卫星测高问题的球谐级数解法

研究了球界面下卫星测高问题的解法,利用有限逼近方法得到了下列结论:若陆地部分是球冠,则卫星测高问题的解可以转换成关于球谐级数位系数的线性方程组.同时证明了常用的Stokes问题、Dirichlet问题、Neumann问题可以看成卫星测高问题的特殊情况.     

利用卫星测高空间技术建立数字化海洋

论述了卫星测高空间技术的主要特征、科学意义及其在军事和经济建设领域的重要价值，阐明了国内外测高卫星系统的发展现状及利用卫星测高空间技术建立数字化海洋所取得的成果，分析卫星测高目前的研究方向，提出了发展我国卫星测高空间技术以及利用该技术建立数字化海洋的一些建议。     

ICEsat激光测高交叉点精度初步分析

本文介绍了icesat卫星激光测高的相关信息、激光测高产品的误差来源及其纠正,并通过对icesat激光测高三期数据交叉点平差初步分析,得出通过交叉点平差可以降低卫星轨道误差对激光测高的影响.     

近海多种卫星测高联合数据处理技术

海域海况复杂多变 ,潮汐不但受外海能量输入的控制 ,而且在复杂的海岸线、浅海海底和内陆河流运输的作用下变得异常复杂。卫星测高由于受复杂的海洋动力环境和陆地反射的影响 ,数据质量普遍较深海差。将多种卫星测高数据联合处理 ,可以大大提高近海海域平均海面高的精度与分辨率 ,增强测高卫星监测近海复杂动力现象与反演近海复杂动力机制的能力。本文讨论近海多种卫星联合数据处理的技术与方法 ,分别从提取海平面稳态和时变信息的角度较系统地研究了多种卫星测高联合数据处理方法 ,通过提取不同测高卫星海平面观测数据中与时间无关的系统偏差 ,建立多种卫星测高数据的海平面时变基准 ,从而将多种测高卫星海面监测数据融合到一个动力系统中。大大提高测高卫星海平面监测的时空分辨率 ,为联合多种卫星测高数据在大地测量与近海海洋动力学研究中的应用创造基本条件。     

卫星测高在物理大地测量应用中的若干问题

总结了卫星测高在物理大地测量领域的应用，描述了卫星测高数据逼近地球重力场、确定海面地形、改善卫星轨道参数以及求解重力异常的数学模型和数学原理。     

卫星测高在物理大地测量应用中的若干问题

总结了卫星测高在物理大地测量领域的应用，描述子卫星测高数据逼近地球重力场、确定海面地形、改善卫星轨道参数以及求解重力异常的数学模型和数学原理。     

卫星测高在大地测量学中的应用及进展

本文介绍了卫星测高技术的发展背景、历史、现状和进展,描述了卫星测高在大地测量学领域诸多方面的应用,评述了地球重力场在地球科学中的作用,并阐述了利用卫星测高数据源在大地测量学领域取得的成果。介绍了最新测高卫星的发展状况,提出了由新一代卫星测高资料确定地球形状的时间变化特征和规律的研究方向,将拓宽卫星测高技术在全球变化研究中的应用。     

现代低轨卫星对地球重力场探测的实践和进展

综述了现代低轨卫星对地球重力场测量的特点和近况，介绍了已经和即将发射的重力卫星CHAMP、GRACE、GOCE和新型测高卫星，讨论了作为现代重力卫星首次实践－－CHAMP卫星的进展和目前尚待解决的问题。     

确定局部海区海平面变化的交叉点平差

卫星雷达测高仪以连续的观测方式对全球海洋进行测量，其轨道升降弧段交叉点构成了交叉点平差的基础。本文根据测高卫星运动的动力学模型，利用交叉点上的测高数据可以看作重复“观测”的特点，通过建立动力学交叉点平差模式，试图更好地消除或削弱轨道误差的影响，提高海面高变化的测定精度。     

卫星测高技术在鄱阳湖水面高获取中的应用

卫星测高作为空间大地测量的前沿发展技术,可以精确获取海平面高、湖泊水面高和平坦地高程。以ICESat激光卫星测高为例,提出利用ICESat卫星测高技术获取鄱阳湖水面高的数据处理方法和技术路线,首次采用EGM 2008模型和江西省二等水准拟合模型相结合的数据处理方法,将卫星测高获取成果转换至1985国家高程基准,与水文站实测水位数据相统一,提高了卫星测高的精度,并通过与其他方法获取的水面高数据进行比对,证明该方法的正确性和技术路线的可靠性,为鄱阳湖水面高获取提供了精确的检核数据和多源数据。     

Finite element method for solving geodetic boundary value problems

The goal of this paper is to present the finite element scheme for solving the Earth potential problems in 3D domains above the Earth surface. To that goal we formulate the boundary-value problem (BVP) consisting of the Laplace equation outside the Earth accompanied by the Neumann as well as the Dirichlet boundary conditions (BC). The 3D computational domain consists of the bottom boundary in the form of a spherical approximation or real triangulation of the Earth’s surface on which surface gravity disturbances are given. We introduce additional upper (spherical) and side (planar and conical) boundaries where the Dirichlet BC is given. Solution of such elliptic BVP is understood in a weak sense, it always exists and is unique and can be efficiently found by the finite element method (FEM). We briefly present derivation of FEM for such type of problems including main discretization ideas. This method leads to a solution of the sparse symmetric linear systems which give the Earth’s potential solution in every discrete node of the 3D computational domain. In this point our method differs from other numerical approaches, e.g. boundary element method (BEM) where the potential is sought on a hypersurface only. We apply and test FEM in various situations. First, we compare the FEM solution with the known exact solution in case of homogeneous sphere. Then, we solve the geodetic BVP in continental scale using the DNSC08 data. We compare the results with the EGM2008 geopotential model. Finally, we study the precision of our solution by the GPS/levelling test in Slovakia where we use terrestrial gravimetric measurements as input data. All tests show qualitative and quantitative agreement with the given solutions.     

球面坐标系非连续变形分析折数学模型

从球面坐标系的弹性力学基础方程出发，推导出球面上块体的位移与6个位移不变量之间的数学关系，进一步建立了联立方程式的球面坐标形式，为大范围现代地壳运动的非连续形变形下了数学基础。     

Elliptical harmonic series and the original Stokes problem with the boundary of the reference ellipsoid

Since the earth is closer to a revolving ellipsoid than a sphere, it is very important to study directly the original model of the Stokes' BVP on the reference ellipsoid, where denotes the reference ellipsoid, is the Somigliana normal gravity, andh is the outer normal direction of. This paper deals with: 1) simplification of the above BVP under preserving accuracy to , 2) derivation of computational formula of the elliptical harmonic series, 3) solving the BVP by the elliptical harmonic series, and 4) providing a principle for finding the elliptical harmonic model of the earth's gravity field from the spherical harmonic coefficients ofg. All results given in the paper have the same accuracy as the original BVP, that is, the accuracy of the BVP is theoretically preserved in each derivation step.     

Spherical panel clustering and its numerical aspects

In modern approximation methods, linear combinations in terms of (space localizing) radial basis functions play an essential role. Areas of application are numerical integration formulae on the unit sphere Ω corresponding to prescribed nodes, spherical spline interpolation and spherical wavelet approximation. The evaluation of such a linear combination is a time-consuming task, since a certain number of summations, multiplications and the calculation of scalar products are required. A generalization of the panel clustering method in a spherical setup is presented. The economy and efficiency of panel clustering are demonstrated for three fields of interest, namely upward continuation of the Earth's gravitational potential, geoid computation by spherical splines and wavelet reconstruction of the gravitational potential. Received: 1 October 1997 / Accepted: 1 April 1998     

非连续变形分析与现代地壳运动研究

介绍了非连续变表分析（DDA）方法的原理、特点及适用范围，分析了DDA方法较常用的有限元法的优越性，进一步提出把现有平面DDA推广到球面DDA方程的基本思路，希望为在大范围内研究地壳运动找到突破口。在此基础上，结合目前我国地学研究的热点，提出了三类最具代表性的实际问题，应用DDA方法可以在此方面进行深入研究。     

Vertical and horizontal spheroidal boundary-value problems

Vertical and horizontal spheroidal boundary-value problems (BVPs), i.e., determination of the external gravitational potential from the components of the gravitational gradient on the spheroid, are discussed in this article. The gravitational gradient is decomposed into the series of the vertical and horizontal vector spheroidal harmonics, before being orthogonalized in a weighted sense by two different approaches. The vertical and horizontal spheroidal BVPs are then formulated and solved in the spectral and spatial domains. Both orthogonalization methods provide the same analytical solutions for the vertical spheroidal BVP, and give distinct, but equivalent, analytical solutions for the horizontal spheroidal BVP. A closed-loop simulation is performed to test the correctness of the analytical solutions, and we investigate analytical properties of the sub-integral kernels. The systematic treatment of the spheroidal BVPs and the resulting mathematical equations extend the theoretical apparatus of geodesy and of the potential theory.     

多镜头全景摄像机球面视频无缝生成EI北大核心CSCD

针对多镜头全景摄像机MPC室内标定参数输出的实际场景球面全景视频存在视差伪影问题,提出一种场景自适应的球面全景视频无缝生成方法,主要包括两方面内容:①MPC球面投影参数最优估计。以实际场景视频重叠区域同名像点为观测值,通过最小化球面投影中心到同名像素对应球面空间点的夹角建立误差方程对球面投影参数进行最小二乘估计,从而降低子相机摄影中心与球面投影中心不重合及场景深度变化对MPC球面全景视频输出质量影响。②MPC球面全景视频生成TPS模型构建。以MPC子摄像机视频像素球面重投影几何为全局变换、以视频拼接线上同名像点为控制点建立TPS模型,实现MPC各子摄像机视频到球面拼接视频的像素直接映射,并能最小化视频重叠区域像素拼接误差,仅通过拼接线附近像素简单混合即可消除视差伪影并实现平滑过渡。模拟成像及实际场景试验结果表明,结合场景内容与摄像机内、外参数,本文方法可实现MPC球面全景视频无缝生成且计算简单、高效,完全满足MPC高帧率视频输出要求,具有良好的应用价值。     

基于俯仰轴相交和球拟合的天线旋转中心测量方法

针对传统天线旋转中心测量时，俯仰轴生成方式不严密对其精度和可靠性产生不利影响的问题，提出了俯仰轴相交和球拟合两种新的旋转中心测量方法。对不同方位下标志点绕俯仰轴的运动轨迹进行圆拟合，得到含有方位信息的俯仰轴，多条俯仰轴求交点作为旋转中心，称之为俯仰轴相交法，较传统方法可靠性更高。对标志点的运动轨迹进行球拟合，取所有球心的均值作为旋转中心，称之为球拟合法，避免了圆拟合及求交点的过程，方法更为严密。以3台φ3 m上行阵天线为实验对象，应用全站仪和工业摄影测量技术获取标志点在规划姿态下的坐标，采用两种新方法处理观测数据，均得到了内符合精度达亚毫米级的旋转中心。     

A Geodesic Map Projection for Quadrilaterals

Part of a cuboctahedron-based geodesic map projection by Buckminster Fuller is expanded to spherical quadrilaterals with opposite sides equal. Points on such a quadrilateral can be described by intersections of geodesics, which provide parameterized coordinate values in a Geodesic Coordinate System. Through a linear transform of the geodesic coordinates, a spherical quadrilateral maps to a parallelogram. The resulting map has the same constant scale on all four sides. Within the map, all lines parallel to the sides correspond to geodesics on the globe. Spherical rectangles, spherical squares, and diamonds (spherical rhombi) are specifically examined; various tiling sets of diamonds can be used to cover the globe. Non-projection applications in geometry, astronomy, and computer graphics are described.