Ellipsoidal Stokes Boundary-Value Problem with Ellipsoidal Corrections in the Boundary Condition

We would like to solve the Stokes boundary-value problem taking into consideration the ellipsoidal corrections in the boundary condition in ellipsoidal coordinates The original problem, i.e., the ellipsoidal Stokes boundary-value problem has been solved by Martinec and Grafarend (1997) We use the same philosophy expressed by Martinec (1998) to solve the spherical Stokes boundary-value problem with ellipsoidal corrections in the boundary condition We wish to show the magnitude of the integration kernel describing the effect of the ellipsoidal corrections in the boundary condition in a cap around the computational point.     

To Pizzetti's Theory of the Level Ellipsoid

The topic of the Earth's reference body, which has now been established as Pizzetti's level rotational ellipsoid, is analysed. Such a body is fully determined by four parameters: a, GM, J ₂ and . At present, the largest discrepancy in determining these parameters occurs in the value of a, which may in future be replaced by the gravity potential of the mean sea level W _o, with respect to Brovar's condition.Pizzetti's four parameters of the reference body are determined by solving the Dirichlet boundary value problem. The Dirichlet problem has only a unique solution, which, however, can be expressed in infinitely many ways. It turns out that the most important part in the form of the solution is played by Lamé's conditions, which determine the type of ellipsoidal coordinates.The solutions given by Pizzetti, Molodensky and another variant are considered. The last variant leads to a simple formula for the potential of the reference ellipsoid, but the formulae for Lamé's coefficients are inconvenient. Of course, all the methods lead to identical solutions, but some of them are more convenient for the historical use of logarithms, whereas others are more appropriate for use in computers.     

Geoid Determination Through Ellipsoidal Stokes Boundary-Value Problem by Splitting Its Solution to the Low-Degree and the High-Degree Parts

The ellipsoidal Stokes boundary-value problem is used to compute the geoidal heights. The low degree part of the geoidal heights can be represented more accurately by Global Geopotential Models (GGM). So the disturbing potential is splitted into a low-degree reference potential and a higher-degree potential. To compute the low-degree part, the global geopotential model is used, and for the high-degree part, the solution of the ellipsoidal Stokes boundary-value problem in the form of the surface integral is used. We present an effective method to remove the singularity of the high-degree of the spherical and ellipsoidal Stokes functions around the computational point. Finally, the numerical results of solving the ellipsoidal Stokes boundary-value problem and the difference between the high-degree part of the solution of the ellipsoidal Stokes boundary-value problem and that of the spherical Stokes boundary-value problem is presented.     

PZ-90与WGS-84的坐标转换参数

主要论述了GLONASS坐标系统PZ-90的定义及与GPS坐标系统WGS-84进行坐标转换的基本方法和数学模型。对现有转换参数的获取方法进行论述与评价，并对各种不同的转换参数进行了分析比较。     

基于椭球面三角格网的数字高程建模

针对传统的DEM在模拟表达大面积地形时具有存在裂缝、地理分析不精确、数据冗余等问题，在椭球面四元三角格网QTM层次剖分的基础上，提出了一种基于椭球面三角格网层次剖分的数字高程建模方法，该方法避免了上述缺陷。应用全球GTOP030数据对该方法进行了验证。     

Hotine函数法的椭球面积分解

本文给出了Hotine 函数法的椭球面积分解,以应用于计算精确的大地水准面起伏。计算表明,当积分半径为20°时,我国近海的椭球改正只有10cm,远比stokes公式的椭球改正要小。     

我国陆地垂线偏差精化计算

我国天文大地网与高精度GPS2000网进行联合平差时,为满足地面观测数据归算到WGS84椭球的需要,采用移去-恢复技术和高阶次地球重力位模型,应用全国重力资料和30″×30″数字地形模型,完成了参加联合平差的48 919个大地点的相应于WGS84椭球垂线偏差的精化计算,并用115个与天文点重合的GPS点的实测垂线偏差对计算结果进行了外部检验,得到全国垂线偏差子午分量的总体精度为±1.45″,卯酉分量的总体精度为±1.50″。     

利用线特征和SIFT点特征进行多源遥感影像配准

提出了一种基于线特征和SIFT点特征的多源遥感影像配准方法。该方法首先匹配待配准影像和参考影像中的线特征,利用匹配直线构建虚拟角点;其次,针对传统SIFT算法匹配多源遥感影像特征点存在的不足,采用线特征约束点特征的方法进行SIFT同名点对的提取;最后结合虚拟角点对及SIFT同名点对构建三角网进行小面元微分纠正。试验结果表明,本文方法能取得较高的配准精度。     

基于椭球面投影的散乱点云建立三角格网方法

空间点云数据建立三角格网是三维激光扫描数据处理中重要的处理内容之一。已有的点云三角格网建立方法的网形结构良好,但存在数据量大、计算效率低的特点。提出借助椭球面进行高斯投影建立点云的空间三角格网建立方法,有效地实现四周型点云数据格网建立过程。结合某矿井点云数据实例,对基于圆柱面和椭球面投影的两种方法建立的三角格网进行对比,结果表明,利用椭球面投影法建立三角格网能更有效地建立顶部和底部点云数据的拓扑关系。     

Closed-form transformation between geodetic and ellipsoidal coordinates

We present formulas for direct closed-form transformation between geodetic coordinates (φ, λ, h) and ellipsoidal coordinates (β, λ, u) for any oblate ellipsoid of revolution. These will be useful for those dealing with ellipsoidal representations of the Earth’s gravity field or other oblate ellipsoidal figures. The numerical stability of the transformations for near-polar and near-equatorial regions is also considered.