Transformation of 3D GPS Cartesian coordinates to ED50 using polynomial fitting by robust re-weighting technique

Soycan, Metin; Soycan, Arzu

doi:10.1179/003962608x253673

Cited by 10 publications

(5 citation statements)

References 3 publications

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“…Aktug (2012), Akyilmaz (2007), Burša (1967), Chen et al (2004), Dermanis (1998), El-Mowafy et al (2009), Ge et al (2013), Kashani (2006), Neitzel (2010), Paláncz et al (2013), Soler and Snay (2004), Soycan and Soycan (2008), Watson (2006), Zeng (2014Zeng ( , 2015. It aims to determine the transformation parameter of the transformation model.…”

Section: Introductionmentioning

confidence: 99%

Iterative approach of 3D datum transformation with a non-isotropic weight

Zeng

2015

Acta Geod Geophys

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The analytical solution of 3D datum transformation with an isotropic weight has been elegantly presented based on Procrustes algorithm (singular value decomposition). But the existence of analytical solution of 3D datum transformation with a nonisotropic weight needs further investigation. Based on the Lagrangian extremum law, the paper derives the analytical formula for translation parameter and scale factor, but because the rotation matrix is unsolved, the analytical solution does not exist. For this reason, the paper presents two kinds of iterative approach of 3D datum transformation with a nonisotropic weight. One is the iterative approach dependent on the objective function value, which uses the Lagrangian minimum function in the variable of rotation matrix as the objective function, and the other is the iterative approach dependent on the derivative of function, which uses the 3D datum transformation model that eliminates the translation parameter. In order to improve the speed and reliability of iterative computation, the form of rotation matrix represented by Rodrigues matrix instead of rotation angles or unit quaternion is adopted for the two iterative approaches. A numerical experiment is demonstrated, and comparison analysis of the two iterative approaches is carried out. The result shows from the view of computing speed and reliability, the iterative approach based on derivatives is preferred.

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Section: Introductionmentioning

confidence: 99%

Iterative approach of 3D datum transformation with a non-isotropic weight

Zeng

2015

Acta Geod Geophys

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“…To date quite a few datum transformation models have been tested to deal with this homogeneity problem, e.g. [7], [12] and [14]. The basic demands for transformation of spatial data between the two reference systems of Slovenia are continuity, reversibility, minimal distortions and best possible positional accuracy [1].…”

Section: Introductionmentioning

confidence: 99%

Local to ETRS89 datum transformation for Slovenia: triangle-based transformation using virtual tie points

Berk

Komadina

2013

Survey Review

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The present paper presents a geodetic datum transformation between the old and new national coordinate reference systems of Slovenia. The basis for transformation is a set of about 2000 points coordinated in both systems. Virtual tie points are used, which form a regular triangular network covering the entire country. In order to enable extrapolation, the network was expanded, thereby reducing its density. Coordinate shifts between both coordinate systems were determined using best-fit transformation in the immediate neighbourhood of each virtual tie point. Weights assigned to these points depend upon their density and distance from the virtual tie point. The results prove significant advantages of the proposed model: high accuracy, minimisation of distortions, continuity and reversibility of transformation. Therefore, the model has been chosen for transformation of all spatial databases which continuously cover the entire territory of the country and require transformation accuracy of better than one metre.

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“…(see, e.g., Aktuğ (2009) ;Aktuğ 2012;Akyilmaz 2007;Arun et al 1987;Burša 1967;Chang 2015;Chang et al 2017;El-Habiby et al 2009;El-Mowafy et al 2009;Grafarend and Awange 2003;Han 2010;Horn 1986Horn , 1987Han and Van Gelder 2006;Horn et al 1988;Jaw and Chuang 2008;Jitka 2011;Kashani 2006;Krarup 1985;Leick 2004;Leick and van Gelder 1975;Mikhail et al 2001;Neitzel 2010;Soler 1998;Soler and Snay 2004;Soycan and Soycan 2008;Teunissen 1986;Teunissen 1988;Wang et al 2014;Závoti and Kalmár 2016;Zeng 2014;Zeng 2015;Zeng et al 2016;Zeng and Yi 2011). Helmert transformation problem is to determine the seven transformation parameters including three rotation angles, three translation parameters and one scale factor using a set of control points (the number of control points should be equal to or more than three because three equations can be constructed for one point).…”

Section: Introductionmentioning

confidence: 99%

A dual quaternion algorithm of the Helmert transformation problem

Zeng

Fang

Chang

et al. 2018

Earth Planets Space

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Rigid transformation including rotation and translation can be elegantly represented by a unit dual quaternion. Thus, a non-differential model of the Helmert transformation (3D seven-parameter similarity transformation) is established based on unit dual quaternion. This paper presents a rigid iterative algorithm of the Helmert transformation using dual quaternion. One small rotation angle Helmert transformation (actual case) and one big rotation angle Helmert transformation (simulative case) are studied. The investigation indicates the presented dual quaternion algorithm (QDA) has an excellent or fast convergence property. If an accurate initial value of scale is provided, e.g., by the solutions no. 2 and 3 of Závoti and Kalmár (Acta Geod Geophys 51: [245][246][247][248][249][250][251][252][253][254][255][256] 2016) in the case that the weights are identical, QDA needs one iteration to obtain the correct result of transformation parameters; in other words, it can be regarded as an analytical algorithm. For other situations, QDA requires two iterations to recover the transformation parameters no matter how big the rotation angles are and how biased the initial value of scale is. Additionally, QDA is capable to deal with point-wise weight transformation which is more rational than those algorithms which simply take identical weights into account or do not consider the weight difference among control points. From the perspective of transformation accuracy, QDA is comparable to the classic Procrustes algorithm (Grafarend and Awange in J Geod 77: [66][67][68][69][70][71][72][73][74][75][76] 2003) and orthonormal matrix algorithm from Zeng (Earth Planets Space 67:105, 2015. https://doi.

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Transformation of 3D GPS Cartesian coordinates to ED50 using polynomial fitting by robust re-weighting technique

Cited by 10 publications

References 3 publications

Iterative approach of 3D datum transformation with a non-isotropic weight

Iterative approach of 3D datum transformation with a non-isotropic weight

Local to ETRS89 datum transformation for Slovenia: triangle-based transformation using virtual tie points

A dual quaternion algorithm of the Helmert transformation problem

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