GOCE卫星测量恢复地球重力场模型的理论与方法
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摘要
本文主要研究了GOCE卫星测量恢复地球重力场模型的理论与方法。作者在文中所做的主要工作和创新点有:
(1)建立了扰动引力梯度张量各分量的传统计算模型;推导了m 2 Pn m(cos ? ) sin2?的去奇异性计算公式,进而建立了扰动引力梯度张量各分量去奇异性的详细计算模型。
(2)研究了卫星重力梯度数据向下延拓的解析法、泊松积分迭代法和卫星重力梯度数据格网化的移动平均法、反距离加权法、普通克里金法,采用“直接法”和“移去-恢复法”两种方案对其向下延拓和格网化效果进行了测试。
(3)分析了能量守恒方程中各项误差对沿轨扰动位计算结果的影响;建立了利用扰动位数据确定地球重力场的最小二乘直接法、调和分析法、最小二乘配置法的实用数学模型。
(4)建立了利用扰动引力梯度张量各单分量和组合分量确定地球重力场的最小二乘直接法去奇异性计算模型;推导了利用扰动引力梯度张量单分量和组合分量解算地球重力场的调和分析法模型;进一步推导了扰动引力梯度张量各个分量之间的自协方差和互协方差函数及其与引力位系数之间协方差函数的具体计算公式。
(5)推导了利用不同类型重力测量数据确定地球重力场的联合平差法数学模型,介绍并分析了模型中各类数据最优定权的参数协方差法和方差分量估计法。
(6)论述了谱组合法的基本原理,给出了多种类型重力测量数据联合处理的谱权及谱组合的通用表达式,基于调和分析方法推导了SST+SGG、SST+SGG+Δg和SST+SGG+Δg+N恢复地球重力场模型的谱组合公式及对应谱权的具体形式。
(7)推导了利用迭代法联合不同类型重力测量数据反演地球重力场模型的基本原理公式,并给出了其具体实现步骤。
(8)分析并计算了重力卫星轨道高度、卫星星间距离和卫星轨道倾角的设计指标;讨论了双星轨道长半轴的一致性要求、双星姿态俯仰角的控制要求以及双星编队保持机动的时间间隔要求。
(9)确定了KBR系统的星间距离、星间距离变化率和星间加速度的精度指标;设计了星载GPS系统的卫星轨道位置和速度以及加速度计测量的精度指标;计算了加速度计检验质量质心到卫星质心的调整距离精度指标;分析了恒星敏感器的姿态角测量精度和稳定度;计算了参考重力场模型对于累计大地水准面精度和积分卫星轨道的影响。
(10)研制了一套利用卫星重力测量数据反演地球重力场模型的软件平台。
This dissertation focuses on the theory and methods of earth‘s gravity field model recovery from GOCE data. The main work and innovation points are listed as follows:
(1) The traditional and non-singular detailed calculation models of all disturbing gravity gradient tensor components are constructed with the non-singular calculation formula of m 2 Pn m(cos ? ) sin2? is derived.
(2) The downward continuation methods such as analytical method, Poisson integral iteration method and the data gridding methods such as moving average method, inverse distance weighting method, ordinary kriging method of satellite gravity gradients(SGG) are studied and modeled, which are applied in two schemes i.e. direct method and remove-restore method to test the downward continuation and gridding accuracy.
(3) Each error of the energy balance approach method that influences the calculation of disturbing potential along the orbit is analyzed. The practical mathematic models of direct least squares method, harmonic analysis method and least squares collocation(LSC) method for solving earth‘s gravity field model from disturbing potential data are established.
(4) The non-singular models of direct leasts square method and calculation model of harmonic analysis method for solving earth‘s gravity field model using each component and combined components of disturbing gravity gradient are constructed. Besides, the practical variance and covariance formulae of the disturbing gravity tensor components and the gravity potential coefficients are deduced.
(5) Combined adjustment model for earth‘s gravity field model determination from various types of gravimetry data is derived, in which the basic principles of parametric covariance approach(PCA) method and variance components estimation(VCE) method in the best selection of weight ratio are introduced and analyzed.
(6) The basic principle of spectral combination method is discussed before the general expressions of the spectral weight and spectral combination using various types of gravimetry data are shown. What‘s more, based on harmonic analysis, the detailed forms of spectral combination formula and the corresponding spectral weights in the earth‘s gravity model determination using SST+SGG, SST+SGG+Δg and SST+SGG+Δg+N are derived.
(7) Basic formulae of earth‘s gravity field model recovery using iteration method from the combination of various types of gravimetry data are deduced, and the detailed realization steps are given.
(8) The design index of gravity satellite orbit altitude, inter-satellite range and the orbit inclination are studied and calculated. The issues towards the two satellites such as alignment of the semimajor axes, pitch attitude control and time interval to keep the satellite formation are discussed.
(9) The precision index of inter-satellite range of KBR system, range change and inter-satellite acceleration are determined, and that of the satellite position, velocity and accelerometer surveying data through satellite-borne GPS receiver. Then, the adjustment distance precision index between the quality center of accelerometer and satellite is calculated, and the measurement accuracy and stability of the star sensor in attitude angles measurement are analyzed. Besides, the influences of reference gravity model towards the accumulated geoid accuracy and the integral satellite orbit are calculated.
(10)A calculation platform for earth‘s gravity field model recovery from satellite gravimety data is developed.
(1)建立了扰动引力梯度张量各分量的传统计算模型;推导了m 2 Pn m(cos ? ) sin2?的去奇异性计算公式,进而建立了扰动引力梯度张量各分量去奇异性的详细计算模型。
(2)研究了卫星重力梯度数据向下延拓的解析法、泊松积分迭代法和卫星重力梯度数据格网化的移动平均法、反距离加权法、普通克里金法,采用“直接法”和“移去-恢复法”两种方案对其向下延拓和格网化效果进行了测试。
(3)分析了能量守恒方程中各项误差对沿轨扰动位计算结果的影响;建立了利用扰动位数据确定地球重力场的最小二乘直接法、调和分析法、最小二乘配置法的实用数学模型。
(4)建立了利用扰动引力梯度张量各单分量和组合分量确定地球重力场的最小二乘直接法去奇异性计算模型;推导了利用扰动引力梯度张量单分量和组合分量解算地球重力场的调和分析法模型;进一步推导了扰动引力梯度张量各个分量之间的自协方差和互协方差函数及其与引力位系数之间协方差函数的具体计算公式。
(5)推导了利用不同类型重力测量数据确定地球重力场的联合平差法数学模型,介绍并分析了模型中各类数据最优定权的参数协方差法和方差分量估计法。
(6)论述了谱组合法的基本原理,给出了多种类型重力测量数据联合处理的谱权及谱组合的通用表达式,基于调和分析方法推导了SST+SGG、SST+SGG+Δg和SST+SGG+Δg+N恢复地球重力场模型的谱组合公式及对应谱权的具体形式。
(7)推导了利用迭代法联合不同类型重力测量数据反演地球重力场模型的基本原理公式,并给出了其具体实现步骤。
(8)分析并计算了重力卫星轨道高度、卫星星间距离和卫星轨道倾角的设计指标;讨论了双星轨道长半轴的一致性要求、双星姿态俯仰角的控制要求以及双星编队保持机动的时间间隔要求。
(9)确定了KBR系统的星间距离、星间距离变化率和星间加速度的精度指标;设计了星载GPS系统的卫星轨道位置和速度以及加速度计测量的精度指标;计算了加速度计检验质量质心到卫星质心的调整距离精度指标;分析了恒星敏感器的姿态角测量精度和稳定度;计算了参考重力场模型对于累计大地水准面精度和积分卫星轨道的影响。
(10)研制了一套利用卫星重力测量数据反演地球重力场模型的软件平台。
This dissertation focuses on the theory and methods of earth‘s gravity field model recovery from GOCE data. The main work and innovation points are listed as follows:
(1) The traditional and non-singular detailed calculation models of all disturbing gravity gradient tensor components are constructed with the non-singular calculation formula of m 2 Pn m(cos ? ) sin2? is derived.
(2) The downward continuation methods such as analytical method, Poisson integral iteration method and the data gridding methods such as moving average method, inverse distance weighting method, ordinary kriging method of satellite gravity gradients(SGG) are studied and modeled, which are applied in two schemes i.e. direct method and remove-restore method to test the downward continuation and gridding accuracy.
(3) Each error of the energy balance approach method that influences the calculation of disturbing potential along the orbit is analyzed. The practical mathematic models of direct least squares method, harmonic analysis method and least squares collocation(LSC) method for solving earth‘s gravity field model from disturbing potential data are established.
(4) The non-singular models of direct leasts square method and calculation model of harmonic analysis method for solving earth‘s gravity field model using each component and combined components of disturbing gravity gradient are constructed. Besides, the practical variance and covariance formulae of the disturbing gravity tensor components and the gravity potential coefficients are deduced.
(5) Combined adjustment model for earth‘s gravity field model determination from various types of gravimetry data is derived, in which the basic principles of parametric covariance approach(PCA) method and variance components estimation(VCE) method in the best selection of weight ratio are introduced and analyzed.
(6) The basic principle of spectral combination method is discussed before the general expressions of the spectral weight and spectral combination using various types of gravimetry data are shown. What‘s more, based on harmonic analysis, the detailed forms of spectral combination formula and the corresponding spectral weights in the earth‘s gravity model determination using SST+SGG, SST+SGG+Δg and SST+SGG+Δg+N are derived.
(7) Basic formulae of earth‘s gravity field model recovery using iteration method from the combination of various types of gravimetry data are deduced, and the detailed realization steps are given.
(8) The design index of gravity satellite orbit altitude, inter-satellite range and the orbit inclination are studied and calculated. The issues towards the two satellites such as alignment of the semimajor axes, pitch attitude control and time interval to keep the satellite formation are discussed.
(9) The precision index of inter-satellite range of KBR system, range change and inter-satellite acceleration are determined, and that of the satellite position, velocity and accelerometer surveying data through satellite-borne GPS receiver. Then, the adjustment distance precision index between the quality center of accelerometer and satellite is calculated, and the measurement accuracy and stability of the star sensor in attitude angles measurement are analyzed. Besides, the influences of reference gravity model towards the accumulated geoid accuracy and the integral satellite orbit are calculated.
(10)A calculation platform for earth‘s gravity field model recovery from satellite gravimety data is developed.
引文
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