Is Newton's iteration faster than simple iteration for transformation between geocentric and geodetic coordinates?

Summary Two iterative algorithms for transformation from geocentric to geodetic coordinates are compared for numerical efficiency: the well known Bowring's algorithm of 1976, which employs the method of simple iteration, and the recent (1989) algorithm by Borkowski, which employs the Newton-Raphson method. The results of numerical tests suggest that the simple iteration method implemented in Bowring's algorithm executes approximately 30% faster than the Newton-Raphson method implemented in Borkowski's algorithm. Only two iterations of each algorithm are considered. Two iterations are sufficient to produce coordinates accurate to the comparable level of 1E-9 m, which exceeds the requirements of any practical application. Therefore, in the class of iterative methods, the classical Bowring's algorithm should be the method of choice.     

罗德里格矩阵在坐标系转换中的应用

在大旋转角度的坐标系转换中,线性转换模型的旋转参数线性化复杂,计算量大,误差大。根据反对称矩阵和罗德里格矩阵的性质,推导了基于罗德里格矩阵的坐标系转换模型。该模型用反对称矩阵中的3个独立参数代替旋转矩阵中9个相关参数,避免了旋转参数的线性化。模型简单、计算简便,通过实验计算,精度较高。     

非线性二维转换模型的稳健总体最小二乘算法

针对应用线性最小二乘估计准则求解非线性平面转换模型参数时,通过定义间接参数将模型线性化的方法不能直接求解转换模型参数的问题,该文在非线性平面转换模型的基础上,建立线性模型,实现平面坐标的转换。为解决控制点已知坐标与观测坐标中均含有误差对转换参数求解的影响,对应用稳健总体最小二乘求解线性模型参数的算法进行讨论。最后,通过算例比较稳健总体最小二乘算法与最小二乘算法在抗差性方面的优势。结果表明,稳健总体最小二乘算法更适用于应用线性模型求解未知控制点的转换坐标。     

Predictor stabilisation of reduction formulae for observations of heavily-damped simple harmonic motions

The paper summarises attempts which have been made to derive general, simple and stable formulae of adequate precision for the reduction of observations to the extremal positions of oscillations which are simple harmonic or near-simple harmonic. A fallacy in the thirty-five year old Schuler Mean is pointed out and general formulae are offered for the reduction of observations for any constant damping, within the range0<f≤1.     

坐标系转换中全国高精度高分辨率格网改正量的确定

确定全国1980西安坐标系向2000国家大地坐标系转换改正量是实现1980西安坐标系测绘成果向2000国家大地坐标系转换的一项重要的基础性工作。本文在对全国已有大地控制点资料进行整理、分析的基础上,通过大量试算与研究,在国内首次提出了利用全国高精度高分辨率格网改正量实现1980西安坐标系测绘成果向2000国家大地坐标系转换的理念与改正量计算方法 -移动转换法,同时利用全国127 210个高精度的控制点成果,在椭球面上建立了控制点上误差很小、能满足大比例尺地形图转换精度要求的全国高精度高分辨率格网1980西安坐标系测绘成果向2000国家大地坐标系转换改正量模型,该模型现已应用于全国多个省、市不同比例尺基础地理信息数据转换实际生产中。     

关于三维直角坐标七参数转换模型求解的讨论

本文针对三维直角坐标转换中7参数量纲不同的问题,设计了"变更求解参数以使形式误差基本相当"的求解模式,有效改善了小参数情况下法方程的条件,并提高了大参数情况下参数解的稳定性。针对大旋转角情况,设计了简洁有效的迭代求解模式,便于模块化编程,并具有收敛快、参数初值动态范围广的特点。针对大平移,采取了预先部分扣除的方式,获得了稳定的参数解。算例验证了这些处理方式的有效性。     

Rigorous transformation of variance–covariance matrices of GPS-derived coordinates and velocities

With the advances in the field of GPS positioning and the global densification of permanent GPS tracking stations, it is now possible to determine at the highest level of accuracy the transformation parameters connecting various international terrestrial reference frame (ITRF) realizations. As a by-product of these refinements, not only the seven usual parameters of the similarity transformations between frames are available, but also their rates, all given at some epoch t _k . This paper introduces rigorous matrix equations to estimate variance–covariance matrices for transformed coordinates at any epoch t based on a stochastic model that takes into consideration all a priori information of the parameters involved at epoch t _k , and the coordinates and velocities at the reference frame initial epoch t ₀. The results of this investigation suggest that in order to attain maximum accuracy, the agencies determining the 14-parameter transformations between reference frames should also publish their full variance–covariance matrix. Electronic Publication     

椭球谐和球谐系数之间一个简单的转换关系

本文推导的椭球谐系数和球谐系数相互之间转换关系的核心思想是在ε~2量级下利用Legendre函数的正交性,从球谐系数求解的积分表示出发,将积分中的椭球坐标变量与球坐标变量相互转换,从而得出椭球谐系数与球谐系数之间的转换关系。本文导出的转换关系有以下优点:①对于第二类Legendre函数的计算采用Laurent级数表示,使计算第二类Legendre函数更为简单;②保留了ε~2量级下,导出的转换关系相比文献[2]的形式更简单,满足物理大地测量边值问题线性化的要求;③顾及了余纬和归化余纬的区别。     

已知平面与高程点不同时的严密三维基准变换

由于常规控制网的平面与高程网分开布设,当求解常规控制网与GNSS三维控制网的基准变换参数时,需要分别利用其平面坐标和高程的已知成果。传统控制网与三维GNSS控制网都存在误差,文中在解算变换参数时,同时对两套坐标引入改正数,并顾及公共点与转换点观测误差的相关性,利用公共点的改正数推估转换点的改正数,实现两套坐标的基准变换。模拟数据的分析结果表明,文中方法能够在常规平面与高程控制网分开布设时,实现与GNSS三维控制网的基准变换。     

A catalog of station coordinates for GEOS-C orbit determination

Center-of-mass coordinates for 57 tracking sites participating in the GEOS-C mission are given in a unified system having a common origin and scale. The positions were obtained either directly from analyses of satellite observations or from survey ties to colocated sites with coordinates previously determined by various investigators from optical, laser of doppler data. The uncertainty of the positions in nearly all cases is 5 m in each coordinate. Data reductions show that station coordinates of this quality introduce a rapidly changing error into the altitude of a satellite unless global tracking constrains the orbit.     

一种曲线拟合圆心坐标算法及精度分析

针对在工程应用中,经常需要根据某些圆形物体上的离散点求取其圆心坐标,而采用何种算法简单易行,其精度又与哪些因素有关的相关研究较少的问题,该文提出一种利用曲线拟合求取圆心坐标的简洁算法,并编程实现。然后采用模拟仿真结合统计分析的方法评估了该算法在不同条件下的拟合精度,得出测点误差越大,拟合精度越低;测点个数越多,分布越均匀,拟合精度越高;圆半径对拟合精度影响甚小等结论。在某工程项目中使用该算法得到的结果精度较高,验证了其有效可行,且与采用其他方法得到的坐标值较为接近,说明了该算法的可靠性高。     

Truncation error formulae for the disturbing gravity vector

Recurrence relations have been derived for truncation error coefficients of the extended Stokes' function and its partial derivatives required in the computation of the disturbing gravity vector at any elevation above the earth's surface. The corresponding formulae, the example of values of the truncation error coefficients for H=30.1 km and ψ₀=30^∘ and the estimations of truncation error are given in this article. Received: 26 January 1996 / Accepted: 11 June 1997     

测绘业向地理信息产业转变的几个问题

本文阐述了地理信息产业的概念和内容,分析了地理信息产业在国民经济建设中的战略地位及对国民经济建设的辐射渗透作用,提出了测绘业向地理信息产业转化的要求和途径。     

三维坐标转换的多元线性回归模型及粗差剔除

将三维直角坐标转换归结为多元线性回归模型,导出其矩阵方程形式及精度评定公式;通过实例研究多元线性回归和7参数解法的异同,得出重要结论;提出一种构造r统计量逐点剔除观测值粗差的有效方法.     

道路平面测设计算的通用公式

基于各类道路线型曲率呈线性变化的共同特性,给出了线元上任意点坐标方位角的统一计算公式,进而提出了适用于所有道路线型平面测设计算的中桩坐标、边桩坐标的通用公式。在此基础上,讨论线路外一点对应中桩的计算以及直线与线路交点的计算,给出了相应的计算方案。     

非对称缓和曲线坐标计算方法

本文重点阐述高等级公路非标准缓和曲线的施工放样测量.缓和曲线是设置在直线和圆曲线之间的一种线型,起缓和过渡作用,其目的在于保证车辆由直线进入圆曲线(或由圆曲线进入直线)时的横向稳定,缓和曲线的曲率半径随曲线长度的增加而均匀连续地变小,本文综合了各种情况下的曲线计算,给出了直接计算和间接计算两种计算方法,并用C编写了计算...