Comparison of Two Polynomial Geoid Models of GNSS/Leveling Geoid Development for Orthometric Heights in FCT, Abuja (original) (raw)
Related papers
Modelling of Orthometric heights from Multi- Networks of GNSS/Precise Levelling in FCT, Abuja
International Journal of Environment, Agriculture and Biotechnology (IJEAB), 2019
The geoid is used as a transformation linkage between ellipsoidal heights (h) determined from DGPS observations and orthometric heights (H). Widespread acceptability and adoption of GPS in local geospatial data acquisitions require the development of a local geoid model (N) for use to obtain orthometric heights in the absence of a national geoid model. Geoid model can be developed by gravimetric approach; global geopotential model (GGM); geometric technique among others. The conventional approach to GPS measurements is the use of one base reference station for field measurements. It has several drawbacks e.g. in signal range/coverage, accuracy degradation of results, etc. Based on Grashof's law of stability of triangles, this study was therefore based on dual reference base stations to improve on DGPS signal range and stability of results. Pro-online matrix solver was applied to the least squares observation equations of the two modelled FCT surfaces (multi - quadratic and bicubic) to determine polynomial coefficients. The geoid undulation was computed and orthometric height generated for production of a topographical plan at 1m contour interval for elevation data in surveying, engineering and environmental applications. Skill =1 and bias = 0 were computed to confirm the predictive capability of the models and that no bias/errors were introduced into the respective modelling exercise. Diagnostic test also confirmed the viability and feasibility of providing vertical datum surface for FCT by this approach. Standard deviation (σ) as accuracy indicator was computed and the multi-quadratic model with σ =11cm was the better geoid surface for modelling of orthometric height in the FCT by the geometric method.
JGISE: Journal of Geospatial Information Science and Engineering
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 mode...
Replacing Orthometric Heights with Ellipsoidal Heights in Engineering Surveys
Nigerian Journal of Technology, 2016
Differential Global Positioning System (DGPS) is one of the most frequently used positioning methods in geodesy. The end products of surveying with Global Navigation Satellite Systems (GNSS)are geodetic latitude (ϕ), geodetic longitude (λ) and ellipsoidal height (h) which are obtained with reference to the ellipsoid. Recent developments in GNSS technology make us to obtain the ellipsoidal height with high accuracy. In engineering practice, orthometric heights (height above sea level) are always used. The orthometric heights are determined by spirit or geodetic leveling. In transforming the GNSS-derived ellipsoidal heights to orthometric heights, it is important to know the separation between the ellipsoidal and the geoid surface. This work investigates the use of ellipsoidal heights in place of orthometric heights for engineering surveys. DGPS observations were carried out to obtain the ellipsoidal heights for a number of points in the study area in Port Harcourt, Nigeria. Orthometric heights for the same set of points were determined using geodetic levelling. The results satisfied third order levelling which is good enough for engineering surveys.
Geodesy and Geodynamics
At present, one of the methods used to determine the height of points on the Earth's surface is Global Navigation Satellite System (GNSS) leveling. It is possible to determine the orthometric or normal height by this method only if there is a geoid or quasi-geoid height model available. This paper proposes the methodology for local correction of the heights of high-order global geoid models such as EGM08, EIGEN-6C4, GECO, and XGM2019e_2159. This methodology was tested in different areas of the research field, covering various relief forms. The dependence of the change in corrected height accuracy on the input data was analyzed, and the correction was also conducted for model heights in three tidal systems: "tide free", "mean tide", and "zero tide". The results show that the heights of EIGEN-6C4 model can be corrected with an accuracy of up to 1 cm for flat and foothill terrains with the dimensionality of 1 Â 1 ; 2 Â 2 ; and 3 Â 3. The EGM08 model presents an almost identical result. The EIGEN-6C4 model is best suited for mountainous relief and provides an accuracy of 1.5 cm on the 1 Â 1 area. The height correction accuracy of GECO and XGM2019e_2159 models is slightly poor, which has fuzziness in terms of numerical fluctuation.
International Journal of Scientific and Research Publications, 2018
Consistency is an important characteristic in height systems which the mean sea level (msl) surface cannot guarantee. Only a geoid surface can provide height consistency. The quality of geoid undulation (N) will obviously affect the resulting orthometric height (H) determined from GNSS. The geoid undulation may be global, regional/national and local. Online software CSRS-PPP was used for post processing rinex data. í µí± í µí°¸í µí°ºí µí±2008 was computed from AllTrans EGM2008 geoid calculator while h was used to compute í µí± í µí°ºí µí±í µí± from the relationship N= h-H. H is the existing orthometric height. Twenty-four controls with FCT 260 P as base reference station were used for this study. The computed standard deviation of differences iní µí± í µí°ºí µí±í µí± − í µí± í µí°¸í µí°ºí µí±2008 (σ) is used as accuracy indicator and σ =0.419m .The root mean square error (RMSE) is 0.934m. This indicates the quality and reliability of the geoid undulation from the EGM2008 model. Comparing the observed í µí± í µí°ºí µí±í µí±í µí± and í µí± í µí°¸í µí°ºí µí±2008 , the use of global models may not satisfy the accuracy level of orthometric height desired for local applications in the FCT, Abuja. GNSS (GPS) may be used along with local geoid model as a way to acquire acceptable orthometric height. The smaller the í µí± í µí°ºí µí±í µí±-í µí± í µí°¸í µí°ºí µí±2008 makes it better model. The range of 1.585m from (í µí± í µí°ºí µí±í µí±-í µí± í µí°¸í µí°ºí µí±2008) in this study is a strong indication that global models should be avoided as much as possible in local applications.
FUDMA Journal of Sciences (FJS), 2020
The conversion of theoretical, as well as geometric heights to practical heights requires the application of geoidal undulations from a geoid model. The various global geopotential models that are readily available for application in any part of the world do not best-fit regions, as well as countries. As a result, there is a need to determine the local geoid models of local areas, regions and countries. This study determines the local geoid model of Kampala in Uganda for orthometric heights computation by comparing three plane geometric geoid surfaces. A total of 19 points were used in the study. The least squares adjustment technique was applied to compute the models' parameters. Microsoft Excel programs were developed for the application of the models in the study area. The Root Mean Square Index was applied to compute the accuracy of the models. The three geometric geoid models were compared using their accuracy to determine which of them is most suitable for application in the study area. The comparison results show that the three models can be applied in the study area with more reliability, with greater confidence in model 2.
Journal of Geodetic Science, 2022
The use of orthometric height in geodetic applications provides elevations on the physical topographic surface of the earth rather than ellipsoidal heights that are not in conformity with the physical topography. Global positioning system (GPS)/levelling produces ellipsoidal heights that are not consistent with levelled heights above mean sea level. The study provides a practical solution of using the GPS levelling approach or the geoidal heights aimed at providing local orthometric height. Many research studies were conducted with a view of finding a viable solution to the derived orthometric heights. It was revealed that the research studies conducted were found lacking in the use of only lower order numerical solutions models, which limit the accuracy derived from the model, the use of online post-processing, RTKlib, and other non-precise software to obtain the coordinates of the stations used in the derivation of orthometric. Finally, the use of gravimetric data, with its temporal variation problem, poses a threat to the derivation of orthometric height, so also to the accuracy of the developed model. Considering factors while developing models for orthometric heights improves the accuracy in achieving required heights for geodetic applications and aids in fast-tracking mapping.
Arabian Journal of Geosciences, 2018
Ellipsoidal heights are determined with high accuracy using Global Navigation Satellite System (GNSS) techniques. In infrastructure projects undertaken for engineering purposes, orthometric heights are used. Geoid determination studies based on these two height systems are growing in importance. Although various methods are employed in geoid determination, one of the most commonly used in practice is local geoid determination. Points with known orthometric and ellipsoidal heights are used as reference points. These reference points are utilized to determine local geoid models for project area. The formation and selection of the most appropriate and true-to-reality model during modeling are a matter of extreme significance for practitioners who employ such models. In this study, we aim to establish a GNSS/leveling geoid in a test network that was formed in Konya for the purpose of local geoid determination. Validity tests are carried out for five different geoid models. These geoid models are determined using polynomial models of up to the third degree, and an exploration of the parameters that could be used in the decision-making process is performed. In accordance with the results of these calculations, the selection of an appropriate model among different potential polynomial models in local geoid modeling is explained in terms of theoretical references, an application is examined using the data from the study area, and the results are compared.
Geodesy and Cartography
correction parameters for different levels of accuracy in real time and offer them to the users continuously. The technique of spirit leveling provides a height that is commonly known as a height above sea level surface. Additionally, with the combination of measured height differences and gravity measurements, it is possible to obtain final values of the heights that are known as orthometric heights and are related to a zero level surface (Geoid). The surface of the geoid is an equipotential surface and it is closely associated with mean sea level on a global basis (Barthelmes 2013). On the other hand, GPS, offers these three-dimensional, geometric relationships (Ellipsoidal coordinates), and in comparison to geodetic leveling, do not depend on local gravity variations. Since ellipsoidal coordinates do not directly express the notion of height related to a zero level surface (Geoid), it is necessary to transform them into above mentioned level surface. However, an approximate difference between these heights can be UDK 528.37
Geodetski glasnik, 2021
Height is an important component in three dimensional coordinates and determination of the position of points for any meaningful development. Ellipsoidal heights from GNSS require geoid model which could be global, regional and local for transformation to orthometric height. The absence of a national geoid model in Nigeria remains a great drawback to develop local geoid for local application in place of global geoid models. The study aims to assess the accuracy of polynomial geoid models in orthometric height determination. Differential Global Positioning System (DGPS) observations were carried out to determine ellipsoidal heights of the point while nine and eleven coefficients were used for the geoid and orthometric height modelling. Model A and Model C used 2-D (x, y) positions with nine and eleven parameters while model B used 3-D (x, y, ∆h) positions with nine parameters. The least-squares method was adopted in computing the parameters of the models. Root Mean Square Error (RMSE) was used to assess the accuracy of the models with the RMSE of model A is 14.3 cm, model B is 15.7 cm and model C is 14.5 cm, respectively. The inclusion of height term (∆h) in model B does not improve the accuracy over model A and model C. Model A with the lowest RMSE is hence the better of the three models. One-way ANOVA test conducted at 95% confidence level,