Hybridized centroid technique for 3D Molodensky-Badekas coordinate transformation in the Ghana geodetic reference network using total least squares approach

Annan, Richard Fiifi; Ziggah, Yao Yevenyo; Ayer, J. A.; Odutola, Christian Amans

doi:10.4314/sajg.v5i3.1

Cited by 9 publications

(6 citation statements)

References 10 publications

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“…Therefore, not rendering them homogeneous. This could be the reason why the results have some high residuals in both the northings and eastings, which is also following the researches performed on the geodetic framework of Ghana by many researchers (including Ayer & Tiennah, 2007;Ayer & Fosu, 2008;Ayer, 2008;Annan et al, 2016;Ziggah et al, 2017) with Dzidefo (2011), who aimed at investigating and further proposing a method for transforming coordinates of points from the War Office coordinate system to the WGS 84 coordinate system and vice versa.…”

Section: Coordinate Conversionsupporting

confidence: 59%

Development of GNSS software for Ghana Survey and Mapping Division

Charles¹,

Afrifa²,

Ayer³

2022

SA J of Geomatics

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Processing of Global Navigational Satellite System (GNSS) data forms the basis for the usage of differential systems for obtaining spatial data. All open sources or commercial software packages developed for data processing give specific details to suit the intended purpose of the software. To obtain a uniform format for submitted survey data, Survey and Mapping Division (SMD) in various jurisdictions have specified formats for data submission for all kinds of surveys. In this regard, “GNSS Ghana” Software (GGS), a GNSS standalone Windows-based application with a modern user-friendly interface was developed for geodetic applications such as, projection and datum transformation worldwide, GNSS data post-processing of Receiver Independent Exchange Format (RINEX) files, and generating reports to meet Ghana SMD reporting standards including cadastral computations and reports for submission. To assess the developed software, GNSS data from two International GNSS Service (IGS) stations (BJCO and YKRO) were processed using GGS and three other commercial software such as GNSS Solution Software (GSS), Spectrum Survey Software (SSS), and Leica Geo Office (LGO), and the positional results compared against the existing coordinate. The results revealed that the GGS outperformed the remaining three commercial software packages with a sub-meter level of accuracy. Further assessment was conducted on datum transformation using the coordinates of 21 existing geodetic control points in Ghana. Utilizing the 7-transformation parameters of Ghana, the results gave uncertainties of [0.10ft. ± 0.99ft.] in the eastings and [0.02ft. ± 1.61ft.] in the northings with a 99% confidence level.

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Section: Coordinate Conversionsupporting

confidence: 59%

Development of GNSS software for Ghana Survey and Mapping Division

Charles¹,

Afrifa²,

Ayer³

2022

SA J of Geomatics

Self Cite

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“…Golub and Van Loan, (1980), invented TLS to rectify the inefficiency associated with the OLS. Thus, accounting for perturbations in data matrix and observation matrix (Annan et al, 2016b). TLS is a mathematical algorithm that yields a unique solution in analytical form in terms of the Singular Value Decomposition (SVD) of the data matrix (Markovsky and Van Huffel, 2007).…”

Section: Ordinary Least Square (Ols) and Total Least Square (Tls)mentioning

confidence: 99%

“…The errors remain in the data could be adjusted. Several adjustment methods exist such as ordinary least squares (Annan et al, 2016a;Okwuashi and Eyoh, 2012a), Total least squares (Acar et al, 2006;Annan et al, 2016b;Okwuashi and Eyoh, 2012b), robust estimation (Wieser and Brunner, 2001), least square collocation (LSC) (Moritz, 1972). Conversely, there is a common belief that data obtain from the GPS instrument are very precise and accurate due to less interference of humans in the collection process and can be used to execute any given task without further adjustments.…”

Section: Introductionmentioning

confidence: 99%

“…Also, the optimal model in adjusting surveying networks whether the OLS and TLS is good enough is the objective of this present study. Researchers such as (Acar et al, 2006;Annan et al, 2016aAnnan et al, , 2016bOkwuashi and Eyoh, 2012;OKwuashi, 2014) have applied TLS to solve many scientific problems and they concluded the TLS working efficiency is encouraging. This present study adopted the OLS and TLS in adjusting DGPS network and to propose the models which is optimal for adjusting DGPS network.…”

Section: Introductionmentioning

confidence: 99%

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Performance evaluation of the Ordinary Least Square (OLS) and Total Least Square (TLS) in adjusting field data: an empirical study on a DGPS data

Peprah¹,

Mensah²

2017

SA J of Geomatics

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“…The most widely adopted techniques in the past decades in literature for such application include the similarity models of Bursa-Wolf, Molodensky-Badekas, Veis model and three-dimensional Affine [10][11][12][13][14][15][16]. However, the major concern here is that, before these aforementioned similarity models could be applied, there is the need to convert all the geodetic dataset of common points to Cartesian coordinates.…”

Section: Introductionmentioning

confidence: 99%

Performance Evaluation of Multivariate Adaptive Regression Splines (MARS) and Multiple Linear Regression (MLR) for Forward Conversion of Geodetic Coordinates (ϕ, λ, h) to Cartesian Coordinates (X, Y, Z)

Peprah¹,

Mensah²,

Akresi³

2017

JGG

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In Ghana's local Geodetic Reference Network, the standard forward transformation equation has played a major role in coordinate transformation between World Geodetic System 1984 (WGS84) and local geodetic datum. Thus, it is an initial step in forward conversion of geodetic coordinates (ϕ , λ, h) to Cartesian coordinates (X, Y, Z) in transformation from global to local datum and vice versa. Several studies in the recent decades have been conducted on converting Cartesian coordinates to geodetic coordinates (reverse procedure) through the utilisation of iterative, approximate, closed form, vector-based and computational intelligence algorithms. However, based on the existing literature covered pertaining to this present study, it was found that the existing knowledge do not fully adhere to the issue of evaluating alternative techniques in the case of the forward conversion. Hence, the aim of this present study was to explore the coordinate conversion performance of the Multivariate Adaptive Regression Splines ( ). The statistical findings revealed that the MARS and MLR offered satisfactory prediction of Cartesian coordinates. However, the MLR compared to MARS showed better stability and more accurate prediction results. From the results of this present study, the main conclusion drawn is that, MLR provides a promising alternative in the forward conversion of geodetic coordinates into Cartesian coordinates. Therefore, the capability of MLR as a powerful tool for solving majority of function approximation problems in mathematical geodesy has been demonstrated in this present study.

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Hybridized centroid technique for 3D Molodensky-Badekas coordinate transformation in the Ghana geodetic reference network using total least squares approach

Abstract: The Molodensky-Badekas model is one of the similarity transformation models used in Ghana for transferring Global Positioning System (GPS) coordinates from the geocentric World Geodetic System 1984 (WGS 84)

Cited by 9 publications

References 10 publications

Development of GNSS software for Ghana Survey and Mapping Division

Development of GNSS software for Ghana Survey and Mapping Division

Performance evaluation of the Ordinary Least Square (OLS) and Total Least Square (TLS) in adjusting field data: an empirical study on a DGPS data

Performance Evaluation of Multivariate Adaptive Regression Splines (MARS) and Multiple Linear Regression (MLR) for Forward Conversion of Geodetic Coordinates (ϕ, λ, h) to Cartesian Coordinates (X, Y, Z)

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