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A Practical Quality Index for the Applied Helmert Transformation
Journal of Surveying Engineering, 2016AbstractThe Helmert transformation is used in different procedures in geodesy, photogrammetry, and in general in geomatics. The assessment of the accuracy of the transformation, and in particular of the transformed coordinates, is often critical. In this paper, a new overall quality index describing the accuracy of the transformed points is proposed ...
Benciolini, Giovanni Battista +2 more
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Helmert transformation with mixed geodetic and Cartesian coordinates
Advances in Space Research, 2019Abstract It is common in geodetic practice that station geodetic coordinates in an old frame are measured/estimated by adjusting conventional leveling and vertical networks (together with a vertical datum), whereas their Cartesian coordinates in a new frame are measured/estimated by adjusting modern 3D Global Navigation Satellite System (GNSS ...
Peng Lin +4 more
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M-estimator for the 3D symmetric Helmert coordinate transformation
Journal of Geodesy, 2017The M-estimator for the 3D symmetric Helmert coordinate transformation problem is developed. Small-angle rotation assumption is abandoned. The direction cosine matrix or the quaternion is used to represent the rotation. The $$3 \times 1$$
Guobin Chang, Tianhe Xu, Qianxin Wang
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Helmert transformation solutions combination and update with new measurements
Acta Geodaetica et Geophysica, 2019This work is concerned with refining the Helmert solutions in two different cases, namely combining different solutions and updating old solutions with newly available measurement data. The parameters to be estimated in the solutions here not only include the transformation parameters, namely the rotation, the translation and the scale, but also the ...
Shengquan Li +4 more
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Confidence regions in Helmert transformation
Studia Geophysica et Geodaetica, 1966Оценивается точность некоторых величин геометрического характера, которые встречаются при Гельмертовой трансформации. Речь идет об определении границ области доверительности коэффициентов трансформации, определенных по методу наименьших квадратов и об определении границ области доверительности трансформированной точки или прямой. Далее решена проблема,
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The Helmert Transformation Approach in Network Densification Revisited
2015The mapping problem of an adjusted network from its initial frame to another target frame through the Helmert transformation (HT) is discussed in this paper. We present an optimal solution which can be easily computed by a closed-form expression in terms of appropriate corrections to the standard HT solution that is often used in geodetic practice. Its
C. Kotsakis, A. Vatalis, F. Sansò
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Representation of the rotation parameter estimation errors in the Helmert transformation model
Survey Review, 2016In the Helmert transformation model, the rotation is more difficult to be treated in terms of representation, estimation, and error analysis. First, two classes of representations of the rotation, i.e. the redundant class including the direction cosine matrix and the unit quaternion, and the minimum class including the rotation vector, the Gibbs vector,
Q. Wang, G. Chang, T. Xu, Y. Zou
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On least-squares solution to 3D similarity transformation problem under Gauss–Helmert model
Journal of Geodesy, 2015In this note, the 3D similarity datum transformation problem with Gauss–Helmert model, also known as the 3D symmetric Helmert transformation, is studied. The closed-form least-squares solution, i.e., without iteration, to this problem is derived. It is found that the rotation parameters in this solution are the same to that for the transformation with ...
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The non-linear 2D symmetric helmert transformation: An exact non-linear least-squares solution
Bulletin Géodésique, 1988In this paper a particular class of non-linear least-squares problems for which it is possible to take advantage of the special structure of the non-linear model, is discussed. The non-linear models are of the ruled-type (Teunisson, 1985a). The proposed solution strategy is applied to the2D non-linear Symmetric Helmert transformation which is defined ...
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Reproducing Estimators via Least-Squares: An Optimal Alternative to the Helmert Transformation
2003One of the classical procedures for geodetic network densification consists in a free net adjustment, followed by a so-called “Helmert transformation” with respect to the fiducial point set which is kept unchanged. Here we show that this approach is not optimal in terms of the Mean-Squared-Error (MSE) risk, and present a direct derivation, based on the
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