and Gradiometers on Low Orbiting Platforms. Journal of Goephysical Research,1991,96(B12):20041–20051
[139] Schrama E J O. The role of orbit errors in processing of satellite altimeter data. NertherlandsGeodetic Commission, Publications on Geodesy, New Series, No.33,1989
[140]陈俊勇，宁津生，章传银等.在嫦娥一号探月工程中求定月球重力场.地球物理学报,2005,48(2):275–281
[141] Binder A B. Lunar Prospector: Overview. Science.1998,281:1475–1476
[142] Konopliv A S, Asmar S W, Carranza E, et al. Recent gravity models as a result of the LunarProspector Mission. Icarus.2001,150:1–18
[143] Konopliv A S, Binder A B, Hood L L, et al. Improved gravity field of the Moon from LunarProspector. Science.1998,281:1476–1480
[144] Bills B G, Ferrari A J. A harmonic analysis of lunar gravity. Journal of Geophysical Research.1980,85(B2):1013–1025
[145] Ferrari A J. Lunar gravity: a harmonic analysis. Journal of Geophysical Research.1977,82(20):3065–3084
[146] Konopliv A S, Binder A B, Hood L L, et al. Improved gravity field of the Moon from LunarProspector. Science.1998,281:1476–1480
[147] Liu Q, Kikuchi F, Matsumoto K, et al. Same-beam VLBI observation of SELENE forimproving lunar gravity field model. Radio Science.2010,45(RS2004)
[148] Kikuchi F, Liu Q, Hanada H, et al. Picosecond accuracy VLBI of the two subsatellite ofSELENE(KAGUYA) using multifrequency and same beam methods. Radio Science.2009,44(RS2008)
[149] Hoffman T L. GRAIL: gravity mapping the moon. In: Aerospace Conference2009, IEEE.2009:1–8
[150] Zuber M T, Smith D E, Watkins M M, et al. Gravity field of the Moon from the GravityRecovery and Interior Laboratory (GRAIL) mission. Science,2013,339(6120):668-671.
[151] Zuber M T, Smith D E, Asmar S W, et al. Gravity Recovery and Interior Laboratory (GRAIL):Extended Mission and Endgame Status. LPI Contributions,2013,1719:1777
[152] Goossens S J, Lemoine F G, Sabaka T J, et al. High Degree and Order Gravity Field Modelsof the Moon Derived From GRAIL Primary and Extended Mission Data. LPI Contributions,2013,1719:2382
[153] Zuber M T, Smith D E, Lehman D H, et al. Gravity Recovery and Interior Laboratory(GRAIL): Mapping the lunar interior from crust to core. Space Science Reviews,2013:1-22.
[154] Asmar S W, Konopliv A S, Watkins M M, et al. The scientific measurement system of theGravity Recovery and Interior Laboratory (GRAIL) mission. Space Science Reviews,2012:1-31
[155] Iwata T, Hanada H, Kawano N, et al. Global lunar gravity mapping using SELENEsub-satellites. In: Workshop on Moon Beyond2002,2002
[156] Sneeuw N, Flury J, Rummel R. Science requirements on future missions and simulatedmission scenarios. Earth, Moon, and Planets.2005,94(1-2):113–142
[157] Cai L, Zhou Z, Gao F, Luo J. Lunar gravity gradiometry and requirement analysis. Advancesin Space Research,2013(Accept)
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