大地主题解算方法综述

大地主题解算是大地测量中的重要问题,由于椭球的复杂性,随之产生的解算方法也是多种多样。本文分析了大地主题解算的一般方法及其公式的适用范围,指出了它们的特点和不足,讨论了现今常用解算方法存在的问题和进一步的研究方向。     

Cartesian to geodetic coordinates conversion on a triaxial ellipsoid

A new method of transforming Cartesian to geodetic (or planetographic) coordinates on a triaxial ellipsoid is presented. The method is based on simple reasoning coming from essentials of vector calculus. The reasoning results in solving a nonlinear system of equations for coordinates of the point being the projection of a point located outside or inside a triaxial ellipsoid along the normal to the ellipsoid. The presented method has been compared to a vector method of Feltens (J Geod 83:129–137, 2009) who claims that no other methods are available in the literature. Generally, our method turns out to be more accurate, faster and applicable to celestial bodies characterized by different geometric parameters. The presented method also fits to the classical problem of converting Cartesian to geodetic coordinates on the ellipsoid of revolution.     

椭球膨胀法在高原长距离工程中的应用

对5种椭球膨胀方法进行系统的理论推导与分析,并在云南滇中引水这一典型的高原长距离工程中应用。研究获取椭球长半轴变化量、基准点大地坐标变化量、测区端点高斯坐标变化量与长度变形值等测算数据,并分析各种椭球膨胀方法数据结果的差异性与合理性。结果表明,平面解析法与广义微分法更适合作为高原长距离工程的椭球膨胀方法。     

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″。     

空间直角坐标计算大地坐标的抛物线逼近法

采用抛物线逼近法求解大地纬度和大地高,先计算空间点在椭球面上的子午面坐标,然后求解点的大地纬度和大地高。     

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.     

Alignment of geodetic and satellite coordinate systems to the average terrestrial system

The parallelism of geodetic and satellite systems to the average terrestrial system is examined, under the assumption that a geodetic system is a fixed framework invariant with respect to geodetic network adjustment. In this case a geodetic system is rotated with respect to the average terrestrial system only about the ellipsoid normal of the initial point. The method is demonstrated using coordinates and covariance matrices for BC-4 and SECOR satellite tracking stations computed by Mueller and his co-workers. It is shown that the NAD geodetic system is scaled significantly larger than the satellite systems; the SECOR satellite systems have significant Z-rotations with respect to the average terrestrial system; and the ETH geodetic system may have a significant rotation with respect to the average terrestrial system.     

Accurate area determination in the cadaster: case study of Slovenia

This paper discusses methodological problems of accurate area determination in the cadaster. The paper contrasts the ambiguous legal definition of the parcel boundary and parcel area in relation to the theoretically well-defined geodetic parcel boundary and the geodetic parcel area on the reference ellipsoid. To align with the real world, parcel area must account for terrain elevation. Various approximate methods for area determination which can be used in the cadaster are tested. A highly accurate method for parcel area computation is proposed, based on an equal-area projection. Considering the geodetic parcel area as a reference, the achievable accuracy of different methods is evaluated. For this analysis, the coordinates of the parcel boundary points are treated as error-free. Finally, the relevance of various systematic errors is discussed in relation to the statistical uncertainty of the parcel area, which could be gained by an a real-time kinematic GNSS survey. A case study is presented for the territory of Slovenia, its georeferencing rules, land demarcation pattern, and characteristics of its topography. Based on the results of this study, some general recommendations for the parcel area determination are given.     

GPS高程转换方法和正常高计算

GPS测量所提供的高程为相对于WGS-84椭球的GPS大地高，而我国使用的是正常高。大地高等于正常高与高程异常之和，要使GPS高程在工程实际中得到应用，必须先求出高程异常，进而获得正常高。结合GPS测量和水准测量资料，用神经网络方法和二次多项式曲面拟合方法拟合高程异常，对拟合精度进行了分析比较，得出了有实用价值的结论。     

GPS测量坐标转换实用性问题的分析

针对ＧＰＳ测量坐标转换方法中存在的问题,提出了强制符合平面四参数法和多项式拟合法,这两种方法能够有效的克服高程系统以及椭球参数不一致造成的误差,比较适合于工程自由坐标之间的转换;同时本文给出了基于“全球大地水准面的几何中心地球质心相重合”这一假设之上的莫洛金斯坐标转换法,该法不需要联测公共点即可将ＷＧＳ－８４坐标转换成本地局部坐标。上述几种方法减少了额外联测的工作量,提高了ＧＰＳ的使用效率。     

The North American datum of 1983: Project methodology and execution

A new adjustment of the geodetic control networks in North America has been completed, resulting in a new continental datum—the North American Datum of 1983 (NAD 83). The establishment ofNAD 83 was the result of an international project involving the National Geodetic Survey of the United States, the Geodetic Survey of Canada, and the Danish Geodetic Institute (responsible for surveying in Greenland). The geodetic data in Mexico and Central America were collected by the Inter American Geodetic Survey and validated by the Defense Mapping Agency Hydrographic/Topographic Center. The fundamental task ofNAD 83 was a simultaneous least squares adjustment involving 266,436 stations in the United States, Canada, Mexico, and Central America. The networks in Greenland, Hawaii, and the Caribbean islands were connected to the datum through Doppler satellite and Very Long Baseline Interferometry (VLBI) observations. The computations were performed with respect to the ellipsoid of the Geodetic Reference System of 1980. The ellipsoid is positioned in such a way as to be geocentric, and its axes are oriented by the Bureau International de l'Heure Terrestrial System of 1984. The mathematical model for theNAD readjustment was the height-controlled three-dimensional system. The least squares adjustment involved 1,785,772 observations and 928,735 unknowns. The formation and solution of the normal equations were carried out according to the Helmert block method. [Authors' note:This article is a condensation of the final report of the NAD 83 project. The full report (Schwarz,1989) contains a more complete discussion of all the topics.]     

一种表示地球椭球体上椭圆的算法

采用常规的投影算法表示地球椭球体上的椭圆时,所得椭圆与实际椭圆存在一定误差。针对上述问题,阐述了一种通过解算大地主题表示地球椭球体上椭圆的算法。通过几个实例,对两种算法进行了比较和分析,结果表明,通过解算大地主题表示地球椭球体上椭圆的算法具有非常高的精度。     

区域椭球面上数字高程模型的建立

提出了在局部区域的椭球面上建立数字高程模型的原理和方法。这种椭球面的DEM是在区域性椭球面上基于新大地坐标系建立的,不同于现有的基于投影平面的DEM。由于未经过从椭球面到平面的投影,从而杜绝了投影变形,也消除了平面位置与水准高程之间作为3维坐标的不兼容性。在具体建模中,直接基于与测区平均高程面最优拟合的区域性椭球面,采用格网DEM的建模方法来建立椭球面DEM。     

大地网的二类优化设计

本文首先分析了当前大地网二类优化设计的各种解算方法,并在此基础上,利用矩阵的谱分解理论以及组成和解算法方程的思想,给出了一种新的解算方法。     

全国天文大地网与空间大地网联合平差

天文大地网与空间大地网联合平差,对于检核、控制与加强天文大地网以及建立与扩展地心坐标系,都具有重要意义,全国天文大地网与全国ＧＰＳ大地网联合平差（Ｉ期）于１９９８年初完成,本文报告平差采用的原则和模型,并提出平差结果,通过联合平差,消除了天文大地网尺度的系统偏差,减弱了它的局部变形,改善了它的整体精度,更重要的是建立了由近５万个大地点坐标体现的地心参考系,其地心坐标的水平分量精度好于０．５ｍ。     

Geoid determination using one-step integration

A residual (high-frequency) gravimetric geoid is usually computed from geographically limited ground, sea and/or airborne gravimetric data. The mathematical model for its determination from ground gravity is based on the transformation of observed discrete values of gravity into gravity potential related to either the international ellipsoid or the geoid. The two reference surfaces are used depending on height information that accompanies ground gravity data: traditionally orthometric heights determined by geodetic levelling were used while GPS positioning nowadays allows for estimation of geodetic (ellipsoidal) heights. This transformation is usually performed in two steps: (1) observed values of gravity are downward continued to the ellipsoid or the geoid, and (2) gravity at the ellipsoid or the geoid is transformed into the corresponding potential. Each of these two steps represents the solution of one geodetic boundary-value problem of potential theory, namely the first and second or third problem. Thus two different geodetic boundary-value problems must be formulated and solved, which requires numerical evaluation of two surface integrals. In this contribution, a mathematical model in the form of a single Fredholm integral equation of the first kind is presented and numerically investigated. This model combines the solution of the first and second/third boundary-value problems and transforms ground gravity disturbances or anomalies into the harmonically downward continued disturbing potential at the ellipsoid or the geoid directly. Numerical tests show that the new approach offers an efficient and stable solution for the determination of the residual geoid from ground gravity data.     

连续网模拟优化方法研究

本文根据连续网精度数字化分析的结数,建立了适用于大规模连续网优化的快速选择最优附加观测量的方法。借此,成功地将解析模拟法应用到较大规模连续网的优化设计和改进中。     

顾及精度与可靠性的测量控制网优化设计

本文从两个准则矩阵——精度准则矩阵与可靠性准则矩阵出发,导出了一种新的测量控制网优化设计方法。利用它不仅能实现同时顾及精度与可靠性的二类优化设计,还可进行以准则矩阵为基础的一类优化设计。另外,这种方法可将一类、二类设计问题同时解决,从而为测量控制网的混合设计开辟了新路。     

国外测绘机构大地测量的新动向

本文概述国外测绘机构大地测量的动向 ,目的在于了解全球大地测量的发展趋势 ,作为借鉴。综观各国的大地测量动向可以看出 ,高精度国家大地控制网的建立 ,都是采用 GPS,无一例外 ,而且它们之间只是细节上的差异。从各国建立高精度大地控制网的目的来看 ,都是为多学科服务的。面对这样的总趋势 ,大地测量工作者必须拓宽知识面 ,迎接新的挑战。     

斜轴变形椭球高斯投影方法

针对东西跨度较大的线路,借助最小二乘法建立斜轴参考椭球,以减小高斯投影横坐标;通过坐标系转换理论,推导出测区在各坐标系下的空间直角坐标,进而确定测区相对于斜轴参考椭球上的大地坐标;利用椭球变换法建立斜轴变形椭球以减小因高程引起的投影变形。以某铁路线为例,可知"斜轴变形椭球高斯投影方法"可大大减小投影后横轴方向分量,避免高斯投影分带现象,同时有效减小高程及其引起的投影变形。该方法数学模型严谨、运算过程清晰,便于编制相关软件,可投入工程使用。