Comparison of Two Corrector Surface Models of Orthometric Heights from GPS/Levelling Observations and Global Gravity Model

Ibrahim Olatunji Raufu(1*), Herbert Tata(2)

(1) Lund University, Sweden
(2) Federal University of Technology, Akure Nigeria
(*) Corresponding Author


The advent of space-based measurement systems such as the Global Positioning System (GPS) offers a new alternative in orthometric height determination over conventional spirit levelling. The ellipsoidal height (h) obtained from GPS observations can be transformed into orthometric height if the geoid undulation (N) is known from a national gravimetric geoid model. However, the lack of a national geoid model in Nigeria hinders the use of the method. This study compares two corrector surface models of orthometric heights from GPS/levelling observations and the Global Gravity Model. Model A (7-parameter) and Model B (8-parameter) are based on the general 7-parameter similarity datum shift transformation.  A network of twenty-one (21) GPS/levelling benchmarks within the study area were used and their geoidal heights were computed using GeoidEval utility software with reference to Global Gravitational Model (EGM08). Least squares adjustment was used to compute the coefficients of the models. Root mean square error (RMSE) was used to assess the accuracy of the models with model A having RMSE=0.171m and model B having RMSE=0.169m. Model B with the lowest RMSE is hence the better of the two models. The t-test and hypothesis test conducted at a 95% confidence level, however, revealed that the two models did not differ significantly. The study shows that the use of corrective surface to combine the gravity field model EGM08 and GPS/levelling significantly improves the determination of heights as observed from GPS in the study area.


Accuracy; Ellipsoidal heights; Geoid model; GPS; Orthometric heights; Hypothesis test

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Abdullah, A. K. (2010). Height Determination using GPS Data, Local Geoid and Global Geopotential Models. Universiti Teknologi Malaysia Institutional Repository, EPrints3.

Eteje, S. O., Ono, M. N. & Oduyebo, O. F. (2018). Practical Local Geoid Model Determination for Mean Sea Level Heights of Surveys and Stable Building Projects. IOSR Journal of Environmental Science, Toxicology and Food Technology (IOSR-JESTFT), 12(6), 30-37.

Fotopoulos, G. (2003). An Analysis on the Optimal Combination of Geoid, Orthometric and Ellipsoidal Height Data. PhD Thesis, Department of Geomatics Engineering, University of Calgary. UCGE Reports No. 20185. Available at:, 258 pages

Fotopoulos, G., Kotsakis, C., & Sideris, M.G. (2001a). How Accurately can we Determine Orthometric Height differences from GPS and Geoid data? Journal of Surveying Engineering, 129(1), 1-10.

Isioye, K. O., Olaleye, J. B., Youngu, T. T., Aleem, K. F. (2011). Modelling Orthometric Heights from GPS-Levelling Observations and Global Gravity Model (EGM08) for Rivers State, Nigeria. Nigerian Journal of Surveying and Geoinformatics, 3(2), 56-69.

Kearsley, A.W., Ahmad, Z., & Chan, A. (1993). National Height Datums, Levelling, GPS Heights, and Geoids. Australian Journal of Geodesy, Photogrammetry, and Surveying, no. 59, 53-88.

Moka, E.C. & Agajelu, S. I., (2006). On the Problem of Computing Orthometric Heights from GPS data. Proceedings of the first international workshop on Geodesy and Geodynamics, pp 85-91

Oluyori, P. D., Ono, M. N., & Eteje, S. O. (2018). Comparison of Two Polynomial Geoid Models of GNSS/Leveling Geoid Development for Orthometric Heights in FCT, Abuja. International Journal of Engineering Research and Advanced Technology (IJERAT), 4(10), 1-9.

Ono, M. N. (2009). On Problems of Coordinates, Coordinate Systems and Transformation Parameters in Local Map Production, Updates and Revisions in Nigeria. FIG Working Week 2009, Eilat, Israel.

Pavlis, N., Holmes, S., Kenyon, S., & Factor, J. (2008). An Earth Gravitational Model to Degree 2160: EGM2008. Presented at the 2008 General Assembly of the European Geosciences Union, Vienna, Austria, April 13–18.

Raizner, C. (2008). A Regional Analysis of GNSS-Levelling. PhD Thesis, Institute of geodesy, University of Stuttgart, 133pages

Rummel, R., & Teunissen, P. (1989). Height Datum definition, Height Datum connection and the Role of the Geodetic Boundary Value Problem. Bulletin Géodésique, vol. 62, 477 - 498.

Sen, A. and Srivastava, M.S. (1990). Regression Analysis: Theory, Methods, and Applications. Springer-Verlag, New York.

Shretha, R., Nazir, A., Dewitt, B., & Smith, S. (1993). Surface Interpolation Techniques to Convert GPS Ellipsoid Heights to Elevations. Surveying and Land Information Systems, 53(2), 133-1404.

Uzun, S. & Cakir, L. (2006). The Reliability of Surface Fitting Methods in Orthometric Height Determination from GPS Observations. XXIII FIG Congress, Munich Germany, October 2006


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