Comparative Review of Molodensky–Badekas and Burša–Wolf Methods for Coordinate Transformation

Abbey, D. A.; Featherstone, Will

doi:10.1061/(asce)su.1943-5428.0000319

Cited by 8 publications

(4 citation statements)

References 20 publications

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“…This would have included a geoid-ellipsoid separation at the origin. Also, Abbey and Featherstone (2020) made a comparative study on the various models that could be of help when using the Helmert's 3D model. This is recommended, however, for a future investigation.…”

Section: Results and Analysismentioning

confidence: 99%

Comparison between the azimuths of astronomical and geodetic coordinates in Ghana

Asante¹,

Ayer²,

Ziggah³

et al. 2023

JGhIE

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Astronomic azimuths are bearings, which are referenced to the true north direction whereas geodetic azimuths are those referenced to a grid north direction. The difference between these two directions can be expressed through the deflection of the vertical. This deflection of the vertical refers to the difference between the normal to the geoid (Astronomic) and the normal to the ellipsoid (geodetic). The deflection of the vertical components are used to convert between astronomic and geodetic coordinates and azimuths using Laplace equations. This paper compares astronomic and geodetically derived coordinates at eight Laplace stations constituting twenty-eight baselines for which both geodetic and astronomic azimuths were derived. The comparison of azimuths shows that differences of 000°00'05.95" up to 000°23'06.93" exist between the two different versions of azimuths. These differences are not accounted for in application of the simplified Laplace equations under the assumptions made in their derivation. It is, thence, recommended that an alternative didactic approach based on rotations of three-dimensional right-handed local frames as used in Helmert’s coordinate transformations be explored for transformation between astronomic and geodetic coordinates.

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Section: Results and Analysismentioning

confidence: 99%

Comparison between the azimuths of astronomical and geodetic coordinates in Ghana

Asante¹,

Ayer²,

Ziggah³

et al. 2023

JGhIE

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“…The 7-Parameters transformation model is the general similarity transformation developed by Helmert in 1876, which is well known in the geodetic community as a conformal datum transformation (Abbey et al 2020), the current form of this model was developed by Burša (1962) and Wolf (1963) known as the Bursa-Wolf model.…”

Section: Transformation Model Of 9-parametersmentioning

confidence: 99%

“…The 7 transformation model (Figure 1) determine three translations, three rotations and a single scale factor (Abbey et al 2020). In Equation ( 01), there a single scale factor to determine, in some case several datum have a problem in orientation and scale factor as the NS59 datum (Medjahed and Zeggai 2012), and to resolve this problem we suppose that each axis has a different scale factor.…”

Section: Transformation Model Of 9-parametersmentioning

confidence: 99%

Study of the geometry influence of the support points in coordonates transformation: application from WGS84 to NS59 datum

Medjahed¹

2023

Bol. Ciênc. Geod.

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The use of a transformation method for the passage from one geodetic system to another requires the use of some common points as support points, these points are used in the determination of the transformation parameters. Generally, the choice of the support points is effected manually by choosing the best distribution of these points in the transformation area. In the present study, we present a methodology of selection of these points where an algorithm takes into account the computation of the transformation parameters with all combinations between the common points and the best result will be adopted. An application of this methodology are carried out in North-East of Algeria to determine the best set of the 09 transformation parameters between the WGS84 system and the National North Sahara system using 10 common points (05 support and 05 control). This methodology is efficient in the case where the common points are near one another.

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“…Bursa-wolf model is one of practical mathematical approach for coordinate transformation and have been used widely for geodetic reference frame in deforming regions (Syetiawan et al, 2019;Abbey et al, 2020). One important characteristic feature of this model is that the shape of the geodetic network containing the coordinates to be transformed is preserved, hence angles are not altered after transformation, but the coordinate difference between the transformed coordinates and their original positions could be changed (Ziggah et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

Performance of Bursa-Wolf Model for Deforming Region: Case Study in Malaysia

Azahar

Aris

Musa

et al. 2022

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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Abstract. Bursa-Wolf model is a common mathematical approach for coordinate transformation practice between two reference frames. For the case of deforming region, the existing reference frame has been experiencing a non-linear shifting over the time due to co-seismic and post seismic occurrences. Imprecise coordinate in the reference frame definition could degrading critical positioning, surveying, and navigation activities. This require a new realization of reference frame and the coordinate transformation linkage is suggested to be developed in relating the new and existing reference frame. This study provides performance of Bursa-Wolf model as coordinate transformation approach for a deforming region that is experiencing non-linear shifting due to the co-seismic and post-seismic events. The Bursa-Wolf were generated from 32 dependent Global Positioning System (GPS) Continuously Operating Reference Stations (CORS) in Malaysia meanwhile another 20 independent neighbouring stations were utilized for assessment purposes. Seven parameters (7p) of Bursa-Wolf were estimated with RMS at ±4.5mm, ±9.2mm and ±2.1mm respectively. The independent stations were classified as internal and external assessment station and the root mean square (RMS) were found at less than 10mm. The internal station has depicted a better RMS in each component which are ±5.1mm, ±6.5mm and ±1.5mm respectively. Meanwhile for external stations RMS in each component are ±6.1mm, ±8.7mm and ±3.5mm respectively. The result shows that Bursa-Wolf model is sufficient to be used as coordinate transformation approach for deforming region.

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Comparative Review of Molodensky–Badekas and Burša–Wolf Methods for Coordinate Transformation

Cited by 8 publications

References 20 publications

Comparison between the azimuths of astronomical and geodetic coordinates in Ghana

Comparison between the azimuths of astronomical and geodetic coordinates in Ghana

Study of the geometry influence of the support points in coordonates transformation: application from WGS84 to NS59 datum

Performance of Bursa-Wolf Model for Deforming Region: Case Study in Malaysia

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