【作者】 丁剑；

【导师】 章传银； 文汉江；

【作者基本信息】 中国测绘科学研究院 ， 大地测量与测量工程， 2006， 硕士

【摘要】 重力场是地球空间最基本的物理场之一，确定地球形状及其外部重力场是物理大地测量学研究的根本任务。随着地球重力场模型、地面重力数据、GPS水准数据、数字地面模型(DTM)、卫星测高数据和卫星重力(SST、SGG)数据及其他地球重力场相关信息的丰富，为确定厘米级大地水准面提供了必要条件。物理大地测量随着观测手段的进步，人们获得了各种不同类型的边值，如陆地上的GPS水准、海洋上的卫星测高以及卫星重力梯度等，同时在边值问题的理论上也由Stokes边值、Molodensky边值发展到今天重力—测高边值、重力梯度边值等超定边值问题。 本文是基于厘米级似大地水准面的精度要求，对似大地水准面精化中的数据融合、精度评定等问题进行较为系统的分析，在此基础上提出了应用GPS水准高程异常的新方法，解决似大地水准面精化中的瓶颈问题。本文利用重力位模型、地面重力观测数据、GPS水准和数字地面模型(DTM)进行似大地水准面精化。简要阐述了最小二乘配置技术在局部重力场逼近中的应用，就最小二乘配置中的核心内容——经验协方差函数的表达方法提出了新的估计技术；关于GPS水准在精化似大地水准面中的应用，就如何有效、合理地应用GPS水准高程异常，提出了解GPS水准超定边值问题的算法。 本文绪论简单介绍了似大地水准精化的研究进展和研究背景，并对厘米级似大地水准面精化面临的实际问题进行简要分析；最后介绍了本文的结构和力求解决的问题。 第二章就当前似大地水准面精化的基本理论做简要叙述，如Stokes边值问题、Molodensky边值问题、移去—恢复法和球冠方法。最小二乘配置法将在第三章中做详细阐述，Molodensky级数解的一阶项、二阶项的结构解析将结合局部地形在第六章做详细阐述。 第三章作为本文的重点内容之一。首先简要阐述了物理大地测量中的统计相关量，以及最小二乘配置在似大地水准面精化中的应用，然后结合球谐展开式和Tscherning／Rapp的经验协方差函数，构造了新的协方差函数估计方法，并对其配置性能进行测试与分析。 第四章就似大地水准面的误差进行分析。本章从似大地水准面精化中所用数据和局部重力场算法两个方面入手，分析了不同类型的数据源对大地水准面精度的误差影响特性，并给出了简单的误差传播关系；以及基于截断理论的Stockes截断误差和参考位模型截断误差影响。 第五章作为本文研究的另一个重点内容。GPS水准所提供的高精度的高程异常或大地水准面高已被人们所接受，GPS水准也被广泛应用于似大地水准面精化。就更有效、更合理地应用GPS水准进行似大地水准面精化，本文提出了解GPS水准超定边值问题的算法，就该方法的原理及其在似大地水准面精化中的应用进行分析。 第六章就地形在似大地水准面精化中的影响进行分析。本章首先介绍了处理地形影响的残余地形模型法和Helmert凝聚法，然后着重分析了Molodensky级数展开式中一阶项和二阶项的解析结构，针对不同的地形分析其影响大小。 第七章概括了本文研究的主要内容，结合似大地水准面精化的要求和本文研究内容，介绍了本文力求解决的关键问题，并简要阐述了似大地水准面精化的未来发展趋势。 本文的主要研究成果： 1．基于全球协方差函数模型和Tscherning／Rapp经验协方差函数模型的组合，构造了协方差函数的通用表达式； 2．似大地水准面精化的的误差分析； 3．基于附有参数的条件平差模型和重力场边值条件的相容性，提出了解GPS水准超定更多还原

【Abstract】 Gavity field is one of the basic physical fields in earth space. Physical geodesy is the science of the figure of the earth and of its gravity field. Along with the abundance of the earth gravity field model, gravity data in the earth surface, GPS/leveling data, DTM, satellite altimetry data, satellite gravity data (SST, SGG) and other related information of the earth gravity field, the determination of cm order geoid has been provided with necessary condition. In physical geodesy, because of the improvement of observation technique, people obtain kinds of boundary value in different type, for exmple, GPS/leveling on land, satellite altimetry on sea surface and satellite gravity gradient, and so on. At the same time, in the theory of boundary value problem, Stokes boundary value and Molodensky boundary value have developed by gravity-altimetry boundary value, gravity gradient boundary value problem, which are belong to over-determined boundary value problems.In the paper, based on the precision demand of cm order qusi-geoid, the data assimilation and precision assess in qusi-geoid refinement are systematically analyzed. And then, in order to solve the key problem in qusi-geoid refinement, a new method is presented which applies GPS/leveling height anomaly. In the paper, gravity potential model, gravity observation data in the surface of the earth, GPS/leveling and DTM are used to refine qusi-geoid. Firstly, the application of least square collocation technique in local gravity field is expatiated briefly. And then, the expression of experiential covariance function which is the kernel of least square configuration is improved. Finally, with regard to the application of GPS/leveling in qusi-geoid refinement and how to use GPS/leveling height anomaly effectively and reasonably, the paper presents the arithmetic of solving GPS/leveling over-determined boundary value problem.In the introduction of the paper, the research development and background in qusi-geoid refinement are introduced simply. Besides, the actual problems in qusi-geoid refinement are analyzed. The structure of the paper and resolved problems are introduced finally.In chapter 2, the basic theories in qusi-geoid refinement are described briefly. For example, Stokes boundary value problem, Molodensky boundary value problem, remove-restore technique and sphere hat method. The method of least square collocation will be expatiated particularly in chapter 3 while the structure of first order item and secondary order item in Molodensky series are in chapter 6 combined with local terrain.Chapter 3 is one of the important content in the paper. Firstly, statistical correlative quantities in physical geodesy, together with the application of least square configuration in qusi-geoid refinement are explained briefly. Then, combined with spherical-harmonic spread formula and Tscherning/Rapp experiential covariance function, a new covariance function estimation method is created, whose configuration capability is tested and analyzed.The error analysis of qusi-geoid is done in chapter 4. With the data and local gravity field arithmetic in qusi-geoid refinement, the chapter analyzes the error effect characteristics from different type data fountain, provides simply error spread connection and error effect of Stokes truncation error and reference potential model based on truncation theory.Chapter 5 is the other important content in the paper. People have accepted high precision height anomaly and geoid undulation provided by GPS/leveling. Also, GPS/leveling has been applied in qusi-geoid refinement. In order to apply GPS/leveling more effectively and more更多还原