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


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.

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

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[1]  Heiskanen, W. A., and Moritz, H., “Physical Geodesy”, San Francisco, WH Freeman, 1967.
[2]  Vanicek, P., and Krakiwsky, E., “Geodesy the Concepts”, 2nd edn., Elsevier, Amsterdam, 1986.
[3]  Tenzer, R., and Vanicek, P., and Santos, M., “Mean gravity along the plumbline”, In: Paper presented to the CGU and AGU annual scientific meeting, Montreal, 2004.
[4]  Strang van Hees, G. L., “Practical formulas for the computation of the Orthometric and dynamic correction”, Zeitschrift fur Vermessungswesen, 1992, 117.
[5]  Drewes, H., Dodson, A. H., Fortes, L. P., Sanchez, L., and Sandoval, P., “Vertical referencing systems”, IAG Symposia 24, Springer, Berlin Heidelberg New York, 2002, 353.
[6]  Lilje, M., “Geodesy and Surveying in the future – the importance of heights”, LMV Rep. 1999.3, National Land Survey, Gavle, Sweden, 1999, 418.
[7]  Helmert, F. R., “Die Schwerkraft im Hochgebirge, insbesondere in den Tyroler Alpen”, Veroff. Konigl. Preuss. Geod. Inst., 1890, 1.
[8]  Niethammer, T., “Nivellement und Schwere als Mittel zur Berechnung wahrer Meereshohen”, Schweizerische Geodatische Kommission, 1932.
[9]  Mader, K., “Die orthometrische Schwerekorrektion des Prazisions-Nivellements in den Hohen Tauern”, Osterreichische Zeitschrift fur Vermessungswesen, Sonderheft 15, 1954.
[10]  Vanicek, P., Huang, J., Novak, P., Pagiatakis, S. D., Veronneau, M., Martinec, Z., and Featherstone, W. E., “Determination of the boundary values for the Stokes-Helmert problem”, J. Geod, 73, 180-192, 1999.
[11]  Allister, N. A., and Featherstone, W. E., “Estimation of Helmert Orthometric heights using digital barcode levelling, observed gravity and topographic mass-density data over part of Darling Scarp, Western Australia”, Geom Res Aust, 75, 25-52, 2001.
[12]  Hwang, C., and Hsiao, Y. S., “Orthometric height corrections from levelling, gravity, density and elevation data: A Case Study in Taiwan”, J. Geod, 77(5-6), 292-302, 2003.
[13]  Ledersteger, K., “Der Schwereverlauf in den Lotlinien und die Berechnung der wahren Geoidschwere”, Publication dedicated to W. A. Heiskanen, Publ. Finn. Geod Inst., 46, 109-124, 1955.
[14]  Rapp, R. H., “The Orthometric height”, MS Thesis, Department of Geodesi Science, Ohio State University, Columbus, 1961.
[15]  Krakiwsky, E. J., “Heights”, MS Thesis, Department of Geodesic Science and Survey, Ohio State University Columbus, 1965, 157.
[16]  Strange, W. E., “An evaluation of Orthometric height accuracy using borehole gravimetry”, Bull Geod, 8, 300-311, 1982.
[17]  Sunkel, H. , “Digital height and density model and its use for the Orthometric height and gravity field determination for Australia”, In: Proceedings of International Symposium on the definition of the geoid, Florence, 1986, 599-604.
[18]  Kao, S. P., Rongshin, H., and Ning, F. S., “Results of field test for computing Orthometric correction based on measured gravity”, Geom Res Aus, 72, 43-60, 2000.
[19]  Tenzer, R., and Vanicek, P., “Correction to Helmert’s Orthometric height due to actual lateral variation of topographical density”, Brazilian J. Cartography-Revista Brasileira de Cartografia, 55(2), 44-47, 2003.
[20]  Tenzer, R., Vanicek, P., Santos, M., Featherstone, W. E., and Kuhn, M., “The rigorous determination of Orthometric heights”, J. Geod, 1-11, 2005.
[21]  Dennis, M. L., and Featherstone, W. E., “Evaluation of Orthometric and related height systems using a simulated mountain gravity field”, In: Tziavos IN (ed) Gravity and geoid 2002, Department of Survey and Geodesy, Aristole Univ Thessaloniki, 2003, 389-394.
[22]  Octavian Roma, R., “Ways of Determining the Orthometric Heights Using GPS Technology, FIG Working Week 2004, Athens, Greece, May 22-27, 2004, 1-10.
[23]  Torge, W., “Physical Geodesy”, 3rd Edition, Walter de Gruyter, Berlin, New York, 2001, 416.
[24]  Featherstone, W and Vanicek, P., “The Role of Coordinate Systems, Coordinates and Heights in Horizontal Datum Transformations, Western Australian Divisions of Institution of Surveyors and Mapping Sciences, Institute and University of New South Wales, 1998.
[25]  Peprah, S. M., Yevenyo, Y. Y., and Issaka, I., “Performance Evaluation of the Earth Gravitational Model (EGM2008) – A Case Study”, South African Journal of Geomatics, 6(1), (in press), 2017.
[26]  Kingdon, R., Vanicek, P., Santos, M., Ellmann, A., and Tenzer, R., “Toward an Improved Orthometric Height System for Canada”, Geomatica, 59(3), 241-249, 2005.
[27]  Erdogan, S., “A Comparison of interpolation methods for producing digital elevation models at the field scale”, In Earth Surface Processes and Landforms, 34, 366-376, 2009.
[28]  Godone, D., and Garnero, G., “The role of morphometric parameters in Digital Terrain Models interpolation accuracy”, European Journal of Remote Sensing, 46, 198-214, 2013.
[29]  Englund, E., and Sparks, A., “Geo-EAS (Geostatistical Environment Assessment Software)”, Las Vegas, NY, U.S, Environmental Protection Agency, 1988, EPA/600/4.88/033a.
[30]  Bater, C. W., and Coops, N. C., “Evaluating error associated with lidar-derived DEM interpolation”, Computers & Geosciences, 35, 289-300, 2009.
[31]  Gold, C. M., “Surface Interpolation, Spatial adjacency and GIS”, (J. Raper, Ed), Taylor & Francis, 1989.
[32]  Sambridge, M., Braun, J., and McQueen, H., “Geophysical parameterization and interpolation of irregular data using natural neighbours”, Geophysical Journal International, 122, 837-857, 1995.
[33]  Watson, D. F., and Philip, G., “Neighbourhood-Based Interpolation”, Geobyte, 2(2), 12-16, 1987.
[34]  Sibson, R., “A brief description of natural neigbour interpolation”, In V Barnett, editor, Interpreting Multivariate Data, 21-36, Wiley, New York, USA, 1981.
[35]  Xianyong, L., and Xiuxiao, Y., “Improvement of the Stability Solving rational polynomial coefficients”, International Archives of the Photogrammetry, Remote Sensing and Spatial Information Science, 2008, XXXVII.
[36]  Martin, B., Klas, J., and Kalle, A., “Fast and Stable Polynomial Equation Solving and its application to computer vision”, International Journal of Computer Vision, 84(3), 237-256, 2009.
[37]  Childs, C., “Interpolation surfaces in ArcGIS Spatial analyst”, ESRI Education Services, 2004.
[38]  Tomlison, R., “Thinking about GIS”, In Geographic Information System Planning for Managers, 2007, 224.
[39]  Fisher, P. F., and Tate, N. J., “Causes and Consequences of error in digital elevation models”, Progress in Physical Geography, 30(4), 467-489, 2006.
[40]  Collins, F. C., “A Comparison of Spatial Interpolation Techniques in Temperature Estimation”, Blacksburg, VA, Virginia Polytechnic Institute and State University, 1995.
[41]  Johnston, K., Ver Hoef, J. M., Krivoruchko, K., and Lucas, N., “ArcGIS9, using ArcGIS Geostatistical Analysis”, Environmental Research Institute, 2003.
[42]  Ayer, J., Agyemang, A. B., Yeboah, F., Osei Jnr, E. M., Abebrese, S., Suleman, I., “A Comparative Analysis of Extracted Heights from Topographic Maps and Measured Reduced Levels in Kumasi, Ghana”, South African Journal of Geomatics, 5(1), 313-324, 2016.
[43]  Thompson, E. H., “Corrections to X-Parallaxes”, The Photogrammetric Records, 6(32), 202-210, 1968.
[44]  Soycan, M., “Determination of Geoid Heights by GPS and Precise Trigonometric levelling, Survey Review, 38(299), 387-396, 2014.
[45]  Erol B., “An automated height transformation using precise geoid models”, Journal of Scientific Research and Essays, 6(6), 1351-1363, 2011.
[46]  Dawod, G. M., Mohammed, H. F., Ismail, S.S., “Evaluation and adaptation of the EGM2008 geopotential model along the Northern Nile Valley, Egypt: Case Study”, Journal of Surveying, 136, 36-40, 2010a.
[47]  Dawod, G., “Towards the redefinition of the Egyptian geoid: performance analysis of recent global geoid models and digital terrain models”, Journal of Spatial Science, 53(1), 31-42, 2008.
[48]  Al-Krargy, E. M., Doma, M. I. and Dawod, G. M., “Towards an Accurate Definition of the Local Geoid Model in Egypt using GPS/levelling Data: A Case Study of Rosetta Zone”, International Journal of Innovative Science and Modern Engineering, 2(11), 1-6, 2014.
[49]  Ziggah, Y. Y., Youjian, H., Tierra, A., Konate, A. A., and Hui, Z., “Performance Evaluation of Artificial Neural Networks for Planimetric Coordinate Transformation-A Case Study, Ghana”, Arab J Geosci, 9, 698-714, 2016a.
[50]  Fu, B., and Liu, X., “Application of artificial neural network in GPS height transformation”, Appl Mech Mater, 501(504), 2162-2165, 2014.
[51]  Liu, S., and Li, J., and Wang, S., “A hybrid GPS height conversion approach considering of neural network and topographic correction”, International Conference on Computer Science and Network Technology, China, 2011.
[52]  Lei, W., and Qi, X., “The application of BP neural network in GPS elevation fitting”, International Conference on Intelligent Computation Technology and Automation, Changsha-China, 2010.
[53]  Tieding, L., Shijian, Z., and Xijiang, C., “A number of issues about converting GPS height by BP neural network”, International Conference on Biomedical Engineering and Computer Science (ICBECS), Wuhan-China, 2010.
[54]  Wu, L. C., Tang, X., and Zhang, S., “The application of genetic neural network in the GPS height transformation”, IEEE Fourth International Conference on Computational and Information Sciences, Chongqing-China, 2010.
[55]  Bao, H., Zhao, D., Fu, Z., Zhu, J., and Gao, Z. (2011), “Application of genetic algorithm improved BP neural network in automated deformation monitoring”, Seventh International Conference on Natural Computation, Shanghai-China, IEEE, 2011.
[56]  Du, S., Zhang, J., Deng, Z., and Li, J., “A new approach of geological disasters forecasting using meteorological factors based on genetic algorithm optimized BP neural network”, Elektronika IR Elektro Technika, 20(4), 57-62, 2014a.
[57]  Du, S., Zhang, J., Deng, Z., and Li, J. “A neural network based intelligent method for mine slope surface deformation prediction considering the meteorological factors”, TELKOMNIKA Indonesian J Elect Eng, 12(4), 2882-2889, 2014b.
[58]  Gao, C. Y., Cui, X. M., and Hong, X. Q., “Study on the applications of neural networks for processing deformation monitoring data”, Appl Mech and Mater, 501(504), 2149-2153, 2014.
[59]  Pantazis, G., and Eleni-Georgia, A., “The use of artificial neural networks in predicting vertical displacements of structures”, Int J Appl Sci Technol, 3(5), 1-7, 2013.
[60]  Yilmaz, I., and Gullu, M, “Georeferencing of historical maps using backpropagation artificial neural network”, Exp Tech, 36, 15-19, 2012.
[61]  Yilmaz, M., “Artificial neural networks pruning approach for geodetic velocity field determination”, Bol Cienc Geod, 19(4), 558-573, 2013.
[62]  Liao, D. C., Wang, Q. J., Zhou, Y. H., Liao, X. H., and Huang, C. L., “Long-term prediction of the earth orientation parameters by the artificial neural network technique”, J Geodyn, 62, 87-92, 2012.
[63]  Schuh, H., Ulrich, M., Egger, D., Muller, J., and Schwegmann, W., “Prediction of earth orientation parameters by artificial neural networks”, J Geod, 76, 247-258, 2002.
[64]  Yu, L., Danning, Z., and Cai, H., “Prediction of length of day using extreme learning machine”, Geod Geodyn, 6(2), 151-159, 2015.
[65]  He-Sheng, W., “Precise GPS orbit determination and prediction using H neural network”, J Chinese Inst Eng, 29(2), 11-219, 2006.
[66]  Li, X., Zhou, J., and Guo, R., “High-precision orbit prediction and error control techniques for COMPASS navigation satellite”, Chinese Sci Bull, 59(23), 2841-2849, 2014.
[67]  Hajian, A., Ardestani, E. V., and Lucas, C., “Depth estimation of gravity anomalies using Hopfield neural networks”, J. Earth Sp Phys, 37(2), 1-9, 2011.
[68]  Hamid, R. S., and Mohammad, R. S., “Neural network and least squares method (ANN-LS) for depth estimation of subsurface cavities case studies: Gardaneh Rokh Tunnel, Iran”, J. Appl Sci Agric, 8(3), 164-171, 2013.
[69]  Tierra, A. R., and De Freitas, S. R. C., “Artificial neural network: a powerful tool for predicting gravity anomaly from sparse data, Gravity, geoid and space missions”, International Association of Geodesy Symposia, Springer, Berlin Heidelberg DA, 2005.
[70]  Kavzoglu, T., and Saka, M. H., “Modelling local GPS/Levelling geoid undulations using artificial neural networks”, J. Geodesy, 78, 520-527, 2005.
[71]  Pikridas, C., Fotiou, A, Katsougiannopoulos, S., and Rossikopoulos, D., “Estimation and evaluation of GPS geoid heights using an artificial neural network model”, Appl Geomat, 3, 183-187, 2011.
[72]  Stopar, B., Ambrozic T., Kuhar, M., and Turk, G., “GPS-derived geoid using artificial neural network and least squares collocation”, Surv Rev, 38(300), 513-524, 2006.
[73]  Sorkhabi, O. M., “Geoid determination based on log sigmoid function of artificial neural networks: (a case study: Iran), J Artif Intell Electr Eng, 3(12), 18-24, 2015.
[74]  Veronez, M. R., Thum, B. A., and De Souza, G. C., “A new method for obtaining geoidal undulations through artificial neural networks”, 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, 2006, 306-316.
[75]  Veronez, M. R., De Souza, G. C., Matsuoka, T. M., Reinhart, A., and Da Silva, R. M. (2011), “Regional mapping of the geoid using GNSS (GPS) measurements and n artificial neural network”, Remote Sens, 3, 668-613, 2011.
[76]  Gullu, M., “Coordinate transformation by radial basis function neural network”, Sci Res Essays, 5(20), 3141-3146, 2010.
[77]  Gullu, M., Yilmaz, M., Yilmaz, I., and Turgut, B., “Datum transformation by artificial neural networks for geographic information systems applications”, International Symposium on Environmental Protection and Planning: Geographic Information Systems (GIS) and Remote Sensing (RS) Applications (ISEPP), Izmir-Turkey, 2011, pp. 13-19.
[78]  Lin, L. S., and Wang, Y. J., “A study on cadastral coordinate transformation using artificial neural network”, Proceedings of the 27th Asian Conference on Remote Sensing, Ulaanbaatar, Mongolia, 2006.
[79]  Mihalache, R. M., “Coordinate transformation for integrating map information in the new geocentric European system using artificial neural networks”, GeoCAD, 2012, 1-9.
[80]  Tierra, A., Dalazoana, R., and De Freitas, S., “Using an artificial neural network to improve the transformation of coordinates between classical geodetic reference frames”, Comput Geosci, 34, 181-189, 2008.
[81]  Tierra, A. R., De Freitas, S. R. C., and Guevara, P. M. (2009), “Using an artificial neural network to transformation of coordinates from PSAD56 to SIRGAS95”, Geodetic reference frames, international association of geodesy symposia, Springe,r 134, 173-178, 2009.
[82]  Tierra, A., and Romero, R., “Planes coordinates transformation between PSAD56 to SIRGAS using a multilayer artificial neural network”, Geod Cartogr, 63(2), 199-209, 2014.
[83]  Turgut, B., “A back-propagation artificial neural network approach for three-dimensional coordinate transformation”, Sci Res Essays, 5(21), 3330-3335, 2010.
[84]  Zaletnyik, P., “Coordinate transformation with neural networks and with polynomials in Hungary”, International Symposium on Modern Technologies, Education and Professional Practice in Geodesy and Related Fields, Sofia, Bulgaria, 2004, 471-479.
[85]  Ziggah, Y. Y., Youjian, H., Yu, X., & Basommi, L. P., “Capability of Artificial Neural Network for forward Conversion of Geodetic Coordinates (Ф, λ, h) to Cartesian Coordinates (X, Y, Z)”, Math Geosci, 48, 687-721, 2016b.
[86]  Lee, T. S., and Chen, I. F., “A two-stage hybrid credit scoring model using artificial neural networks and multivariate adaptive regression splines”, Expert Syst Appl, 28, 743-752, 2005.
[87]  Samui, P., “Multivariate Adaptive Regression Spline (MARS) for prediction of Elastic Modulus of jointed Rock Mass”, Geotech Geol Eng, 31, 249-253, 2013.
[88]  Friedman, J. H., “Multivariate adaptive regression splines”, Annals Statistics, 19, 1-67, 199.
[89]  Leathwick, J. R, Rowe, D., Richardson, J., Elith, J., and Hastie, T., “Using multivariate adaptive regression splines to predict the distributions of New Zealand’s freshwater diadromous fish”, Freshw Biol, 50, 2034-2051, 2005.
[90]  Alreja, J., Parab, S., Mathur, S., and Samui, P., “Estimating hysteretic energy demand in steel moment resisting frames using Multivariate Adaptive regression Spline and Least Square Support Vector Machine”, Ains Shams Engineering Journal, 2015.
[91]  Lall, U., Sangoyomi, T., Abarbanel, H. D. I., “Nonlinear dynamics of the Great Salt Lake: nonparametric short term forecasting”, Water Resour Res, 32, 975-985, 1996.
[92]  Attoh-Okine, N. O., Mensah, S., Nawaiseh, M., “A new technique for using multivariate adaptive regression splines (MARS) in pavement roughness prediction”, Proc ICE Trans, 156(1), 51-55, 2003.
[93]  Attoh-Okine, N. O., Cooger, K., Mensah, S., “Multivariate Adaptive Regression (MARS) and hinged hyperplanes (HHP) for doweled pavement performance modelling”, Constr Build Mater, 23(9), 3020-3023, 2009.
[94]  Wang, L. J., Guo, M., Sawada, K., Lin, J., and Zhang, L., “Landslide Susceptibility mapping in Mizunami city, Japan: A comparison between logistic regression, bivariate statistical analysis and multivariate adaptive regression spline models”, Journal of Catena, 135, 271-282, 2015.
[95]  Kisi, O., and Parmar, K. S. (2015), “Application of Least Square Support Vector Machine and Multivariate Adaptive Regression Spline Models in Long term Prediction of River Water Pollution”, Journal of Hydrology , 2015, 1-28, Accessed: February 10, 2017.
[96]  Samui, P. and Kim, D., “Modelling of reservoir-induced earthquakes: a multivariate adaptive regression spline”, Journal of Geophysics and Engineering, 9, 494-497, 2012.
[97]  Laurin, G. V., Puletti, N., Chen, Q., Piermaria, C., Papale, D., and Valentini, R., “Above ground biomass and tree species richness estimation with airborne Lidar in tropical Ghana forest”, International Journal of applied Earth Observation and Geoinformation, 52, 371-379, 2016.
[98]  Durmaz, M., Karslioglu, M. O., and Nohutcu, M., “Regional VTEC modelling with multivariate adaptive regression splines”, Advances in Space Research, 46, 180-189, 2010.
[99]  Durmaz, M. and Karslioglu, M. O., “Non-parametric regional VTEC modelling with Multivariate Adaptive Regression B-Splines”, Advances in Space Research, 48, 1523-1530, 2011.
[100]  Chen, M., Tompson, A. F. B., Mellors, R. S., Ramirez, A. L., Dyer, K. M., Yang, X., and Wagoner, J. L., “An efficient Bayesian inversion of a geothermal prospect using a multivariate adaptive regression spline method”, Journal of Applied Energy, 136, 619-627, 2014.
[101]  Dawod, G. M., Mirza, N. M., Al-Ghamdi, A. K., “Simple precise coordinate transformations for geomatics applications in Makkah metropolitan area, Saudi-Arabia”, Bridging the gap between cultures FIG working week, Marrakech Morocco, 2010b, 18-22.
[102]  Featherstone, W. E., “A comparison of existing co-ordinate transformation models and parameters in Australia”, Cartogr , 26(1), 13-26, 1997.
[103]  Odutola, C. A., Beiping, W., and Ziggah, Y. Y., “Testing Simple Regression Model for Coordinate Transformation by Comparing its Predictive Result for Two Regions”, Academic Research International, SAVAP International Publishers, 4(6), 540-549, 2013.
[104]  Ziggah Y. Y., “Regression Models for 2-Dimensional Cartesian Coordinates Prediction: A Case Study at University of Mines and Technology (UMaT)”, International Journal of Computer Science and Engineering Survey (ISCSES), 3(6), 62, 2012.
[105]  Owusu, B., “An Assessment of Job Satisfaction and Its Effect on Employees’ Performance: A Case of Mining Companies in the [ Bibiani- Anhwiaso – Bekwai District] in the Western Region”, A Master Thesis of Business Administration submitted to the Department of Managerial Science, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana, 108, 2014.
[106]  Peprah, S. M., “Field Trip and Technical Report”, Unpublished BSc Report Notes, University of Mines and Technology, Tarkwa, Ghana, 26, 2015.
[107]  Mohammed, A. S., “Performance Assessment of the Methods used in Transformation from Cartesian Coordinates to Geodetic Coordinates”, Unpublished BSc report, University of Mines and Technology, Tarkwa, Ghana, 65, 2015.
[108]  Quarshie, E., Nyarko, B. J. B., and Serfor – Armah, Y., “Studies of the Levels of some Toxic Elements in Soil and Tailings from Bibiani Mining Area of Ghana”, Research Journal of Environmental and Earth Sciences, 3(5), 512-520, 2011.
[109]  Zabihi, M., Pourghasemi, H. R., Pourtjhi, Z. S., and Behzadfar, M., “GIS-based multivariate adaptive regression spline and random forest models for groundwater potential mapping in Iran”, Environ Earth Sci, 75(665), 646-665, 2016.
[110]  Petrie, G., and Kennie, T. J. M., “Terrain modelling in surveying and civil engineering”, 19(4), 171-187, 1984.
[111]  Miller, S. J., “Methods of Least Squares”, Statistics Theory, Cornell University, USA, 3, 1-2, 2006.
[112]  Annan, R. F., Ziggah, Y. Y., Ayer, J., and Odutola, C. A., “Accuracy Assessment of heights obtained from Total station and level instrument using Total Least Squares and Ordinary Least Squares Methods”, Journal of Geomatics and Planning, 3(2), 87-92, 2016a.
[113]  Schaffrin, B., “A note on Constrained Total Least Square estimation”, Linear Algebra and Its Application, 417, 245-258, 2006.
[114]  Akyilmaz, O., “Total Least Squares Solution of Coordinate Transformation”, Survey Review, 39(303), 68-80, 2007.
[115]  Golub, G. H., and Van Loan, C. F., “An analysis of the Total Least Squares problem”, SIAM Journal on Numerical Analysis, 17(6), 883-893, 1980.
[116]  Annan, R. F., Ziggah, Y. Y., Ayer, J., Odutola, C. A., “A Hybridized Centroid Technique for 3D Molodensky-Badekas Coordinate Transformation in the Ghana Reference Network using Total Least Squares Approach”, South African Journal of Geomatics, 5(3), 269-284, 2016b.
[117]  Markovsky, I., and Van Huffel, S., “Overview of Total Least Square Methods”, Signal Processing, 87(10), 2283-2302, 2007.
[118]  Okwuashi, O., and Eyoh, A., “Application of total least squares to a linear surveying network”, Journal of science and Arts, 4(21), 401-404, 2012a.
[119]  Ge, X., and Wu, J., “A New Regularized Solution to Ill-Posed Problem in Coordinate Transformation”, International Journal of Geosciences, 3, 14-20, 2012.
[120]  Okwuashi, O., and Eyoh, “3D Coordinate transformation using total least squares”, Academic Research International, 3(1), 399-405, 2012b.
[121]  Mueller, V. A., and Hemond, F. H., “Extended artificial neural networks: in-corporation of a priori chemical knowledge enables use of ion selective electrodes for in-situ measurement of ions at environmental relevant levels”, Talenta, 117, 112-118, 2013.
[122]  Yegnanarayana, B., “Artificial neural networks”, Prentice-Hall of India Private Limited, 2005.
[123]  Hornik, K., Stinchcombe, M., and White, H., “Multilayer feed forward networks are universal approximators”, Neural Netw, 2, 359-366, 1989.
[124]  Yonaba, H., Anctil, F., and Fortin, V., “Comparing sigmoid transfer functions for neural network multistep ahead stream flow forecasting”, J Hydrol Eng, 15(4), 275-283, 2010.
[125]  Konaté, A. A., Pan, H., Khan, N., and Ziggah, Y. Y., “Prediction of porosity in crystalline rocks using artificial neural networks: an example from the Chinese continental scientific drilling main hole”, Stud Geophys Geod, 59(1), 113–136, 2015.
[126]  Gope, D., Gope, P. C., Thakur, A., and Yadav, A., “Application of artificial neural network for predicting crack growth direction in multiple cracks geometry”, App Soft Comput, 30, 514-528, 2015.
[127]  Samui, P. and Kothari, D. P., “A Multivariate Adaptive Regression Spline Approach for Prediction of Maximum Shear Modulus (Gmax) and Minimum Damping Ratio (£min), Engineering Journal, 16(5), 1-10, 2012.
[128]  Craven, P. and Wahba, G., “Smoothing noisy data with spline function: estimating the correct degree of smoothing by the method of generalized cross-validation”, Numer Math, 31, 317-403, 1979.