Journal Article•
Curvilinear geodetic datum transformations
About: This article is published in Oceanographic Literature Review.The article was published on 1996-01-01 and is currently open access. It has received 46 citations till now. The article focuses on the topics: Geodetic datum.
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TL;DR: In this article, the robust estimation of geodetic datum transformation is discussed, where the robust initial estimates of the transformation parameters should have a high breakdown point in order to provide reliable residuals for the following estimation.
Abstract: 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.
149 citations
TL;DR: In this article, it is shown how a Gauss-Newton method in the rotation parameters alone can easily be implemented to determine the parameters of the nine-parameter transformation (when different scale factors for the variables are needed).
101 citations
Cites background from "Curvilinear geodetic datum transfor..."
...For a study of this and other transformations in this context, see [6, 7, 8, 9, 10]....
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TL;DR: In this paper, the authors introduce quaternions to represent rotation parameters and derive the formulae to compute quaternion, translation and scale parameters in the Bursa-Wolf geodetic datum transformation model from two sets of co-located 3D coordinates.
Abstract: This paper briefly introduces quaternions to represent rotation parameters and then derives the formulae to compute quaternion, translation and scale parameters in the Bursa–Wolf geodetic datum transformation model from two sets of co-located 3D coordinates. The main advantage of this representation is that linearization and iteration are not needed for the computation of the datum transformation parameters. We further extend the formulae to compute quaternion-based datum transformation parameters under constraints such as the distance between two fixed stations, and develop the corresponding iteration algorithm. Finally, two numerical case studies are presented to demonstrate the applications of the derived formulae.
72 citations
Cites background from "Curvilinear geodetic datum transfor..."
...A number of papers have been published on geodetic datum transformation (e.g., Yang 1999; Grafarend et al. 1995; Shen and Wei 1999; Vaniy cek and Steeves 1996; Welsch 1993; Soler 1998), and linearization is needed for solving the transformation parameters in order to simplify the model....
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TL;DR: In this article, the authors derived and tested the equations of a curvilinear datum transformation of ellipsoidal GPS coordinates in a global datum to conformai coordinates of UMP type in a local datum.
Abstract: A key problem of contemporary static and kinematic positioning is the problem of transformation of conformai coordinates of universal Mercator projection (UMP) type from a local datum (regional, national) to a global datum, for instance, the World Geodetic System 1984 (WGS 84) with reference to Boyle (1987) Such a problem is met if we use WGS 84 GPS‐derived ellipsoidal coordinates of a point for localization in a local chart of UMP type In this article we derive and test the equations of a curvilinear datum transformation of ellipsoidal GPS coordinates in a global datum to conformai coordinates of UMP type in a local datum The curvilinear datum transformation includes three parameters for translation, three parameters for rotation, one scale parameter, and two form parameters which account for a change in the semimajor axis and in the relative eccentricity of the reference ellipsoid
33 citations
TL;DR: In this article, a new method through Gauss-Helmert model of adjustment is presented for the solution of the similarity transformations, either 3D or 2D, in the frame of errors-in-variables (EIV) model.
Abstract: A new method through Gauss–Helmert model of adjustment is presented for the solution of the similarity transformations, either 3D or 2D, in the frame of errors-in-variables (EIV) model. EIV model assumes that all the variables in the mathematical model are contaminated by random errors. Total least squares estimation technique may be used to solve the EIV model. Accounting for the heteroscedastic uncertainty both in the target and the source coordinates, that is the more common and general case in practice, leads to a more realistic estimation of the transformation parameters. The presented algorithm can handle the heteroscedastic transformation problems, i.e., positions of the both target and the source points may have full covariance matrices. Therefore, there is no limitation such as the isotropic or the homogenous accuracy for the reference point coordinates. The developed algorithm takes the advantage of the quaternion definition which uniquely represents a 3D rotation matrix. The transformation parameters: scale, translations, and the quaternion (so that the rotation matrix) along with their covariances, are iteratively estimated with rapid convergence. Moreover, prior least squares (LS) estimation of the unknown transformation parameters is not required to start the iterations. We also show that the developed method can also be used to estimate the 2D similarity transformation parameters by simply treating the problem as a 3D transformation problem with zero (0) values assigned for the z-components of both target and source points. The efficiency of the new algorithm is presented with the numerical examples and comparisons with the results of the previous studies which use the same data set. Simulation experiments for the evaluation and comparison of the proposed and the conventional weighted LS (WLS) method is also presented.
30 citations