Journal of Geosciences and Geomatics
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Journal of Geosciences and Geomatics. 2017, 5(3), 96-108
DOI: 10.12691/jgg-5-3-1
Open AccessArticle

Appraisal of Methods for Estimating Orthometric Heights – A Case Study in a Mine

M. S. Peprah1, and S. A. Kumi2

1Department of Geomatic Engineering, University of Mines and Technology, Tarkwa-Western Region, Ghana

2Department of Geological Engineering, University of Mines and Technology, Tarkwa-Western Region, Ghana

Pub. Date: May 03, 2017

Cite this paper:
M. S. Peprah and S. A. Kumi. Appraisal of Methods for Estimating Orthometric Heights – A Case Study in a Mine. Journal of Geosciences and Geomatics. 2017; 5(3):96-108. doi: 10.12691/jgg-5-3-1

Abstract

The concept of orthometric heights system determination plays a major key role in geodesy, and it has broad applications in various fields and activities. In geodesy, one significant quantity is the orthometric height, the height above or below the geoid along the gravity plumbline. Conventionally, the orthometric height is determined by gravimetry and levelling techniques. However, the aforementioned techniques has its own demerits. Thus, the error is accumulated with the increase of the propagation measurement line, it is difficult to convert two separated points which is located in two continents or islands separated by sea. These techniques are tedious, time consuming and expensive. In order to resolve this challenge, many researchers resort to various techniques and approaches of obtaining orthometric heights for an area using various mathematical models. It is in this quest that, this study seek to estimate orthometric heights of a mine by utilizing plausible alternative techniques based on artificial neural networks (ANN), multivariate adaptive regression splines (MARS), polynomial regression models and multiple linear regression (MLR). The working efficiency and performance of each model has been assessed based on statistical indicators of Mean (M), Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Bias Error (MBE), Mean Absolute Error (MAE), Standard Deviation (SD), Correlation coefficient (R), Correction of determination (R2), and Signal to Noise Ratio (SNR). The statistical findings reveal that all the models produce satisfactory results in estimating the orthometric heights in the mine. MARS and ANN models compare to the MLR and polynomial models achieved higher results in terms of accuracy with mean and standard deviation of -0.000001888 m, +2.24736 m, and +0.005835 m and 0.095063 m respectively. This study will create the opportunity for geospatial practitioners to recognize the significant of ANN, MARS, MLR, and Polynomial model in solving some of the problems in geoscientific community.

Keywords:
orthometric heights geoid ellipsoid multivariate adaptive regression splines vertical coordinates artificial neural network multiple linear regression polynomial mathematical model ordinary least square total least square

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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