Comparison of Two Polynomial Geoid Models of GNSS/Leveling Geoid Development for Orthometric Heights in FCT, Abuja

Oluyori, Paul Dare; Ono, Matthew Nnonyelu; Eteje, S. O.

doi:10.31695/ijerat.2018.3330

Cited by 6 publications

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This means that the accuracy of the model is highest at 11 measurement points. This is as the number of points used (11) is very close to the number of the third-degree geometric model terms(10). This again, implies that the accuracy of the geometric geoid model tends to the highest as the number of measurement points approximates the number of the model terms.…”

mentioning

confidence: 83%

Relationship between Polynomial Geometric Surfaces Terms and Observation Points Numbers and Effect in the Accuracy of Geometric Geoid Models

Eteje¹,

Oduyebo²,

Oluyori³

2019

IJEAB

View full text Add to dashboard Cite

The application of the geometric method of local geoid model determination which requires the fitting of geometric surfaces to known geoid heights to enable geoid heights of new points to be interpolated involves the use of least squares technique for computation of the models' parameters. The selection of polynomial geometric surfaces depends on the size of the study area, the variation of the geoid heights and the number of measurement points. The accuracy of the geometric geoid model increases as the number of observation points approximates the number of geometric surface terms. But in most cases, the number of observation points is not considered. To this effect, this paper presents the relationship between geometric surfaces terms and observation points numbers and effect in the accuracy of geometric geoid models. A total of 23 points of known local gravimetric geoid heights were used. Two polynomial geometric (third and fifth degrees) surfaces were fitted to the geoid heights at various observation point numbers and compared to determine the relationship between the number of model terms and that of observation points and effect in the accuracy of the models. Least squares adjustment technique was applied to obtain the model parameters. The differences between the models and the known geoid heights of the points were computed and used to obtain the RMSEs as well as the accuracy of the models. The obtained results showed that the accuracy of the polynomial geometric geoid models tends to the highest as the number of measurement points approximates the number of the model terms and in a unique solution where the number of observation points is equal to the number of the polynomial geometric model terms, the model accuracy is highest. The paper recommends that the geometric method of local geoid model determination should be strictly applied in small areas. Where the method will be applied in considerable large areas, higher degrees polynomial geometric surfaces with a larger number of terms approximating the number of observation points should be applied. This will enable a proper fit of the polynomial surface to the known geoid heights, as well as high accuracy to be obtained.

show abstract

mentioning

confidence: 83%

Relationship between Polynomial Geometric Surfaces Terms and Observation Points Numbers and Effect in the Accuracy of Geometric Geoid Models

Eteje¹,

Oduyebo²,

Oluyori³

2019

IJEAB

View full text Add to dashboard Cite

show abstract

“…The fitting of the geometric geoid surfaces to gravimetric geoid heights of the points requires the computation of the model parameters using the least squares adjustment technique. The models' parameters were computed using equation (18). Microsoft Excel programs were developed with the computed models' parameters.…”

Section: Data Processingmentioning

confidence: 99%

Comparison of Three Gravimetric-Geometric Geoid Models for Best Local Geoid Model of Benin City, Nigeria

Oduyebo¹,

Ono²,

Eteje³

2019

IJAERS

View full text Add to dashboard Cite

The conversion of geometric as well as ellipsoidal heights from GNSS observations to practical heights for engineering constructions has necessitated the determination of the local geoid model of areas. Benin City is a developing area which requires a local geoid model for conversion of geometric heights to orthometric heights for physical developments in the area. This paper is on the best local geoid model of Benin City, Nigeria by comparing three gravimetric-geometric geoid models of the study area. GNSS and gravimetric observations were carried out on 49 points to respectively obtain their coordinates and absolute gravity values. The theoretical gravity values of the points were computed on the Clarke 1880 ellipsoid, subtracted from the absolute gravity values and corrected for the air (free air) to obtain the free air gravity anomalies of the points. The computed free air gravity anomalies were applied to compute the geoid heights of the points using the integration of the modified Stokes integral. Three geometric geoid surfaces (plane, second degree and third degree surfaces) were fitted to the computed gravimetric geoid heights using the least squares technique to obtain the gravimetric-geometric geoid models of the study area. The RMSE of the three gravimetric-geometric geoid models were computed to determine their (the models) accuracy. The three gravimetric-geometric geoid models were compared using their accuracy to obtain the most suitable geoid model of the study area. The results of the comparison showed that the third degree gravimetric-geometric geoid model is most suitable for application in the study area. It is recommended that ellipsoidal heights obtained from GNSS observation within Benin City, Nigeria should be converted to orthometric heights using the third degree geoid model.

show abstract

“…Geodesy deals with the measurement and monitoring of Earth's dimensions, shape, gravity field, and the precise determination of point locations on its surface (NOAA, 2021). Thus, the basic geodetic surfaces that describe the earth consist of its actual surface, the ellipsoid that provides the best mathematical approximation of the Earth's shape, and the geoid, which represents an equipotential surface perpendicular to the direction of gravity at all points [Oluyori et al, 2018]. The physical surface of the earth contains a variety of landforms like plains, valleys, mountains, water features, etc.…”

Section: Introductionmentioning

confidence: 99%

“…However, Odera & Fakuda (2015) opined that global models tend to be overly generalized for localized applications. Furthermore, the absence of a national geoid model in Nigeria, as emphasized by [Raufu & Tata, 2021;Oluyori et al, 2018], highlights the significance of developing local geoid models for precise localized applications.…”

Section: Introductionmentioning

confidence: 99%

Modelling local geoid undulations using unmanned aerial vehicles (UAVS): a case study of the Federal University of Technology, Akure, Nigeria

Raufu,

Tata,

Olaosegba

2023

ISTCGCAP

View full text Add to dashboard Cite

The study was aimed at developing a geoid model using Unmanned Aerial Vehicle (UAV) technology. To accomplish this, a UAV was deployed to capture imagery of the study area from a height of 150m, with a ground resolution of 4.19cm. A total of 3737 images were obtained, covering an area of 725.804 hectares. The existing ellipsoidal and orthometric heights were used to georeferenced the acquired images. For the analysis, 35 points were utilized, with 20 points designated as ground control points (GCPs) and the remaining 15 points as check points (CPs). Using the UAV-derived Digital Terrain Models (DTMs), a dataset comprising 18,492 points was generated for both ellipsoidal (h) and orthometric (H) heights. The differences between these heights, referred to as geoid heights (N), were calculated as N = h - H for all 18,492 points. These geoid heights were subsequently employed to generate a geoid model, including contour maps and 3D maps, of the study area. To assess the accuracy of the UAV-derived geoid heights, a root mean square error (RMSE) analysis was performed by comparing them with the existing geoid heights and was found to be 0.113 m. The scientific novelty and practical significance are in the development of a local geoid model of the study area with centimetre-level precision. Thus, the output of this study can be used for a wide range of applications, including land management, construction, and environmental impact assessments in the study area.

show abstract

Comparison of Two Polynomial Geoid Models of GNSS/Leveling Geoid Development for Orthometric Heights in FCT, Abuja

Cited by 6 publications

References 0 publications

Relationship between Polynomial Geometric Surfaces Terms and Observation Points Numbers and Effect in the Accuracy of Geometric Geoid Models

Relationship between Polynomial Geometric Surfaces Terms and Observation Points Numbers and Effect in the Accuracy of Geometric Geoid Models

Comparison of Three Gravimetric-Geometric Geoid Models for Best Local Geoid Model of Benin City, Nigeria

Modelling local geoid undulations using unmanned aerial vehicles (UAVS): a case study of the Federal University of Technology, Akure, Nigeria

Contact Info

Product

Resources

About