北京1954坐标系和西安1980坐标系转换的探讨

基于大地坐标全微分公式探讨了北京1954坐标系和西安1980坐标系之间的相互转换问题,对常用的3参数法和7参数法做了一些改进,并基于湖北省内的控制成果做了大量的实验分析,进而总结了获得参数法最佳转换结果的一些条件。     

平面直角坐标与空间直角坐标间的协方差转换

推导出由大地坐标转换为高斯平面直角坐标严密的全微分公式,导出由高斯平面直角坐标向大地坐标再由大地坐标向空间直角坐标严密的协方差转换公式,并在此基础上,导出直接由高斯平面直角坐标向空间直角坐标近似的协方差转换公式,且举例说明其转换过程。结果表明,两种转换方法是等价的。     

平面坐标系统转换的微分方法

本文利用微分算子的方法，提出了坐标系统转换的几种实用公式，即：改进幂级数公式，台劳级数公式，牛顿二项公式及应用范围。     

大地基准变化对大地方位角的影响

大地方位角与所采用的大地基准密切相关。为了不同坐标系统的大地方位角相互比较和转换，本文推荐了大地基准变化对大地方位角的影响与转换模型，并作了数字分析。     

大地坐标和地心坐标精度对联合平差的精度影响

采用影响系数、影响率的概念可以精确地讨论不同类观测值精度对平差结果的影响。本文着重讨论影响率的概念以及在地面网与卫星网联合平差中的计算公式；通过对模拟的联合平差中平差结果之影响率的数字分析，讨论大地经纬度、大地高和地心坐标精度对两网公共点的大地坐标及转换参数的精度影响情况，提出了一些看法，并对有关微分公式的准确性作了考察。     

四种大地线微分公式的研究

本文对四种地图投影法微分公式（平展法）作了详细的分析和比较,这四种公式郎黑尔默特公式、赫里斯托夫公式、博德米累尔公式和奥凯夫公式（奥凯夫的等参数法）,并找出它们之间的内部联系,然后指出了所有这些公式是最一般的公式,即赫里斯托夫公式的特殊形式．在推导博德米累尔方法中的方向改化和距离改化,以及赫里斯托夫方法中的长度畸变和角度畸变时,本文利用了奥凯夫的等参数法．奥凯夫应用了张量和流形推导出他的由于等参数法所引起的长度畸变公式．木文利用非常简单但却严格的方法来研究等参数法的理论根据和它的精度．最后本文还对这四种微分公式作了评价．     

三维基线向量与大地坐标差间的微分公式及其应用

本文导出了以直角坐标差表示的三维基线向量(△Y X△ △Z)~T与其两端点之间的大地坐标差(△B △L △H)~T 间的微分公式。讨论了这一公式在处理GPS基线向量的坐标系统转换,某些量间的微分结构研究,误差传播,以及GPS基线向量的协方差阵到高斯平面二维向量的协方差阵转换上的应用。     

两种不同三轴椭球之间的一般性转换公式

本文导出了两个三轴椭球之间沿法线投影的转换公式，这些公式包括空间直角坐标与大地坐标之间的转换公式；大地方位角及长度的转换公式。转换时顾及坐标长度因子，椭球中心、大小及本身轴向等十种变化因素。     

应用GPS建立区域独立坐标系中椭球变换的研究

阐述了在应用GPS技术建立区域独立坐标系过程中的椭球变换问题。通过椭球变换的广义模型,系统地描述了椭球膨胀法、平移法、变形法三种常用的椭球变换方法,并利用广义大地坐标微分公式从理论角度分析了各方法的共同点和区别,提出了量化分析指标,分别从不同角度反映和量化了椭球变换前后对长度和平面坐标影响的情况。     

1984世界大地测量系统（WGS84）

自１９６０年以来，美国国防制图局（ＤＭＡ）已建立了四个世界大地测量系统（ＷＧＳ）；ＷＧＳ６０，ＷＧＳ６６，ＷＧＳ７２和ＷＧＳ８４。最新的ＷＧＳ８４与前三者相比，是最为精确的大地参考框架，它是利用了广泛的，最新的大地测量数据全球确定的。ＷＧＳ８４提供了精确的参照框架，地球重力场模型，正常重力公式，大地水准面和包括全部大陆和主要海洋岛屿在内的１０５个局部（和区域）大地测量基准的转换参数。这些成果使测绘     

广义球谐函数定积分计算方法的改进

运用球谐函数定积分的基本递推公式，推导了在重力场球谐综合与球谐分析中出现的广义球谐函数定积分的计算公式；给出了其适用于超高阶次的改良型递推公式。数值试验表明，该改良公式具有较高的计算精度和计算速度，解决了超高阶次广义球谐函数定积分计算的溢出问题，拓展了这类定积分的计算公式。他们的数值实现为利用位模型计算高分辨率扰动重力场元格网平均值、重力场球谐综合分析等奠定了基础。     

The deviations of the sea surface from the geoid and their effect on geoid computation

The effects of the deviations of sea surface topography from the geoid are estimated for terrestrial geoid computations as obtained from Stokes' formula. The results are based on an equal-area expansion of Lisitzin's sea surface topography data in a spherical harmonic series. It is realized that those data affect mainly the harmonics of degree n≤10. Consequently, in geoids obtained from combination solutions (where low harmonics are dominated by harmonics as obtained from differential orbit improvement) the sea surface topography effects are relatively small.     

球外部空间的Neumann逆问题及逆 Stokes公式

基于修改的Poisson积分 ,首先给出了球面扰动位向上延拓的积分表达式。在此基础上 ,由微分原理得出了球外部空间Neumann逆问题的解式 ,利用物理大地测量学的基本微分方程 ,导出了球外部空间的逆Stokes公式 ,并对这两类积分公式的核函数进行了讨论     

Integral formulas for computing the disturbing potential, gravity anomaly and the deflection of the vertical from the second-order radial gradient of the disturbing potential

Integral formulas are derived which can be used to convert the second-order radial gradient of the disturbing potential, as boundary values, into the disturbing potential, gravity anomaly and the deflection of the vertical. The derivations are based on the fundamental differential equation as the boundary condition in Stokes’s boundary-value problem and the modified Poisson integral formula in which the zero and first-degree spherical harmonics are excluded. The rigorous kernel functions, corresponding to the integral operators, are developed by the methods of integration.     

On computing ellipsoidal harmonics using Jekeli’s renormalization

Gravity data observed on or reduced to the ellipsoid are preferably represented using ellipsoidal harmonics instead of spherical harmonics. Ellipsoidal harmonics, however, are difficult to use in practice because the computation of the associated Legendre functions of the second kind that occur in the ellipsoidal harmonic expansions is not straightforward. Jekeli’s renormalization simplifies the computation of the associated Legendre functions. We extended the direct computation of these functions—as well as that of their ratio—up to the second derivatives and minimized the number of required recurrences by a suitable hypergeometric transformation. Compared with the original Jekeli’s renormalization the associated Legendre differential equation is fulfilled up to much higher degrees and orders for our optimized recurrences. The derived functions were tested by comparing functionals of the gravitational potential computed with both ellipsoidal and spherical harmonic syntheses. As an input, the high resolution global gravity field model EGM2008 was used. The relative agreement we found between the results of ellipsoidal and spherical syntheses is 10^?14, 10^?12 and 10^?8 for the potential and its first and second derivatives, respectively. Using the original renormalization, this agreement is 10^?12, 10^?8 and 10^?5, respectively. In addition, our optimized recurrences require less computation time as the number of required terms for the hypergeometric functions is less.     

用双频GPS观测值建立小区域电离层延迟模型研究

介绍了用双频GPS伪距观测值建立区域性电离层模型的基本原理和方法。模型的初步结果表明，该电离层模型建立后，可为性病区域的广大单频用户提供在天顶方向优于0．4m精度的电离层延迟改正量，且具有30min以内天顶方向优于0．4m的预报精度。     

APPLICATION OF THE HARTLEY TRANSFORM IN THE COMPUTATION OF THE GEOID IN CHINA

This paper presents a method for the computation of the Stokes for-mula using the Fast Hartley Transform（FHT）techniques.The algorithm is mostsuitable for the computation of real sequence transform,while the Fast FourierTransform（FFT）techniques are more suitable for the computaton of complex se-quence transform.A method of spherical coordinate transformation is presented inthis paper.By this method the errors,which are due to the approximate term inthe convolution of Stokes formula,can be effectively eliminated.Some numericaltests are given.By a comparison with both FFT techniques and numerical integra-tion method,the results show that the resulting values of geoidal undulations byFHT techniques are almost the same as by FFT techniques,and the computation-al speed of FHT techniques is about two times faster than that of FFT techniques.     

SARC model for three-dimensional coordinate transformation

IntroductionThree coordinate transformation models, Bursa-Wolf, Molodensky and WTUSM[1]are generallyused in 3D coordinate transformation. They are lin-ear models which have seven parametersΔX,ΔY,ΔZ,θ,,ψ[2]. Referecne [2] improved these line-ar mode     

On the indirect effect in the Stokes–Helmert method of geoid determination

The classical integral formula for determining the indirect effect in connection with the Stokes–Helmert method is related to a planar approximation of the sea level. A strict integral formula, as well as some approximations to it, are derived. It is concluded that the cap- size truncated integral formulas will suffer from the omission of some long-wavelength contributions, of the order of 50 cm in high mountains for the classical formula. This long-wavelength information can be represented by a set of spherical harmonic coefficients of the topography to, say, degree and order 360. Hence, for practical use, a combination of the classical formula and a set of spherical harmonics is recommended. Received: 10 March 1998 / Accepted: 16 November 1998     

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。