应用低轨卫星跟踪数据反演地球重力场模型
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摘要
低轨卫星跟踪测量技术(CHAMP卫星和GRACE卫星)可提供覆盖全球的、高精度的空间重力观测资料：精密轨道数据、GRACE卫星的K波段观测数据等，这些观测数据包含了丰富的地球重力场信息，尤其是GRACE卫星的K波段观测数据。在当代低轨卫星的定轨精度达到比较高的程度(约2cm)，K波段观测数据将是地球重力场信息提取的主要载体，如何充分利用此类信息进行反演地球重力场模型的研究是当代大地测量研究的前沿和热点之一。其研究成果将对现代大地测量、地球物理、海洋科学以及地球动力学等学科的发展起到巨大的推动作用。
本文围绕应用低轨卫星跟踪数据反演地球重力场模型这一主题展开讨论，主要研究内容和创新点如下：
(1)在查阅大量国内外相关文献的基础上，对卫星重力探测技术的发展历程、国内外研究现状以及研究意义进行了阐述。讨论了目前常用的几种地球重力场模型反演算法，并分析了它们的优缺点。
(2)详细研究了卫星跟踪卫星重力测量所涉及到的时间系统、坐标系统以及空间运行卫星所受到的各类摄动力模型，给出了卫星重力测量的基本原理、常用的算法以及各类偏导数的计算。定性分析了卫星初始位置误差对应用卫星精密轨道数据反演地球重力场模型的影响，若不顾及其它测量误差(如加速度计测量误差)的影响，以2小时反演弧长为宜。
(3)详细讨论了CHAMP卫星和GRACE卫星相关观测数据的预处理方法，分析了姿态数据间断的三种情况，给出了利用二次插值法对间断的姿态数据进行填补，算例表明：在姿态数据间断40历元的情况下，二次插值法完全能满足精度要求。
(4)利用动力学法对CHAMP卫星的加速度计观测数据进行了重新标定，结果表明：加速度计的标定参数并不是一成不变的，一天标定结果的变化范围比1小时的要小，更接近GFZ给出的结果。加速度计重新标定后的重力场模型的精度要高于未标定的结果，因此对加速度计观测数据进行重新标定是十分必要的。
(5)详细介绍了笔者独立自主开发的卫星重力数据处理软件—GRASTAR，该软件是利用Visual C++语言平台开发完成的，可对CHAMP卫星和GRACE卫星观测数据进行处理，具有很好的可移植性和可拓展性。
(6)基于应用低轨卫星精密轨道数据反演地球重力场模型的动力学法，推导了将加速度计观测数据的尺度和偏差以及卫星初始状态向量与地球重力场位系数一起求解的数学模型，利用120天CHAMP卫星精密轨道和加速度计观测数据解算出50阶次的地球重力场模型TJCHAMP01S，检核结果表明：TJCHAMP01S模型精度优于相同阶次的EGM96和EIGEN-1S模型，并且更接近EIGEN-2模型。在我国区域，TJCHAMP01S和EIGEN-2模型与EIGEN-CG01C模型前30阶所表示的大地水准面差值的中误差分别为4.4cm和3.3cm。
(7)基于动力学法，利用26天GRACE卫星精密轨道和加速度计观测数据解算出36阶次的地球重力场模型TJGRACE01S_OR，检核结果表明：该模型的精度要优于相同阶次的EGM96和EIGEN-2模型，前20阶模型位系数与EIGEN-CHAMP03S精度相当。
(8)基于应用GRACE卫星星间距离变率数据反演地球重力场模型的动力学法，推导了将加速度计观测数据的尺度和偏差以及卫星初始相对速度向量与地球重力场位系数一起求解的数学模型，利用31天GRACE卫星星间距离变率和加速度计观测数据解算出60阶次的地球重力场模型TJGRACE01S，检核结果表明：TJGRACE01S模型的精度要明显优于相同阶次的EIGEN-CHAMP03S模型，但要稍逊于EIGEN-GRACE01S。利用EGM96、EIGEN-CHAMP03S、TJGRACE01S和EIGEN-GRACE01S模型的前60阶分别计算全球1°×1°格网点的大地水准面高度，并与EIGEN-GL04C模型的大地水准面高度做比较，相应差值的中误差分别为：0.446m、0.144m、0.027m和0.008m。
(9)利用67天GRACE卫星星间距离变率和加速度计观测数据解算出80阶次的地球重力场模型TJGRACE02S，检核结果表明：TJGRACE02S模型的精度要明显优于相同阶次的EIGEN-CHAMP03S模型，但要稍逊于GGM01S。利用EGM96、EIGEN-CHAMP03S、GGM01S和TJGRACE02S模型的前72阶分别计算全球2.5°×2.5°格网点的大地水准面高度和重力异常，并与EIGEN-GL04C模型的计算结果进行比较，大地水准面高度差值的中误差分别为：0.524m、0.305m、0.021m和0.052m，而重力异常差值的中误差分别为：4.00mGal、3.07mGal、0.21mGal和0.50mGal。
(10)对本文的工作进行总结，对未来的工作进行展望和规划。
The global coverage, high accuracy space gravity data, such as precision orbits andK-Band observables of GRACE, and so on can be provided by satellite-to-satellitetracking missions (e.g. CHAMP, GRACE), which contain abundant Earth gravity fieldinformation, specially K-Band observables of GRACE. Nowadays, the orbit of LEOsatellite has been determined with an accuracy of a few cm (approximately 2cm), therefore the K-band observables will be the main carrier of Earth gravity fieldinformation. How to recover the gravity model based on the K-Band observables willbecome one of the hotspots in the world, and its results have a wide applicationforeground in modern geodesy, geophysics, oceanography, geodynamics, and so on.
The gravity model recovery on the basis of satellite-to-satellite tracking data ismainly discussed in this dissertation, and the main work and contributions aresummarized as following:
(1) The development history, domestic and overseas study present state andsignificance of satellite gravity technology are presented. A few methods forrecovering the Earth gravity field are discussed and their advantages anddisadvantages are also analyzed.
(2) The time system, coordinate system and the various perturbation force models ofsatellite-to-satellite tracking measurements are introduced in detail, the basis theoryand algorithm of satellite gravity measurements, and the calculation of partialderivative are also given in this dissertation. We analyzed the effect of initial stateerror of LEO satellite on the Earth gravity model recovery using the precision orbits.In the dissertation, simulated results also showed if the other measurement errors (e.g.accelerometer errors) are not considered, the arc length of two hours should be used.
(3) The preprocessing approaches for CHAMP and GRACE observables are discussedin detail, three cases of attitude data gap are analyzed and a quadratic interpolationmethod is proposed to fill the attitude data gap, The results can satisfy the requirementaccuracy in case of data gap less than 40 epochs.
(4) The scale factor and bias parameters of CHAMP satellite accelerometer data arere-calibrated based on the dynamical method, the results show that the calibrationparameters which are consistent with the results provided by GFZ are variational, andthe change scope of those parameters from one day data is smaller than that from an hour. The accuracy of Earth gravity field based on the calibrated accelerometer data ishigher, so it is necessary to do the re-calibrating work.
(5) The GRASTAR developed independently with Visual C++ has been introduced, which is used for processing satellite gravity data, including CHAMP and GRACEdata, and this software can be easily transplanted and maintained.
(6) The dynamical method for recovering gravity field model based on the precisionorbits and accelerometer data of CHAMP is discussed and the mathematical algorithmis enduced, in which the accelerometer scale and bias, the satellite's initial state vectorand the model coefficients are estimated simultaneously. The gravity field modelTJCHAMP01S up to degree/order 50 has been computed with this algorithm from the120-day CHAMP data including dynamical orbits and accelerometer data, and themodel is validated using various criteria. The results show that the modelTJCHAMP01S is more accurate than EGM96 and EIGEN-1S model of the samedegree and order, and is close to the model EIGEN-2. The geoid height differences ofTJCHAMP01S, EIGEN-2 with respect to EIGEN-CG01C are 4.4cm and 3.3cm up todegree/order 30 in our country.
(7) The gravity field model TJGRACE01 S_OR up to degree/order 36 has been computedfrom the 26-day GRACE data including dynamical orbits and accelerometer data, andthe model is validated using various criteria. The results show that the modelTJGRACE01S OR is more accurate than EGM96 and EIGEN-2 model of the samedegree and order, and is close to the model EIGEN-CHAMP03S up to degree/order 20.
(8) The dynamical method for recovering gravity field model based on the range rateand accelerometer data of GRACE is discussed and the mathematical algorithm isenduced, in which the accelerometer scale and bias, the satellite's initial relativevelocity vector and the model coefficients are estimated simultaneously. The gravityfield model TJGRACE01S up to degree/order 60 has been computed with this algorithmfrom the 31-day GRACE data including Range rate data and accelerometer data, andthe model is validated using various criteria. The results show that the modelTJGRACE01S is more accurate than EIGEN-CHAMP03S model of the same degreeand order, but is little inferior to the model EIGEN-GRACE01S. The EGM96, EIGEN-CHAMP03S, TJGRACE01S and EIGEN-GRACE01S are further evaluatedwith the global 1°×1°grids geoid height differences with respect to EIGEN-GL04Ccomputed until degree/order 60, corresponding mean error of geoid height differencesare 0.446m, 0o144m, 0.027m and 0.008m respectively.
(9) The gravity field model TJGRACE02S up to degree/order 80 has been computed withdynamical algorithm from the 67-day GRACE data including Range rate data andaccelerometer data, and the model is validated using various criteria. The results showthat the model TJGRACE02S is more accurate than EIGEN-CHAMP03S model ofthe same degree and order, but is little inferior to the model GGM01S. The EGM96, EIGEN-CHAMP03S, GGM01S and TJGRACE02S are further evaluated with theglobal 2.5°×2.5°grids geoid height differences and gravity anomaly differenceswith respect to EIGEN-GL04C computed until degree/order 72, corresponding meanerror of geoid height differences are 0.524m, 0.305m, 0.021m and 0.052mrespectively, and mean error of gravity anomaly differences are 4.00mGal, 3.07mGal, 0.21 mGal and 0.50 mGal respectively.
(10) The main results are summarized in the last chapter, and the outlook for futurework is also made.
本文围绕应用低轨卫星跟踪数据反演地球重力场模型这一主题展开讨论，主要研究内容和创新点如下：
(1)在查阅大量国内外相关文献的基础上，对卫星重力探测技术的发展历程、国内外研究现状以及研究意义进行了阐述。讨论了目前常用的几种地球重力场模型反演算法，并分析了它们的优缺点。
(2)详细研究了卫星跟踪卫星重力测量所涉及到的时间系统、坐标系统以及空间运行卫星所受到的各类摄动力模型，给出了卫星重力测量的基本原理、常用的算法以及各类偏导数的计算。定性分析了卫星初始位置误差对应用卫星精密轨道数据反演地球重力场模型的影响，若不顾及其它测量误差(如加速度计测量误差)的影响，以2小时反演弧长为宜。
(3)详细讨论了CHAMP卫星和GRACE卫星相关观测数据的预处理方法，分析了姿态数据间断的三种情况，给出了利用二次插值法对间断的姿态数据进行填补，算例表明：在姿态数据间断40历元的情况下，二次插值法完全能满足精度要求。
(4)利用动力学法对CHAMP卫星的加速度计观测数据进行了重新标定，结果表明：加速度计的标定参数并不是一成不变的，一天标定结果的变化范围比1小时的要小，更接近GFZ给出的结果。加速度计重新标定后的重力场模型的精度要高于未标定的结果，因此对加速度计观测数据进行重新标定是十分必要的。
(5)详细介绍了笔者独立自主开发的卫星重力数据处理软件—GRASTAR，该软件是利用Visual C++语言平台开发完成的，可对CHAMP卫星和GRACE卫星观测数据进行处理，具有很好的可移植性和可拓展性。
(6)基于应用低轨卫星精密轨道数据反演地球重力场模型的动力学法，推导了将加速度计观测数据的尺度和偏差以及卫星初始状态向量与地球重力场位系数一起求解的数学模型，利用120天CHAMP卫星精密轨道和加速度计观测数据解算出50阶次的地球重力场模型TJCHAMP01S，检核结果表明：TJCHAMP01S模型精度优于相同阶次的EGM96和EIGEN-1S模型，并且更接近EIGEN-2模型。在我国区域，TJCHAMP01S和EIGEN-2模型与EIGEN-CG01C模型前30阶所表示的大地水准面差值的中误差分别为4.4cm和3.3cm。
(7)基于动力学法，利用26天GRACE卫星精密轨道和加速度计观测数据解算出36阶次的地球重力场模型TJGRACE01S_OR，检核结果表明：该模型的精度要优于相同阶次的EGM96和EIGEN-2模型，前20阶模型位系数与EIGEN-CHAMP03S精度相当。
(8)基于应用GRACE卫星星间距离变率数据反演地球重力场模型的动力学法，推导了将加速度计观测数据的尺度和偏差以及卫星初始相对速度向量与地球重力场位系数一起求解的数学模型，利用31天GRACE卫星星间距离变率和加速度计观测数据解算出60阶次的地球重力场模型TJGRACE01S，检核结果表明：TJGRACE01S模型的精度要明显优于相同阶次的EIGEN-CHAMP03S模型，但要稍逊于EIGEN-GRACE01S。利用EGM96、EIGEN-CHAMP03S、TJGRACE01S和EIGEN-GRACE01S模型的前60阶分别计算全球1°×1°格网点的大地水准面高度，并与EIGEN-GL04C模型的大地水准面高度做比较，相应差值的中误差分别为：0.446m、0.144m、0.027m和0.008m。
(9)利用67天GRACE卫星星间距离变率和加速度计观测数据解算出80阶次的地球重力场模型TJGRACE02S，检核结果表明：TJGRACE02S模型的精度要明显优于相同阶次的EIGEN-CHAMP03S模型，但要稍逊于GGM01S。利用EGM96、EIGEN-CHAMP03S、GGM01S和TJGRACE02S模型的前72阶分别计算全球2.5°×2.5°格网点的大地水准面高度和重力异常，并与EIGEN-GL04C模型的计算结果进行比较，大地水准面高度差值的中误差分别为：0.524m、0.305m、0.021m和0.052m，而重力异常差值的中误差分别为：4.00mGal、3.07mGal、0.21mGal和0.50mGal。
(10)对本文的工作进行总结，对未来的工作进行展望和规划。
The global coverage, high accuracy space gravity data, such as precision orbits andK-Band observables of GRACE, and so on can be provided by satellite-to-satellitetracking missions (e.g. CHAMP, GRACE), which contain abundant Earth gravity fieldinformation, specially K-Band observables of GRACE. Nowadays, the orbit of LEOsatellite has been determined with an accuracy of a few cm (approximately 2cm), therefore the K-band observables will be the main carrier of Earth gravity fieldinformation. How to recover the gravity model based on the K-Band observables willbecome one of the hotspots in the world, and its results have a wide applicationforeground in modern geodesy, geophysics, oceanography, geodynamics, and so on.
The gravity model recovery on the basis of satellite-to-satellite tracking data ismainly discussed in this dissertation, and the main work and contributions aresummarized as following:
(1) The development history, domestic and overseas study present state andsignificance of satellite gravity technology are presented. A few methods forrecovering the Earth gravity field are discussed and their advantages anddisadvantages are also analyzed.
(2) The time system, coordinate system and the various perturbation force models ofsatellite-to-satellite tracking measurements are introduced in detail, the basis theoryand algorithm of satellite gravity measurements, and the calculation of partialderivative are also given in this dissertation. We analyzed the effect of initial stateerror of LEO satellite on the Earth gravity model recovery using the precision orbits.In the dissertation, simulated results also showed if the other measurement errors (e.g.accelerometer errors) are not considered, the arc length of two hours should be used.
(3) The preprocessing approaches for CHAMP and GRACE observables are discussedin detail, three cases of attitude data gap are analyzed and a quadratic interpolationmethod is proposed to fill the attitude data gap, The results can satisfy the requirementaccuracy in case of data gap less than 40 epochs.
(4) The scale factor and bias parameters of CHAMP satellite accelerometer data arere-calibrated based on the dynamical method, the results show that the calibrationparameters which are consistent with the results provided by GFZ are variational, andthe change scope of those parameters from one day data is smaller than that from an hour. The accuracy of Earth gravity field based on the calibrated accelerometer data ishigher, so it is necessary to do the re-calibrating work.
(5) The GRASTAR developed independently with Visual C++ has been introduced, which is used for processing satellite gravity data, including CHAMP and GRACEdata, and this software can be easily transplanted and maintained.
(6) The dynamical method for recovering gravity field model based on the precisionorbits and accelerometer data of CHAMP is discussed and the mathematical algorithmis enduced, in which the accelerometer scale and bias, the satellite's initial state vectorand the model coefficients are estimated simultaneously. The gravity field modelTJCHAMP01S up to degree/order 50 has been computed with this algorithm from the120-day CHAMP data including dynamical orbits and accelerometer data, and themodel is validated using various criteria. The results show that the modelTJCHAMP01S is more accurate than EGM96 and EIGEN-1S model of the samedegree and order, and is close to the model EIGEN-2. The geoid height differences ofTJCHAMP01S, EIGEN-2 with respect to EIGEN-CG01C are 4.4cm and 3.3cm up todegree/order 30 in our country.
(7) The gravity field model TJGRACE01 S_OR up to degree/order 36 has been computedfrom the 26-day GRACE data including dynamical orbits and accelerometer data, andthe model is validated using various criteria. The results show that the modelTJGRACE01S OR is more accurate than EGM96 and EIGEN-2 model of the samedegree and order, and is close to the model EIGEN-CHAMP03S up to degree/order 20.
(8) The dynamical method for recovering gravity field model based on the range rateand accelerometer data of GRACE is discussed and the mathematical algorithm isenduced, in which the accelerometer scale and bias, the satellite's initial relativevelocity vector and the model coefficients are estimated simultaneously. The gravityfield model TJGRACE01S up to degree/order 60 has been computed with this algorithmfrom the 31-day GRACE data including Range rate data and accelerometer data, andthe model is validated using various criteria. The results show that the modelTJGRACE01S is more accurate than EIGEN-CHAMP03S model of the same degreeand order, but is little inferior to the model EIGEN-GRACE01S. The EGM96, EIGEN-CHAMP03S, TJGRACE01S and EIGEN-GRACE01S are further evaluatedwith the global 1°×1°grids geoid height differences with respect to EIGEN-GL04Ccomputed until degree/order 60, corresponding mean error of geoid height differencesare 0.446m, 0o144m, 0.027m and 0.008m respectively.
(9) The gravity field model TJGRACE02S up to degree/order 80 has been computed withdynamical algorithm from the 67-day GRACE data including Range rate data andaccelerometer data, and the model is validated using various criteria. The results showthat the model TJGRACE02S is more accurate than EIGEN-CHAMP03S model ofthe same degree and order, but is little inferior to the model GGM01S. The EGM96, EIGEN-CHAMP03S, GGM01S and TJGRACE02S are further evaluated with theglobal 2.5°×2.5°grids geoid height differences and gravity anomaly differenceswith respect to EIGEN-GL04C computed until degree/order 72, corresponding meanerror of geoid height differences are 0.524m, 0.305m, 0.021m and 0.052mrespectively, and mean error of gravity anomaly differences are 4.00mGal, 3.07mGal, 0.21 mGal and 0.50 mGal respectively.
(10) The main results are summarized in the last chapter, and the outlook for futurework is also made.
引文
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