卫星跟踪卫星测量确定地球重力场的理论与方法
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摘要
测定地球重力场,确定高分辨高精度的地球重力场模型和大地水准面,是大地球测量学的主要任务之一,也是与相关地球学科交叉研究的重要领域。卫星技术的出现和迅速发展,使物理大地测量学家有了进行全球重力测量的有效工具,卫星的轨道运动主要受制于地球重力场,可视为承载地球重力场信息的一种传感器,研究利用卫星轨道跟踪观测数据恢复地球重力场的理论和方法,形成了卫星重力学这一新的学科分支,已经历了40余年的发展,从上世纪60年代开始,利用地面站对卫星的激光测距(SLR)跟踪数据,至今建立了近百个不同序列的长波重力场模型,可确定分米级精度的全球大地水准面,上世纪末研制成功能在高动态条件下接收和处理GPS导航信号的星载GPS接收机,实现了高轨GPS卫星对低轨专用重力卫星的精密跟踪测轨,精度达到厘米级,同时突破了两颗低轨卫星之间的同轨跟踪测距和星载加速度计测定大气阻力等非保守力的技术,以及制成星载重力梯度仪,据此,本世纪初实施了新一代国际卫星重力探测计划,发射了GHAMP和GRACE卫星,2006年预计发射重力梯度测量卫星GOCE,研究利用新一代卫星重力观测数据建立高精度地球重力场模型,提出新方法,发展新技术,研制新软件,是当前物理大地测量学者高度关注的研究前沿,也是本论文选题的研究方向。本文的研究目标是,在消化总结国内外研究成果的基础上,比较全面地掌握利用GHAMP和GRACE数据恢复地球重力场的实用计算模型和算法细节,重点研究发展其中的能量守恒法,研制计算软件系统,利用GRACE实测数据,完成一个有应用价值的GRACE重力场模型的研制,并对模型的可靠性和精度进行检验分析和评价,提出需进一步研究的问题和建议。
本文的主要工作包括以下几方面:
1.评述精化地球重力场模型在现代大地测量发展及其与相关地球科学交叉研究中的作用;对实现确定1cm级精度大地水准面及相应地球重力场模型可能存在的问题和困难提出作者的思考;总结卫星重力技术的发展阶段和现有研究成果,概括理解表述各种卫星重力技术和方法的一般原理和共性,根据作者的研究实践提出目前面临的有待解决的关键性技术问题。
2.从卫星重力学的角度出发,研究总结卫星轨道理论,给出涉及的不同时空参考系统的精确定义和数学表述及互相转换的实用计算模型,研究总结解开普勒轨道的实用算法,总结各种摄动力的数学模型,重点作详细的数值分析。该项工作在为低轨卫星星载GPS动力法定轨作准备和提供选择模型的依据。
3.研究总结星载GPS精密动力法定轨所涉及的概念和实用计算模型,重点是卫星状态转移矩阵和参数敏感矩阵的结构和数学表述以及基于此两类矩阵的变分方程的建立,用于确定卫星观测方程线性化所需偏导数矩阵;详细研究现有轨道数值积分方法,给出可供实用计算的计算公式及其系数值,以及并行积分器的设计;给出动力法定轨的详细计算模型和流程,作为软件编制的依据。
4.总结研究现有的基于GPS精密定轨的三类求解重力场模型的方法和实用算法,即动力法,能量法和加速度法,重点研究能量守恒法,导出改进的严密计算模型,对该法进行误差分析。
5.研究总结重力场模型现有各种数值解法及优化算法技巧,包括时域法和空域法,重点
Gravity field measurements and determination of geopotential model and global geoid are one of the main tasks of geodesy, and it is also an important domain for cross research between geodesy and various related earth science discipline. With the coming and development of satellite technique, they provide the efficient tools for physical geodesists to map the global gravity field. Because satellite orbital motion is dominated by the field, a satellite orbit can be taken as a sensor carrying gravity information of the earth. The study of the theory and methology for earth's gravity field recovery with satellite tracking data constitutes a new discipline branch, named satellite gravimetry which has experienced a development period for more than forty years. Since the 60s of the last century, by use of SLR tracking data from ground stations, about hundred of long wave geopotential models with different series names have been released from some institutes and universities in the world. The accuracy of geoid determined by the models has a decimeter order. In the late last century, satellite borne GPS receiver was successfully invented which can receive GPS navigation signal under moving state with high speed, consequently, the orbit of gravity satellite can be precisely measured by GPS positioning technique with accuracy of a few centimeter order. In addition, the breakthrough of some crucial techniques for supporting new satellite gravimetry strategy and mission was made after study and experiment of long period efforts about 20 decades, including K-band microwave ranging between two satellites with micron(μ) accuracy, on-board accelerometer for measuring non-conservative forces like air-drag with 10~(-8)~10~(-9) accuracy and satellite gradiometer with 10~(-1)~10~(-2)E accuracy. Based on these advanced technique achievements, the international satellite gravity exploring missions of a new generation were performed in the early part of this century, which included launching projects of CHAMP and GRACE satellites for HL-SST and LL-SST gravimetric modes respectively. According to a complete satellite gravimetric plan, GOCE satellite for SGG will be launched into its orbit in the next year (2006). Therefore, the study of new methods, techniques and software for determination of geopotential models using satellite observation data of the new generation has been a front research area to which physical geodesists pay high attention at present, and it is just the selected main subject of this dissertation. The research objects include: based on understanding and summarizing the research results from the domestic-oversea literatures, being more completely familiar with the practical computation models and algorithm details for gravity field recovery using CHAMP and GRACE data by various methods, particularly, by energy method as a stress one to be investigation in this dissertation; developing a software system for computation as well as completing a GRACE gravity model comparable to other existing similar models.The main research work in this dissertation comprises the following aspects:Comment on the roles of refined earth's gravity model in development of contemporary geodesy and cross research with related earth's science disciplines; thinking about the problem and
difficulty possible arising from the intent to realize an ambitious task of geoid determination with one centimeter accuracy and corresponding gravity model; summarizing the developing stages of satellite gravimetry technique and the existing study results; generalizing and understanding the common principle of various different satellite gravimetry technique and method; presenting some crucial technical problems to be addressed in gravity model solution according to author's research experience.From the point of view of satellite gravimetry, studying and summarizing the theory of satellite orbit; presenting the strict definition and mathematical expressions of associated different time/ space reference systems and practical computation models for mutual transformation; investigating the applied algorithm for solving Keplerian orbit; summarizing mathematical models of various perturbation forces laying stress on the detail numerical analyses about the models. The purpose of all above mentioned work in this item is to prepare necessary base for orbit determination of low-orbiting satellite by dynamic method.Studying and summarizing the concepts and computational models for practical uses associated with precise orbit determination of spaceborne GPS by dynamic method putting stress on the construction and mathematical expressions of satellite state transition matrix and parameter sense matrix, and on establishing variational equation according to the two matrices used for providing the needed partial derivatives in linearization of observation equations; investigating existing numerical integration approach of orbit determination in detail, and giving the computational formulas with corresponding coefficient values for practical use and the design of parallel integrator; presenting the detail computation models and flow chart for orbit determination with dynamic method used in software programming.Studying and summarizing, from the point of view of practical use, the existing three kinds of methods and algorithm for solving geopotential model, i. e. dynamic method, energy method and acceleration method, laying stress on the second one in which the strict computation model will be derived for modification, and the error analyses will also performed.Investigating and summarizing the existing various numerical solution method and optimization skill for estimating geopotential coefficients as unknown parameters including the methods of time-wise and space-wise modes, laying stress on the practical algorithm and its modification of preconditioned conjugate gradient method used in solving normal equation with respect to geopotential coefficient unknowns; and discussing the parallel algorithm and computational technique of solving for geopotential model using a super-computer with parallel calculation function.Studying the algorithm of GRACE data preprocessing and related technical problems including the data of accelerometer, KBR and orbit determination from on-board GPS kinematic positioning, the editing and creating of data files, the designing of software system for computation of geopotential model in terms of energy conservation method emphasizing the design of functional module, and solving for geopotential models with 90 degree and 120'degree respectively using GRACE in situ data of eighteen months.
Studying the strategy and method of examination and evaluation on the quality of satellite geopotential models resulting from satellite tracking data only, making a complete comparison, test and a preliminary assessment on the global geopotential models presented in this dissertation.The main research achievements and contributions are as follows:With the purpose of practical uses, according to author's study, realization and summarization, a complete set of formulas are systematically presented which can be used for computation of geopotential model based on dynamic method using satellite tracking data, and a detailed algorithm descriptions for each computation step are given with some related numerical analyses; the program modules for executing some key computation step or calculation of some special functions are also presented in which the computation of epochs and coordinates and mutual transform between different systems, spherical harmonic function, Keplerian orbit elements with some numerical analyses, various perturbation forces with numerical analyses, orbit integrator with numerical analyses, the formation of variational equation and numerical integral solution, and so on, are included.Based on the principle of energy conservation and analytical mechanics, the detailed mathematical model for earth's gravity field recovery are derived in which a strict expression of the difference of kinetic energy between two satellite on the same orbit by KBR observation of range-rate is firstly presented instead of an approximate expression published in Journal of Geodesy in 1999, and the theory formulas for error analyses of this method and their numerical analysis results are also given, consequently, some related conclusions are reached as well.The problem on accelerometer data preprocessing is investigated in detail. Based on energy conservation principle, a strict formula (6-3-14) for solving the scale and bias parameters of accelerometer data is firstly presented adopting cross-over point method using orbital data and accelerometer observations. The formula can be used for precise correction to accelerometer data instead of current method which is based on an a priori geopotential model.The application of preconditioned conjugate gradient method in the solution of the normal equation with geopotential coefficient unknowns is investigated in detail. A precondition matrix with the most high speed convergence is proposed, which is successfully used in the development of WHU-GM-05 models. Therefore, the key problem to solve the geopotential coefficients of degree 120 on GS80 server taking acceptable consuming time is overcome. In real solution operation, it takes 96 hours for solving the normal equation with 14 637 geopotential coefficients corresponding to geopotential model of degree 120, using GRACE data of one month with 30 seconds of sampling intervals that implies 86 400 observation equations.The application technique of parallel algorithm running on supercomputer like GS80 in solution of satellite gravimetry geopotential model is investigated. This advanced computational technique will provide possibility of directly solution for inverse of high dimension normal matrix with full elements, that means, our computational technique in this area will approach to international advanced level by one step.
A software system with multi-function for computing satellite gravimetric models is developed which is tentatively named "SATGRAS" (implied satellite gravimetry software). The software system can be used for establishing the earth's gravity model by use of the methods of "dynamic", "energy" and "acceleration excluding p" under both modes of HL-SST and LL-SST. Whencomplementing a program module for gravity gradient data processing into the software system, it can also be used for GOCE mission to solve geopotential model using SGG data.The method of GRACE data processing is investigated in detail, including accelerometer data, KBR range-rate data and orbit data of GPS tracking, etc.. The module for the data processing is created with an interface to SATGRAS, which has several functions including blunder/gross error detection and deletion, calibration and correction, and smoothing and interpolation, etc. A series of geopotential models are successfully developed that each one is expanded to degree 60, 90 and 120 using total eighteen months GRACE data by single satellite energy method and double satellites one respectively, which are tentatively named WHU-GM-S05 (for single satellite) and WHU-GM-D05 (for double satellites) (implied Wuhan University Gravity model of year 2005). The comparisons between WHU-GM-05 series and several analogous international geopotential models with corresponding geoidal heights are performed by use of GPS leveling data in the areas of U.S and China (some regions), and the RMS of the differences about 0.28m and 0.42m.
本文的主要工作包括以下几方面:
1.评述精化地球重力场模型在现代大地测量发展及其与相关地球科学交叉研究中的作用;对实现确定1cm级精度大地水准面及相应地球重力场模型可能存在的问题和困难提出作者的思考;总结卫星重力技术的发展阶段和现有研究成果,概括理解表述各种卫星重力技术和方法的一般原理和共性,根据作者的研究实践提出目前面临的有待解决的关键性技术问题。
2.从卫星重力学的角度出发,研究总结卫星轨道理论,给出涉及的不同时空参考系统的精确定义和数学表述及互相转换的实用计算模型,研究总结解开普勒轨道的实用算法,总结各种摄动力的数学模型,重点作详细的数值分析。该项工作在为低轨卫星星载GPS动力法定轨作准备和提供选择模型的依据。
3.研究总结星载GPS精密动力法定轨所涉及的概念和实用计算模型,重点是卫星状态转移矩阵和参数敏感矩阵的结构和数学表述以及基于此两类矩阵的变分方程的建立,用于确定卫星观测方程线性化所需偏导数矩阵;详细研究现有轨道数值积分方法,给出可供实用计算的计算公式及其系数值,以及并行积分器的设计;给出动力法定轨的详细计算模型和流程,作为软件编制的依据。
4.总结研究现有的基于GPS精密定轨的三类求解重力场模型的方法和实用算法,即动力法,能量法和加速度法,重点研究能量守恒法,导出改进的严密计算模型,对该法进行误差分析。
5.研究总结重力场模型现有各种数值解法及优化算法技巧,包括时域法和空域法,重点
Gravity field measurements and determination of geopotential model and global geoid are one of the main tasks of geodesy, and it is also an important domain for cross research between geodesy and various related earth science discipline. With the coming and development of satellite technique, they provide the efficient tools for physical geodesists to map the global gravity field. Because satellite orbital motion is dominated by the field, a satellite orbit can be taken as a sensor carrying gravity information of the earth. The study of the theory and methology for earth's gravity field recovery with satellite tracking data constitutes a new discipline branch, named satellite gravimetry which has experienced a development period for more than forty years. Since the 60s of the last century, by use of SLR tracking data from ground stations, about hundred of long wave geopotential models with different series names have been released from some institutes and universities in the world. The accuracy of geoid determined by the models has a decimeter order. In the late last century, satellite borne GPS receiver was successfully invented which can receive GPS navigation signal under moving state with high speed, consequently, the orbit of gravity satellite can be precisely measured by GPS positioning technique with accuracy of a few centimeter order. In addition, the breakthrough of some crucial techniques for supporting new satellite gravimetry strategy and mission was made after study and experiment of long period efforts about 20 decades, including K-band microwave ranging between two satellites with micron(μ) accuracy, on-board accelerometer for measuring non-conservative forces like air-drag with 10~(-8)~10~(-9) accuracy and satellite gradiometer with 10~(-1)~10~(-2)E accuracy. Based on these advanced technique achievements, the international satellite gravity exploring missions of a new generation were performed in the early part of this century, which included launching projects of CHAMP and GRACE satellites for HL-SST and LL-SST gravimetric modes respectively. According to a complete satellite gravimetric plan, GOCE satellite for SGG will be launched into its orbit in the next year (2006). Therefore, the study of new methods, techniques and software for determination of geopotential models using satellite observation data of the new generation has been a front research area to which physical geodesists pay high attention at present, and it is just the selected main subject of this dissertation. The research objects include: based on understanding and summarizing the research results from the domestic-oversea literatures, being more completely familiar with the practical computation models and algorithm details for gravity field recovery using CHAMP and GRACE data by various methods, particularly, by energy method as a stress one to be investigation in this dissertation; developing a software system for computation as well as completing a GRACE gravity model comparable to other existing similar models.The main research work in this dissertation comprises the following aspects:Comment on the roles of refined earth's gravity model in development of contemporary geodesy and cross research with related earth's science disciplines; thinking about the problem and
difficulty possible arising from the intent to realize an ambitious task of geoid determination with one centimeter accuracy and corresponding gravity model; summarizing the developing stages of satellite gravimetry technique and the existing study results; generalizing and understanding the common principle of various different satellite gravimetry technique and method; presenting some crucial technical problems to be addressed in gravity model solution according to author's research experience.From the point of view of satellite gravimetry, studying and summarizing the theory of satellite orbit; presenting the strict definition and mathematical expressions of associated different time/ space reference systems and practical computation models for mutual transformation; investigating the applied algorithm for solving Keplerian orbit; summarizing mathematical models of various perturbation forces laying stress on the detail numerical analyses about the models. The purpose of all above mentioned work in this item is to prepare necessary base for orbit determination of low-orbiting satellite by dynamic method.Studying and summarizing the concepts and computational models for practical uses associated with precise orbit determination of spaceborne GPS by dynamic method putting stress on the construction and mathematical expressions of satellite state transition matrix and parameter sense matrix, and on establishing variational equation according to the two matrices used for providing the needed partial derivatives in linearization of observation equations; investigating existing numerical integration approach of orbit determination in detail, and giving the computational formulas with corresponding coefficient values for practical use and the design of parallel integrator; presenting the detail computation models and flow chart for orbit determination with dynamic method used in software programming.Studying and summarizing, from the point of view of practical use, the existing three kinds of methods and algorithm for solving geopotential model, i. e. dynamic method, energy method and acceleration method, laying stress on the second one in which the strict computation model will be derived for modification, and the error analyses will also performed.Investigating and summarizing the existing various numerical solution method and optimization skill for estimating geopotential coefficients as unknown parameters including the methods of time-wise and space-wise modes, laying stress on the practical algorithm and its modification of preconditioned conjugate gradient method used in solving normal equation with respect to geopotential coefficient unknowns; and discussing the parallel algorithm and computational technique of solving for geopotential model using a super-computer with parallel calculation function.Studying the algorithm of GRACE data preprocessing and related technical problems including the data of accelerometer, KBR and orbit determination from on-board GPS kinematic positioning, the editing and creating of data files, the designing of software system for computation of geopotential model in terms of energy conservation method emphasizing the design of functional module, and solving for geopotential models with 90 degree and 120'degree respectively using GRACE in situ data of eighteen months.
Studying the strategy and method of examination and evaluation on the quality of satellite geopotential models resulting from satellite tracking data only, making a complete comparison, test and a preliminary assessment on the global geopotential models presented in this dissertation.The main research achievements and contributions are as follows:With the purpose of practical uses, according to author's study, realization and summarization, a complete set of formulas are systematically presented which can be used for computation of geopotential model based on dynamic method using satellite tracking data, and a detailed algorithm descriptions for each computation step are given with some related numerical analyses; the program modules for executing some key computation step or calculation of some special functions are also presented in which the computation of epochs and coordinates and mutual transform between different systems, spherical harmonic function, Keplerian orbit elements with some numerical analyses, various perturbation forces with numerical analyses, orbit integrator with numerical analyses, the formation of variational equation and numerical integral solution, and so on, are included.Based on the principle of energy conservation and analytical mechanics, the detailed mathematical model for earth's gravity field recovery are derived in which a strict expression of the difference of kinetic energy between two satellite on the same orbit by KBR observation of range-rate is firstly presented instead of an approximate expression published in Journal of Geodesy in 1999, and the theory formulas for error analyses of this method and their numerical analysis results are also given, consequently, some related conclusions are reached as well.The problem on accelerometer data preprocessing is investigated in detail. Based on energy conservation principle, a strict formula (6-3-14) for solving the scale and bias parameters of accelerometer data is firstly presented adopting cross-over point method using orbital data and accelerometer observations. The formula can be used for precise correction to accelerometer data instead of current method which is based on an a priori geopotential model.The application of preconditioned conjugate gradient method in the solution of the normal equation with geopotential coefficient unknowns is investigated in detail. A precondition matrix with the most high speed convergence is proposed, which is successfully used in the development of WHU-GM-05 models. Therefore, the key problem to solve the geopotential coefficients of degree 120 on GS80 server taking acceptable consuming time is overcome. In real solution operation, it takes 96 hours for solving the normal equation with 14 637 geopotential coefficients corresponding to geopotential model of degree 120, using GRACE data of one month with 30 seconds of sampling intervals that implies 86 400 observation equations.The application technique of parallel algorithm running on supercomputer like GS80 in solution of satellite gravimetry geopotential model is investigated. This advanced computational technique will provide possibility of directly solution for inverse of high dimension normal matrix with full elements, that means, our computational technique in this area will approach to international advanced level by one step.
A software system with multi-function for computing satellite gravimetric models is developed which is tentatively named "SATGRAS" (implied satellite gravimetry software). The software system can be used for establishing the earth's gravity model by use of the methods of "dynamic", "energy" and "acceleration excluding p" under both modes of HL-SST and LL-SST. Whencomplementing a program module for gravity gradient data processing into the software system, it can also be used for GOCE mission to solve geopotential model using SGG data.The method of GRACE data processing is investigated in detail, including accelerometer data, KBR range-rate data and orbit data of GPS tracking, etc.. The module for the data processing is created with an interface to SATGRAS, which has several functions including blunder/gross error detection and deletion, calibration and correction, and smoothing and interpolation, etc. A series of geopotential models are successfully developed that each one is expanded to degree 60, 90 and 120 using total eighteen months GRACE data by single satellite energy method and double satellites one respectively, which are tentatively named WHU-GM-S05 (for single satellite) and WHU-GM-D05 (for double satellites) (implied Wuhan University Gravity model of year 2005). The comparisons between WHU-GM-05 series and several analogous international geopotential models with corresponding geoidal heights are performed by use of GPS leveling data in the areas of U.S and China (some regions), and the RMS of the differences about 0.28m and 0.42m.
引文
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