Computing geodetic coordinates from geocentric coordinates

A closed-form algebraic method to transform geocentric coordinates to geodetic coordinates has previously been proposed. The validity domain of latitude and height formulae in the vicinity of the Earths core is specified. A new expression of longitude is proposed, excluding indetermination and sensitivity to round-off error around the ±180 degrees longitude discontinuity.     

现代大地测量参考系统

概述现代大地测量参考系统的定义及不同参考系统之间的关系.主要讨论我国当代大地测量界常使用的3种用以表示几何位置的参考系统1980年国家大地坐标系、全球大地测量系统 1984 (WGS 84)、国际地球参考系统(ITRS),和一种用以表示物理位置,高程的参考系统1985年国家高程基准.并讨论大地测量中框架和基准的概念.     

现代大地测量参考系统

概述现代大地测量参考系统的定义及不同参考系统之间的关系。主要讨论我国当代大地测量界常使用的3种用以表示几何位置的参考系统－1980年国家大地坐标系、全球大地测量系统1984（WGS84）、国际地球参考系统（ITRS），和一种用以表示物理位置，高程的参考系统－1985年国家高程基准。并讨论大地测量中框架和基准的概念。     

Direct transformation from geocentric coordinates to geodetic coordinates

 The transformation from geocentric coordinates to geodetic coordinates is usually carried out by iteration. A closed-form algebraic method is proposed, valid at any point on the globe and in space, including the poles, regardless of the value of the ellipsoid's eccentricity. Received: 14 August 2000 / Accepted: 26 June 2002     

浅谈地球坐标系及2000国家大地坐标系

介绍了地球坐标参考系统和国际地球参考系及参考框架;阐述了2000国家大地坐标系,指出2000国家大地坐标系可按精度划分为国家级连续运行基准站、GPSA、B级网、天文大地网三个层次。     

An analytical method to transform geocentric into geodetic coordinates

A closed-form analytical method needing no approximation and deduced from a single quartic equation is offered to transform geocentric into geodetic coordinates. It is valid at any point inside and outside the Earth including the polar axis, the equatorial plane and the Earth’s center. Comparison with the method of extrema with constraints to obtain this quartic equation is made.     

Fast transform from geocentric to geodetic coordinates

 A new iterative procedure to transform geocentric rectangular coordinates to geodetic coordinates is derived. The procedure solves a modification of Borkowski's quartic equation by the Newton method from a set of stable starters. The new method runs a little faster than the single application of Bowring's formula, which has been known as the most efficient procedure. The new method is sufficiently precise because the resulting relative error is less than 10⁻¹⁵, and this method is stable in the sense that the iteration converges for all coordinates including the near-geocenter region where Bowring's iterative method diverges and the near-polar axis region where Borkowski's non-iterative method suffers a loss of precision. Received: 13 November 1998 / Accepted: 27 August 1999     

ITRF框架与CGCS2000国家大地坐标系的转换方法研究

按两种思路实现ITRF框架与CGCS2000国家大地坐标系的转换：一是同时考虑历元和框架差异求解参数进行转换;二是转换过程分两步进行,先将ITIF框架基于当前历元的定位结果转换至2000．0历元,然后在历元相同的情况下,实现ITRF框架和CGCS2000的转换。基于VB．NET语言实现转换结果表明：方法二先根据若干基准点的位置与速度信息采用加权平均法内插转换点的速度实现历元间的转换,统一历元后再采用七参数法实现框架间的转换,能满足转换精度要求。     

联系不同大地参考系的回归模型及RCT软件的应用

为综合应用不同参考坐标系中的测量成果，必须实现不同参考坐标系的统一。本文研究了回归模型在坐标转换中的应用，结合坐标转换实际提出并采用了多项式回归及逐次剔除的回归方法。文中介绍了坐标转换软件ＲＣＴ的主要功能，应用该软件计算了 １９５４年北京坐标系至 １９８０ＮＮＳＳ（ＢＥ）的最优回归转换模型。     

Transformation from geocentric to geodetic coordinates using Newton's iteration

Summary A new procedure for the transformation from geocentric to geodetic coordinates is introduced and analyzed. This new procedure which contains only one trigonometric function uses the Newton's iteration to solve the root of a non-linear equation. Compared with the well-known Bowring's iterative algorithm which uses a number of trigonometric functions, the new procedure is more efficient in computation. Numeric examples are used to test the two algorithms and the results show that the new procedure converges just as well as Bowring's algorithm but requires less time for completion.     

大地测量数据标准体系的研究

针对大地测量数据标准在数字化大地测量生产、应用和服务过程中的重要性，讨论大地测量技术基础标准、信息系统标准和数据服务标准的内容框架，建立大地测量数据标准体系的层次关系和门类关系。     

Direct gravity formula for the Geodetic Reference System 1967

A Direct Gravity Formula, polynomial in latitude, has been obtained from the series expansion of the closed gravity formula of Somigliana by a telescoping procedure. The use of the 7 coefficient formula gives a result as accurate as the closed expression. With 6 coefficients it gives an order of magnitude better accuracy than that of the widely used Chebyshev approximation and with 5 coefficients a result that is accurate to better than that of the conventional form of computing theoretical gravity. The derived approximation is not only simpler than other forms, but also at least 11 and 17 times faster on the CDC CYBER 74 computer than the Chebyshev approximation and the closed gravity formula respectively. Contribution from the Earth Physics Branch N^o 720.     

Transformation of coordinates between two horizontal geodetic datums

The following topics are discussed in this paper: the geocentric coordinate system and its different realizations used in geodetic practice; the definition of a horizontal geodetic datum (reference ellipsoid) and its positioning and orientation with respect to the geocentric coordinate system; positions on a horizontal datum and errors inherent in the process of positioning; and distortions of geodetic networks referred to a horizontal datum. The problem of determining transformation parameters between a horizontal datum and the geocentric coordinate system from known positions is then analysed. It is often found necessary to transform positions from one horizontal datum to another. These transformations are normally accomplished through the geocentric coordinate system and they include the transformation parameters of the two datums as well as the representation of the respective network distortions. Problems encountered in putting these transformations together are pointed out.     

基于ArcGIS的1980西安坐标系到2000国家坐标系的转换研究

分析了2000国家坐标系与WGS-84坐标系的椭球参数及定向参数,通过实验证实了在ArcGIS中采用WGS-84坐标系的大地坐标代替2000国家坐标系的大地坐标的可行性.本文在自编写的程序中,使用不同大地坐标转换的布尔莎公式计算出了1980西安坐标系与2000国家坐标系的7个转换参数,并将该参数输入到AreGIS的坐标转换参数文件中,从而实现矢量数据与栅格数据从1980西安坐标系到2000国家大地坐标系的转换.通过对转换结果进行精度分析,认为可选用控制测区范围的3～5个转换公共点,使用本文所述方法与流程可以满足1∶1 000或更大比例尺图件的坐标系统转换.     

我国大地坐标系的换代问题

首先指出了我国现有大地坐标系在先进性和实用性方面存在的问题,提出了我们面临的选择与采用地心坐标系的建议,然后就地心坐标系的定义和实现、参考椭球常数、正常重力公式等问题提出了初步意见,并就坐标系改变对旧地形图的影响问题进行了研究。我国大地坐标系应由局部坐标系更新为地心坐标系。我国大地坐标系的定义应与IERS(国际地球自转服务)协议相一致,采用国际常用的参考椭球和正常重力公式。本文提出的参考椭球和正常重力公式符合这些原则,提出的地形图坐标系变化改正方案应是基本可行的。     

Iterative vector methods for computing geodetic latitude and height from rectangular coordinates

 Two iterative vector methods for computing geodetic coordinates (φ, h) from rectangular coordinates (x, y, z) are presented. The methods are conceptually simple, work without modification at any latitude and are easy to program. Geodetic latitude and height can be calculated to acceptable precision in one iteration over the height range from −10⁶ to +10⁹ m. Received: 13 December 2000 / Accepted: 13 July 2001