DOI: http://dx.doi.org/10.18203/issn.2454-2156.IntJSciRep20201267

### Impact of different centroid means on the accuracy of orthometric height modelling by geometric geoid method

Oluyori P. Dare, Eteje S. Okiemute

#### Abstract

Background: Orthometric height, as well as geoid modelling using the geometric method, requires centroid computation. And this can be obtained using various models, as well as methods. These methods of centroid mean computation have impacts on the accuracy of the geoid model since the basis of the development of the theory of each centroid mean type is different. This paper presents the impact of different centroid means on the accuracy of orthometric height modelling by geometric geoid method.

Methods: DGPS observation was carried out to obtain the coordinates and ellipsoidal heights of selected points. The centroid means were computed with the coordinates using three different centroid means models (arithmetic mean, root mean square and harmonic mean). The computed centroid means were entered accordingly into a Microsoft Excel program developed using the Multiquadratic surface to obtain the model orthometric heights at various centroid means. The root means square error (RMSE) index was applied to obtain the accuracy of the model using the known and the model orthometric heights obtained at various centroid means.

Results: The computed accuracy shows that the arithmetic mean method is the best among the three centroid means types.

Conclusions: It is concluded that the arithmetic mean method should be adopted for centroid computation, as well as orthometric height modelling using the geometric method.

#### Keywords

Geoid, Centroid, Arithmetic, Root mean square, Harmonic, Mean, Orthometric height

PDF

#### References

Geodetic Glossary Survey. Geodetic Glossary, United States National Geodetic Survey, Rockville, Maryland, USA 1986.

Reichmann WJ. Use and Abuse of Statistics, Penguin Books, Middlesex, England 1961.

Apostol TM. Calculus, Vol. 1, 2nd Edn, Blaisdell Publishing Co., London 1967.

Deakin RE, Grenfell RI, Bird SC. The Centroid, where would you like it to be, RMIT University, GPO Box 2476V Melbourne VIC 3001 2002.

Madler F, Behrends E, Knorr K. A Geometric Centroid Principle and its Application. Acta Cryst. 2001;57:20-33.

Erol B, Celik RN. Precise Local Geoid Determination to Make GPS Technique More Effective in Practical Applications of Geodesy. FIG Working Week, Athens, Greece. 2004;22:1-13.

Odera PA, Musyoka SM, Gachari MK. Practical Application of the Geometric Geoid for Heighting Over Nairobi County and Its Environs. Jomo Kenyatta University of Agriculture and Technology. 2014;16(2):175-85.

Gwaleba MJ. Comparison of Global Geoid Models Against the GPS/Levelling-Derived Geoid Heights in Tanzania. J of Geomatics. 2018;12(2):174-82.

Tata H, Ono MN. A Geometric Approach for Determination of Geoidal Height in Akure Environs, Ondo State, Nigeria. Inte J of Scientific and Res Pub. 2018;8(8):668-77.

Oluyori PD, Eteje SO. Spatial Distribution of Survey Controls and Effect on Accuracy of Geometric Geoid Models (Multi-quadratic and Bicubic) in FCT, Abuja. Scientific Res J (SCIRJ). 2019;7(5):29-35.

Oluyori PD, Ono MN, Eteje SO. Comparison of Two Polynomial Geoid Models of GNSS/Levelling Geoid Development for Orthometric Heights in FCT, Abuja. Inte J of Engineering Res and Advanced Techno (IJERAT). 2018;4(10):1-9.

Oduyebo OF, Ono MN, Eteje SO. Comparison of Three Gravimetric-Geometric Geoid Models for Best Local Geoid Model of Benin City, Nigeria. Inte J of Advanced Engineering Res and Sci (IJAERS). 2019;6(12):261-72.