Determination of Indian absolute geodetic datum by least-square solution technique

The Everest spheroid, 1830, in general use in the Survey of India, was finally oriented in an arbitrary manner at the Indian geodetic datum in 1840; while the international spheroid, 1924, in use for scientific purposes; was locally fitted to the Indian geoid in 1927. An attempt is here made to obtain the initial values for the Indian geodetic datum in absolute terms on GRS 67 by least-square solution technique, making use of the available astro-geodetic data in India, and the corresponding generalised gravimetric values at the considered astro-geodetic points, as derived from the mean gravity anomalies over1°×1° squares of latitude and longitude in and around the Indian sub-continent, and over5° equal area blocks covering the rest of the earth’s surface. The values obtained independently by gravimetric method, were also considered before actual finalization of the results of the present determination.     

Robust estimation of geodetic datum transformation

The robust estimation of geodetic datum transformation is discussed. The basic principle of robust estimation is introduced. The error influence functions of the robust estimators, together with those of least-squares estimators, are given. Particular attention is given to the robust initial estimates of the transformation parameters, which should have a high breakdown point in order to provide reliable residuals for the following estimation. The median method is applied to solve for robust initial estimates of transformation parameters since it has the highest breakdown point. A smooth weight function is then used to improve the efficiency of the parameter estimates in successive iterative computations. A numerical example is given on a datum transformation between a global positioning system network and the corresponding geodetic network in China. The results show that when the coordinates are contaminated by outliers, the proposed method can still give reasonable results. Received: 25 September 1997 / Accepted: 1 March 1999     

日本大地基准及其现代化的思考

介绍了日本曾采用了百余年的大地基准TD1918,阐述了它不能适应当前日本的经济、社会和军事发展的需求,日本于2002年开始采用新的地心三维大地基准JGD2000.概要介绍了JGD2000大地系统的定义及其框架,最后给出了这两个新老大地基准的转换.     

Height datum definition,height datum connection and the role of the geodetic boundary value problem

Vertical datum definition is identical with the choice of a potential (or height) value for the fundamental bench mark. Also the connection of two adjacent vertical datums poses no principal problem as long as the potential (or height) value of two bench marks of the two systems is known and they can be connected by levelling. Only the unification of large vertical datums and the connection of vertical datums separated by an ocean remains difficult. Two vertical datums can be connected indirectly by means of a combination of precise geocentric positions of two points, as derived by space techniques, their potential (or height) value in the respective height datum and their geoid height difference. The latter requires the solution of the linear geodetic boundary value problem under the assumption that potential and gravity anomalies refer to a variety of height datums. The unknown off-sets between the various datums appear in the solution inside and outside the Stokes integral and can be estimated in a least squares adjustment, if geocentric positions, levelled heights and adequate gravity material are available for all datum zones. The problem can in principle also be solved involving only two datums, in case a precise global gravity field becomes available purely from satellite methods.     

A bias-free geodetic boundary value problem approach to height datum unification

A geodetic boundary value problem (GBVP) approach has been formulated which can be used for solving the problem of height datum unification. The developed technique is applied to a test area in Southwest Finland with approximate size of 1.5° × 3° and the bias of the corresponding local height datum (local geoid) with respect to the geoid is computed. For this purpose the bias-free potential difference and gravity difference observations of the test area are used and the offset (bias) of the height datum, i.e., Finnish Height Datum 2000 (N2000) fixed to Normaal Amsterdams Peil (NAP) as origin point, with respect to the geoid is computed. The results of this computation show that potential of the origin point of N2000, i.e., NAP, is (62636857.68 ± 0.5) (m²/s²) and as such is (0.191 ± 0.003) (m) under the geoid defined by W ₀ = 62636855.8 (m²/s²). As the validity test of our methodology, the test area is divided into two parts and the corresponding potential difference and gravity difference observations are introduced into our GBVP separately and the bias of height datums of the two parts are computed with respect to the geoid. Obtaining approximately the same bias values for the height datums of the two parts being part of one height datum with one origin point proves the validity of our approach. Besides, the latter test shows the capability of our methodology for patch-wise application.     

Generalized inverses of nonlinear mappings and the nonlinear geodetic datum problem

Motivated by the existing theory of the geometric characteristics of linear generalized inverses of linear mappings, an attempt is made to establish a corresponding mathematical theory for nonlinear generalized inverses of nonlinear mappings in finite- dimensional spaces. The theory relies on the concept of fiberings consisting of disjoint manifolds (fibers) in which the domain and range spaces of the mappings are partitioned. Fiberings replace the quotient spaces generated by some characteristic subspaces in the linear case. In addition to the simple generalized inverse, the minimum-distance and the x ₀-nearest generalized inverse are introduced and characterized, in analogy with the least-squares and the minimum-norm generalized inverses of the linear case. The theory is specialized to the geodetic mapping from network coordinates to observables and the nonlinear transformations (Baarda's S-transformations) between different solutions are defined with the help of transformation parameters obtained from the solution of nonlinear equations. In particular, the transformations from any solution to an x ₀-nearest solution (corresponding to Meissl's inner solution) are given for two- and three-dimensional networks for both the similarity and the rigid transformation case. Finally the nonlinear theory is specialized to the linear case with the help of the singular-value decomposition and algebraic expressions with specific geometric meaning are given for all possible types of generalized inverses. Received: 11 April 1996 / Accepted: 19 April 1997     

Local datum definition and geodetic network positioning using global navigation satellite systems

The problem of datum definition as applied to local-area geodetic networks is investigated using data collected from global navigation satellite systems (GNSS). It is shown that the process of double differencing makes the model more sensitive to computational errors that reduce the ability of the satellites alone to control the translation component of the datum definition, and as a result additional regularization is required. Traditionally, datum definition has been accomplished by constraining one station to set coordinates. Alternative regularization strategies are analysed in terms of their effects on positioning and ambiguity resolution. In doing so, processing strategies are developed which can improve the quality of global positioning system (GPS)-based position solutions in geodetic network applications of limited spatial extent, such as high-precision engineering and deformation monitoring networks.     

Geocentric indian geodetic datum by astrogeodetic — gravimetric method using smoothened geoidal heights

The astrogeodetic—gravimetric method based on the principle of least—squares solution has been used to determine the geocentric Indian geodetic datum making use of the available nongeocentric astrogeodetic data and the gravimetric geocentric geoidal heights in the form of smoothened values. Everett's method of interpolation has been used to obtain the smoothened geoidal heights at the astrogeodetic stations in India from the available generalized values at 1°×1° corners. The values of the geoidal height and deflections of the vertical at the geodetic datum Kalianpur H.S. so obtained have the negligible difference from the values computed earlier by the same method using directly computed gravimetric geoidal heights at the astrogeodetic stations, indicating that the use of the interpolated values in the astrogeodetic—gravimetric method employed would be an economical approach of absolute orientation of a nongeocentric system if the gravimetric geoidal heights are available at 1°×1° corners in the area of interest.     

World geodetic datum WD 1 and WD 2 from satellite and terrestrial observations

By minimizing the global distance between the (quasi-) geoid and an ellipsoid of revolution, the best parameters of an ellipsoid and its location parameters are estimated. Input data are the absolute value of the geopotential at (quasi-) geoid level, a set of harmonic coefficients from satellite, terrestrial or combined observations, the mean rotational speed of the earth, and approximate values of the seminajor axis and the eccentricity of the ellipsoid. The output ranges from 6378137,63 m and 6378141,62 m for the best semimajor axis and from 298.259758 and 298.259651 for the reciprocal value of the best ellipsoidal flattening within WD 1 and WD 2. The best translational parameters are 6.4 cm (Greenwich-direction), 0.8 cm (orthogonal to Greenwich-direction), and 1.9 cm (parallel to rotational axis of the earth); the best rotational parameters are −0.2” (around Greenwich-direction) and 1.1” (around orthogonal to Greenwich-direction). The dependence of the datum of the (quasi-) geoid geopotential is studied in detail.     

海底大地基准点圆走航模式定位模型及分析

圆走航模式是确定海底大地基准点位置的常用测量模式.本文对圆走航模式的定位效能进行了系统分析.首先分析了顾及声速剖面变化规律的声学测距非差定位模型和削弱系统误差影响的历元间差分定位模型,然后分析了圆走航模式下非差、单差定位模型的定位效能,包括位置参数的可估性,不同分量位置精度的最佳测量半径、所达到的理论精度,以及测距误差...     

基于CGCS2000下地方大地坐标基准的建立与应用

随着现代空间定位技术的发展,原有地方独立坐标系统和控制测量成果存在诸多的问题,迫切需要建立基于CGCS2000下的新一代地方大地坐标基准。文中对地方坐标系的建设要求进行分析,研究新一代地方坐标系的参数选择和首级控制网的布设方法,并运用实际案例进行说明。     

The present extent of the astro-geodetic geoid and the geodetic world datum derived from it

Since the presentation of “The Hough Ellipsoid” at the Toronto meeting in 1957, the astro-geodetic geoid was extended into the Caribbean, India, and Japan. The two hemispheres were tentatively connected across the North Atlantic by a reasonable assumption about the unknown geoid profile there. A series of solutions for a world ellipsoid and world datum was made, with and without enforcing the flattening of 1/298.3, with and without gravimetric orientation. The resulting ellipsoids are very small, with an equatorial radius of around 6378 160 m. The agreement between astro-geodetic and gravimetric geoid profiles is greatly improved by the small ellipsoid.     

Accuracy analysis for the NAD 83 geodetic reference system

The North American Datum of 1983 (NAD 83) provides horizontal coordinates for more than 250,000 geodetic stations. These coordinates were derived by a least squares adjustment of existing terrestrial and space-based geodetic data. For pairs of first order stations with interstation distances between 10km and 100km, therms discrepancy between distances derived fromNAD 83 coordinates and distances derived from independentGPS data may be suitably approximated by the empirical rulee=0.008 K^0.7 where e denotes therms discrepancy in meters and K denotes interstation distance in kilometers. For the same station pairs, therms discrepancy in azimuth may be approximated by the empirical rule e=0.020 K^0.5. Similar formulas characterize therms discrepancies for pairs involving second and third order stations. Distance and orientation accuracies, moreover, are well within adopted standards. While these expressions indicate that the magnitudes of relative positional accuracies depend on station order, absolute positional accuracies are similar in magnitude for first, second, and third order stations. Adjustment residuals reveal a few local problems with theNAD 83 coordinates and with the weights assigned to certain classes of observations.     

Comparison between geodetic and oceanographic approaches to estimate mean dynamic topography for vertical datum unification: evaluation at Australian tide gauges

The direct method of vertical datum unification requires estimates of the ocean’s mean dynamic topography (MDT) at tide gauges, which can be sourced from either geodetic or oceanographic approaches. To assess the suitability of different types of MDT for this purpose, we evaluate 13 physics-based numerical ocean models and six MDTs computed from observed geodetic and/or ocean data at 32 tide gauges around the Australian coast. We focus on the viability of numerical ocean models for vertical datum unification, classifying the 13 ocean models used as either independent (do not contain assimilated geodetic data) or non-independent (do contain assimilated geodetic data). We find that the independent and non-independent ocean models deliver similar results. Maximum differences among ocean models and geodetic MDTs reach >150 mm at several Australian tide gauges and are considered anomalous at the 99% confidence level. These differences appear to be of geodetic origin, but without additional independent information, or formal error estimates for each model, some of these errors remain inseparable. Our results imply that some ocean models have standard deviations of differences with other MDTs (using geodetic and/or ocean observations) at Australian tide gauges, and with levelling between some Australian tide gauges, of \({\sim }\pm 50\,\hbox {mm}\). This indicates that they should be considered as an alternative to geodetic MDTs for the direct unification of vertical datums. They can also be used as diagnostics for errors in geodetic MDT in coastal zones, but the inseparability problem remains, where the error cannot be discriminated between the geoid model or altimeter-derived mean sea surface.     

Application of the gravimetric method for a world geodetic system

It is desirable to unify the various unconnected geodetic systems of the world into a common earth-centered world datum. This can be achieved by gravimetric means. The gravimetric deflection components have been determined at a certain number of stations in different areas. Utilizing the differences between the gravimetric and astro-geodetic deflection components, the reduction of the major geodetic datums into a common world geodetic system has been accomplished. Geophysical Studies Section Aeronautical Chart and Information Center Presented at the Twelfth General Assembly of the International Union of Geodesy and Geophysics Helsinki, Finland     

经纬仪测量系统尺度基准测定及误差分析

针对经纬仪测量系统缺少距离观测值而难以构建其尺度基准的问题,该文分别基于相似原理和垂直角视距法,阐述了通过交会测量已知长度的基准尺构建尺度基准的原理与方法;依据误差传播定律,分析指出水平基线中误差是衡量尺度基准精度的重要数字指标,而基准尺摆放位置与姿态、基准尺长度和水平基线长度等构形要素对尺度基准误差影响较大;最后基于Matlab GUI编制了水平基线中误差仿真计算程序,定量分析了各类构形要素对水平基线中误差的影响规律,归纳总结出提高尺度基准测定精度、优化系统测量空间构形的若干措施。     

湖南省CGCS2000国家大地坐标系统转换方法

基于湖南省大地控制点布设现状、各等级控制点成果以及信息扩散估计理论,分析现有CGCS2000坐标成果和北京54、西安80两类坐标系建模共点的数据质量,为后续模型优选和模型质量保障奠定基础.在此基础上,研究各类大地坐标系统转换算法,实例计算各类算法的坐标转换结果,进行精度比较与分析,提出适宜于湖南省CGCS2000坐标系...