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ETEJE, S. O., P. D. OLUYORI, and M. N. ONO. "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, no. 10 (2018): 1–9. https://doi.org/10.5281/zenodo.2525684.
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Ellipsoidal heights from GNSS require geoid model for conversion to orthometric height. The geoid model could be global, regional or local. The lack of national geoid model in Nigeria makes development of local geoid very critical to local applications in place of integrated global geoid models. This study compares two polynomial geoid models for terrain representation in the FCT, Abuja. Nine coefficients were used to model the FCT surface for geoid interpolation and orthometric height modeling. Model A involved the use of the 2-D (x, y) positions while model B used 3-D (x, y, ) where = ( – ) the difference in average ellipsoidal height ( ) and each point’s ellipsoidal height ( ). The term is based on the assumption that the geoid varies with topography and may hence possibly lead to some improvements in accuracy of orthometric height determination. DGPS observations were carried out to determine ellipsoid heights. Least squares adjustment was performed to compute the coefficients of the models. Model A achieved standard deviation of σ = 11 cm while Model B achieved σ = 13cm. Though, Model B has a term that included highly accurate ellipsoidal height differences ( ), it has not resulted into any accuracy improvement over the model A. Model A based on 2-D positions is hence the better of the two models. The t-test and hypothesis test at 95% confidence limit, however, showed that the two models did not differ significantly. Model A having lower standard deviation is recommended with GNSS determined ellipsoidal heights to determine orthometric heights within the FCT. This becomes an easy alternative to conventional spirit leveling technique for production of topographical maps, cadastral surveys, and engineering/environmental applications.
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Menegbo, Emmanuel. "Determination of orthometric elevations using gnss-derived height with the egm2008 geoid height model." International Journal of Advanced Geosciences 5, no. 1 (2017): 13. http://dx.doi.org/10.14419/ijag.v5i1.7190.
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The Global navigation satellite systems (GNSS) has imparted positively on civilian positioning & surveying in the horizontal component in Nigeria for the past two decades. The GNSS receivers’ data are longitude, latitude & elevation. However, the vertical distance measurement have not been fully exploited by geodetic and land surveyors. The GNSS derived heights are ellipsoidal elevation. To convert the GNSS elevation to orthometric heights, a geoidal elevation models is needed. The Earth Gravitational Model, 2008 (EGM2008) is a global geoidal models that can be used to obtain GNSS orthometric heights by defining the relationship with the ellipsoid. This work determines GNSS-derived orthometric heights with ellipsoid-geoidal relationship using GPS ellipsoidal heights and EGM2008 geoidal model GIS data. The EGM2008 GIS data was downloaded and interpolated with GPS data to obtain geoidal heights using ArcGIS 10.1. GNSS-derived heights determined with geoid-ellipsoid relationship formula. The result shows minimum elevation of -2.37599m and maximum elevation of 53.8566m.The derived orthometric heights use to create a model in raster format. The orthometric elevation models created useful in all vertical surveying work, construction work and urban planning. The GNSS orthometric heights models need to be compare with spirit levelling and the local geoidal model determined for improve accuracy.
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Eteje, S. O., and V. N. Ugbelase. "Comparative Analysis of the Molodensky and Kotsakis Ellipsoidal Heights Transformation between Geocentric and Non-Geocentric Datums Models." Journal of Geography, Environment and Earth Science International 25, no. 10 (2021): 171–77. https://doi.org/10.9734/JGEESI/2021/v25i1030323.
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The non-availability of ellipsoidal heights of local geodetic Datums has made it necessary for the application of ellipsoidal heights transformation models to the available global ellipsoidal heights to obtain their respective theoretical heights in local Datums. It is required to know the accuracy, as well as reliability of any model of interest before its application. For that reason, this study comparatively analyses the Molodensky and Kotsakis models for the transformation of ellipsoidal heights between geocentric and non-geocentric Datums to determine the reliability of the Kotsakis model. The Global Navigation Satellite System (GNSS) data of the used stations were processed in World Geodetic System 1984 (WGS84) datum to obtain their global geographic coordinates and ellipsoidal heights. The coordinates, ellipsoidal heights and the transformation parameters between WGS84 and Minna Datums were applied to the Molodensky and Kotsakis models to compute the Clarke 1880 theoretical heights of the stations. The Molodensky model was used as a reference to which the Kotsakis model ellipsoidal heights were compared to obtain the Kotsakis model ellipsoidal heights discrepancies, as well as residuals. The residuals were used to compute the Root Mean Square Error (RMSE) of the Kotsakis model. The computed RMSE, as well as reliability of the model is 1.244 m. The study concluded that the low reliability, as well as accuracy of the Kotsakis model might be as a result of the two rotation datum shift parameters in it as they are the main differences between the two models.
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David Mayunga, Selassie. "Determination and Analysis of Height Differences between Orthometric and Ellipsoidal Heights for Engineering Applications." International Journal of Science and Research (IJSR) 12, no. 8 (2023): 1653–61. http://dx.doi.org/10.21275/sr23815133647.
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ETEJE, S. O., O. F. ODUYEBO, and S. A. OLULADE. "Procedure for the Determination of Local Gravimetric-Geometric Geoid Model." International Journal of Advances in Scientific Research and Engineering (ijasre) 4, no. 8 (2018): 206–14. https://doi.org/10.5281/zenodo.2525708.
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As the surface adopted for geodetic computation is a mathematical surface which is different from the physical surface, the geoid adopted as a reference for the vertical coordinate system, the ellipsoidal heights obtained from GPS observation are transformed to practical heights known as orthometric heights. The transformation of the ellipsoidal heights to orthometric heights requires the knowledge of the geoid-ellipsoid separation at the point of observation. Since the geometric method requires the computation of geoid heights of points from GPS observation and geodetic leveling carried out over long distances which are labor intensive and prone to human errors, the accurate geoid heights of the points should be obtained from gravity measurement and a geometric geoid surface fitted to the gravimetric geoid heights. This paper presents detailed procedures for determining local gravimetric-geometric geoid model of an area or a region. The detailed procedures which consist of selection of suitable/evenly distributed points, DGPS and gravity observations of selected points, processing of DGPS and gravity observations, computation of gravimetric geoid heights of the points, fitting of geometric geoid surface to the computed gravimetric geoid heights and computation of accuracy of the geoid model are presented in sequential order.
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Kuhar, Miran, Robert Brglez, and Božo Koler. "Quality determination of mean sea level heights with GNSS levelling on the Ljubljana city area." Geodetski vestnik 65, no. 02 (2021): 219–33. http://dx.doi.org/10.15292/geodetski-vestnik.2021.02.219-233.
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This paper describes the quality determination of heights above mean sea level using RTK GNSS-levelling and new height reference surface SLO_VRP2016/Koper on the city area of Ljubljana. At 57 chosen benchmarks, quasigeoid heights were determined using ellipsoidal heights, determined with RTK GNNS-levelling technique and heights above mean sea level in the new height system SVS2010. The measured quasigeoid heights were compared with values interpolated from the new height reference surface SLO_VRP2016/Koper.
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Badejo, OT, KFA Aleem, and JB Olaleye. "REPLACING ORTHOMETRIC HEIGHTS WITH ELLIPSOIDAL HEIGHTS IN ENGINEERING SURVEYS." Nigerian Journal of Technology 35, no. 4 (2016): 761. http://dx.doi.org/10.4314/njt.v35i4.10.
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Goli, M., and M. Najafi-Alamdari. "Planar, spherical and ellipsoidal approximations of Poisson's integral in near zone." Journal of Geodetic Science 1, no. 1 (2011): 17–24. http://dx.doi.org/10.2478/v10156-010-0003-6.
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Planar, spherical and ellipsoidal approximations of Poisson's integral in near zonePlanar, spherical, and ellipsoidal approximations of Poisson's integral for downward continuation (DWC) of gravity anomalies are discussed in this study. The planar approximation of Poisson integral is assessed versus the spherical and ellipsoidal approximations by examining the outcomes of DWC and finally the geoidal heights. We present the analytical solution of Poisson's kernel in the point-mean discretization model that speed up computation time 500 times faster than spherical Poisson kernel while preserving a good numerical accuracy. The new formulas are very simple and stable even for regions with very low height. It is shown that the maximum differences between spherical and planar DWC as well as planar and ellipsoidal DWC are about 6 mm and 18 mm respectively in the geoidal heights for a rough mountainous area such as Iran.
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Zlinszky, A., G. Timár, R. Weber, et al. "Observation of a local gravity potential isosurface by airborne lidar of Lake Balaton, Hungary." Solid Earth 5, no. 1 (2014): 355–69. http://dx.doi.org/10.5194/se-5-355-2014.
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Abstract. Airborne lidar is a remote sensing method commonly used for mapping surface topography in high resolution. A water surface in hydrostatic equilibrium theoretically represents a gravity potential isosurface. Here we compare lidar-based ellipsoidal water surface height measurements all around the shore of a major lake with a local high-resolution quasi-geoid model. The ellipsoidal heights of the 87 km2 we sampled all around the shore of the 597 km2 lake surface vary by 0.8 m and strong spatial correlation with the quasi-geoid undulation was calculated (R2 = 0.91). After subtraction of the local geoid undulation from the measured ellipsoidal water surface heights, their variation was considerably reduced. Based on a network of water gauge measurements, dynamic water surface heights were also successfully corrected for. This demonstrates that the water surface heights of the lake were truly determined by the local gravity potential. We conclude that both the level of hydrostatic equilibrium of the lake and the accuracy of airborne lidar were sufficient for identifying the spatial variations of gravity potential.
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Mihalache, Raluca Maria, and Andreea Manescu. "Interpolation Grid for Local Area of Iasi City." Present Environment and Sustainable Development 8, no. 1 (2014): 157–64. http://dx.doi.org/10.2478/pesd-2014-0014.
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Abstract Definitive transition to GNSS technology of achieving geodetic networks for cadastre implementation in cities and municipalities, enforce establishing a unique way of linking between current measurements and existing geodetic data, with a sufficient accuracy proper to urban cadastre standards. Regarding city of Iasi, is presented a different method of transformation which consist in an interpolation grid for heights system. The Romanian national height system is „Black Sea-1975” normal heights system. Founded in 1945 by Molodenski, this system uses the quasigeoid as reference surface, being in relation with the ellipsoid through the height anomalies sizes in each point. The unitary transformation between the ETRS- 89 ellipsoidal height system and the normal one, at national level is provided through the „TransdatRo” program developed by NACLR (National Agency for Cadastre and Land Registration).
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Zlinszky, A., G. Timár, R. Weber, et al. "Observation of a local gravity isosurface by airborne LIDAR of Lake Balaton, Hungary." Solid Earth Discussions 6, no. 1 (2014): 119–44. http://dx.doi.org/10.5194/sed-6-119-2014.
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Abstract. Airborne LIDAR (Light Detection and Ranging) is a remote sensing method commonly used for mapping surface topography in high resolution. A water surface in hydrostatic equilibrium theoretically represents a gravity isosurface. Here we compare LIDAR-based ellipsoidal water surface height measurements all around the shore of a major lake with a local high resolution geoid model. The ellipsoidal heights of the 87 km2 we sampled all around the shore of the 597 km2 lake surface vary by 0.8 m and strong spatial correlation with the geoid undulation was calculated (R2=0.91). After subtraction of the local geoid undulation from the measured ellipsoidal water surface heights, their variation was considerably reduced. This demonstrates that the water surface heights of the lake were truly determined by the local gravity potential. We conclude that the accuracy of airborne LIDAR is sufficient for identifying the spatial variations of gravity potential over large inland water surfaces.
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FEDORCHUK, A. "Analysis of erypsoidal heights errors based on GNSS-leveling results." Modern achievements of geodesic science and industry 41, no. I (2021): 37–45. http://dx.doi.org/10.33841/1819-1339-1-41-37-45.
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Research the influence of errors on the measurement results is always an urgent task. Analysis of such values makes it possible to assess the nature of the change and the magnitude of the impact of errors for their further consideration or compensation, or minimization. In this paper, the errors in determining ellipsoidal heights from GNSS observations are considered. In determining the ellipsoidal heights, this method can achieve an accuracy of 1–2 cm in static mode (Static) and 2–4 cm in real time mode (RTK). Thus, the accuracy of the chosen mode of observations will indicate the initial limits of the ellipsoidal heights errors influence, and the factors that arise directly during observations and data processing will determine the extent to which these errors will change relative to the initial limits. The purpose of this work is to analyze the errors of ellipsoidal heights based on the results of GNSS-leveling obtained in the static and RTK modes. Method. The study used GNSS-leveling data at 17 points (wall and soil benchmarks) of leveling lines of I–II classes, which are located within a radius of 15 km from the permanent station SULP of the Lviv Polytechnic National University. Observations were performed in static mode (4-hour) and RTK (8–10 measurements). Points are divided into three categories (5–6 points): 1) statics on wall benchmarks; 2) real-time mode on wall benchmarks; 3) static mode on soil benchmarks. By combining methods and categories, four GNSS networks were formed, including 11, 11, 12 and 17 points. Results. For each category, the percentages within which the errors of ellipsoidal heights change in static observation mode and real-time mode using the GNSS leveling method are presented. On the basis of the received information it is established that for the first case errors of ellipsoidal heights on the average change within ± 43 %, for the second ± 36 %, and for the third ± 14 %. The analysis of statistical characteristics for each category shows that the standard deviation of the static mode data is 2 % and 19 %, and the RTK mode – 12 %, respectively. Scientific novelty and practical significance. The nature of the change in the error limits of the ellipsoidal heights determination gives an idea of what accuracy should be expected when performing GNSS-leveling depending on the mode of observation. Such data play an important role in solving scientific and applied problems by GNSS leveling, such as the constructions of new leveling networks or monitoring the height points of existing networks.
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ETEJE, S. O., M. N. ONO, and O. F. ODUYEBO. "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, no. 6 (2018): 30–37. https://doi.org/10.5281/zenodo.2525661.
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A local geoid model for Evboriaria, Benin City using the geometric (GPS/Levelling) method was determined for calculation of mean sea level heights. Fifty points were established for the model and ten points were used for interpolation. The geoid heights were determined by finding the difference between the observed orthometric heights and the ellipsoidal heights. The polynomial regression model D was used for the interpolation of the orthometric heights. The computed mean standard deviation between the observed orthometric heights and the interpolated orthometric heights was ± 21cm. A mean geoidal undulation of 28.410m was computed using the gravimetric method. The computed orthometric heights using the gravimetry mean geoidal undulation were compared with the observed orthometric heights and seen to be identical. It is recommended that orthometric heights of project areas should be determined from GPS observations with the local geoid model of the area also determined.
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Madufor, M.O., M.N. Ono, A.O. Oliya, and W. A. Ojanikele. "Modeling of Orthometric Heights from Multi-Networks of GNSS/Precise Levelling in Owerri and Environs, Imo State, Nigeria." Journal of Scientific and Engineering Research 10, no. 11 (2023): 35–40. https://doi.org/10.5281/zenodo.10465693.
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<strong>Abstract </strong>Orthometric heights based on GNSS require a geoid model to convert highly accurate ellipsoidal height (h) to the much-desired orthometric height (H) critical to many cadastral, surveying, mapping, engineering and environmental applications. The GNSS uses the default integrated global geoid models (EGM96/EGM2008) for ellipsoidal height conversion to orthometric but for local applications, global model is inadequate and hence development of local geoid models in the absence of a national geoid becomes very critical. The aim of this research is to model orthometric heights from multi-networks of GNSS/Precise levelling in Owerri and environs, Imo State by using ellipsoid heights (h) and the existing orthometric heights (H) from the relationship N= (h-H) for geoid modelling. The objectives are to: investigate the physical status/stability of the existing orthometric heights in Owerri and environs; to carry out GNSS observations on existing controls for ellipsoidal height determination by relative technique, determine geoid undulation of existing controls using N= (h-H); develop Microsoft excel program for interpolation of geoid undulation and hence model orthometric heights; to compare height obtained from model with existing orthometric height by statistical t test. This research adopted the dual-base reference stations approach, static 2 hours DGPS mode for data capture and connection to core stations. The polynomial models used to represent Owerri and environs surface are i) multi-quadratic model and ii) bi-cubic model. For each point, observation equation of the form AX-L was derived. The least squares equation was solved using the online matrix solver (Huobi.pro) for (X) to determine the model coefficient parameters used to develop the geometric geoid model program using the Microsoft Excel 2010. The standard deviations of the geoid model determined orthometric height H are: σ_multiquadratic=11cm and σ_bicubic=14cm. Computation of t from formula and compared with value of t from t table distribution revealed 〖(H〗_multiquadratic and H_MSL) the possibility of coincidence/fit of the two surfaces though based on different vertical datum (geoid and MSL). From computed F1, test statistics and using the standard deviation, no other surface than multi-quadratic is needed to model orthometric heights. Coefficient of correlation (R) and coefficient of Determination (R²) values of 0.995m and 99% respectively indicate the multi-quadratic model has a high predictive ability. Diagnostic tests confirmed that a multi-quadratic model at 95% confidence limits can be sufficiently adequate for geoid modelling. Also computing N∑▒〖ai〗^2 and comparing with (1.98/√N (N is no of controls=24) at 95% confirmed the validity of using the models for orthometric heights determination. The bias value of zero and skill parameter of one implies total agreement between technique, observations, processing and the model results. The developed model will serve as reliable alternative for orthometric height acquisition at centimeter level accuracy which is adequate for producing topographic maps (at Im contour interval), base maps for planning and production of large scale engineering plans. Kriging interpolation method was used to generate contour maps, geoidal maps and the digital elevation models. It is hereby recommended that the developed model (multi-quadratic) be adopted for elevation data acquisition for day to day geospatial data needs in cadastral, mapping, engineering/ Environmental applications.
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Herbert, Tata, and Raufu Ibrahim Olatunji. "Comparative Analysis of Change between Ellipsoidal Height Differences and Equivalent Orthometric Height Difference." Ghana Journal of Geography 12, no. 1 (2020): 132–44. http://dx.doi.org/10.4314/gjg.v12i1.7.
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Height is an important component in the determination of the position of a point. The study aimed at performing a comparative analysis of change between ellipsoidal height differences and the equivalent orthometric height difference of points. A hi-target Differential Global Positioning System (DGPS) was used to acquire GPS data with an occupation period of thirty (30) minutes on each point, which were processed using Hi-target Geomatics Office (HGO) software to obtain the ellipsoidal heights. An automatic level instrument was used to acquire leveling data, which were processed using the height of collimation method to obtain the orthometric heights. A total of fifty (50) points were occupied as common points for both the GPS and levelling observations at 20-meter intervals. The accuracy of the height difference was determined using standard deviation with the ellipsoidal height difference as 53.59cm and the orthometric height as 53.07cm respectively. A Root Mean Square Error value of 0.0621m was obtained as the accuracy of the change between the two height differences. Statistical analysis using the independent-sample Z test was used to analyze the data at a 5% significant level. The result shows no significant difference in the performance of the two height systems. It is worthy to note that GPS and spirit levelling height differences can be used interchangeably for any heighting in short distances for surveying and engineering applications.
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Erol, Serdar, Emrah Özögel, Ramazan Alper Kuçak, and Bihter Erol. "Utilizing Airborne LiDAR and UAV Photogrammetry Techniques in Local Geoid Model Determination and Validation." ISPRS International Journal of Geo-Information 9, no. 9 (2020): 528. http://dx.doi.org/10.3390/ijgi9090528.
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This investigation evaluates the performance of digital terrain models (DTMs) generated in different vertical datums by aerial LiDAR and unmanned aerial vehicle (UAV) photogrammetry techniques, for the determination and validation of local geoid models. Many engineering projects require the point heights referring to a physical surface, i.e., geoid, rather than an ellipsoid. When a high-accuracy local geoid model is available in the study area, the physical heights are practically obtained with the transformation of global navigation satellite system (GNSS) ellipsoidal heights of the points. Besides the commonly used geodetic methods, this study introduces a novel approach for the determination and validation of the local geoid surface models using photogrammetry. The numeric tests were carried out in the Bergama region, in the west of Turkey. Using direct georeferenced airborne LiDAR and indirect georeferenced UAV photogrammetry-derived point clouds, DTMs were generated in ellipsoidal and geoidal vertical datums, respectively. After this, the local geoid models were calculated as differences between the generated DTMs. Generated local geoid models in the grid and pointwise formats were tested and compared with the regional gravimetric geoid model (TG03) and a high-resolution global geoid model (EIGEN6C4), respectively. In conclusion, the applied approach provided sufficient performance for modeling and validating the geoid heights with centimeter-level accuracy.
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Aziz, Khaled Mahmoud Abdel, Karim Samir Rashwan, and Nasr Saba. "Evaluation of EGM96 and EGM08 based on GPS/Levelling Heights in Egypt." South African Journal of Geomatics 12, no. 1 (2023): 44–55. http://dx.doi.org/10.4314/sajg.v12i1.3.
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The heights determined by Global Positioning System (GPS) refer to the ellipsoid called the World Geodetic System 1984 (WGS84). Global Geopotential Models (GGMs) that are available on GNSS commercial software are generally used to transform ellipsoidal heights to orthometric heights. In this study, the geoid heights of GPS/Levelling were computed to evaluate the accuracy of the geoid heights obtained from two GGMs, namely, the Earth Gravitational Model 96 (EGM96) and the Earth Gravitational Model 08 (EGM08). Seventeen (17) GPS/Levelling stations of the High Accuracy Reference Network (HARN) over Egypt were used for this purpose. The standard deviations for the differences between the geoid heights obtained through GPS/Levelling and those obtained from EGM96 and EGM08 were determined as ± 1.212 m and ± 0.543 m, respectively. This research confirms that the geoid heights obtained from EGM08 are closer to the geoid heights determined using GPS/Levelling over Egypt.
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Kao, Szu-Pyng, Fang-Shii Ning, Chao-Nan Chen, and Chia-Ling Chen. "USING PARTICLE SWARM OPTIMIZATION TO ESTABLISH A LOCAL GEOMETRIC GEOID MODEL." Boletim de Ciências Geodésicas 23, no. 2 (2017): 327–37. http://dx.doi.org/10.1590/s1982-21702017000200021.
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There exist a number of methods for approximating the local geoid surface and studies carried out to determine a local geoid. In this study, performance of geoid by PSO method in modeling local geoid was presented and analyzed. The ellipsoidal heights (h), derived from GPS observations, and known orthometric heights from first-order benchmarks were first used to create local geometric geoid model, then the PSO method was used to convert ellipsoidal heights into orthometric heights (H). The resulting values were used to compare between the spirit leveling and GPS methods. The adopted PSO method can improve the fitting of local geometric geoid by quadratic surface fitting method, which agrees with the known orthometric heights within ±1.02cm
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Raufu, Ibrahim Olatunji, and Herbert Tata. "Accuracy Assessment of Different Polynomial Geoid Models in Orthometric Height Determination for Akure, Nigeria." Geodetski glasnik, no. 52 (December 31, 2021): 61–73. http://dx.doi.org/10.58817/2233-1786.2021.55.52.61.
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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, however, revealed that the three models did not differ significantly. Model A having lower RMSE is recommended with GPS determined ellipsoidal heights as an alternative to conventional spirit levelling for orthometric height determination within Akure for engineering and environmental applications.
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Negedu, Achimugu Amos, and Matthew Nnonyelu Ono. "ESTABLISHMENT OF ORTHOMETRIC HEIGHT CONTROLS IN THE EASTERN PART OF KOGI STATE USING GNSS AND EGM 2008." FUDMA JOURNAL OF SCIENCES 8, no. 2 (2024): 180–87. http://dx.doi.org/10.33003/fjs-2024-0802-2346.
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The aim of this study was to model the orthometric heights in parts of Kogi East, Kogi State using GNSS and EGM 2008 with the objectives of establishing the best geoid undulation for height determination. The Hardwares used for this study include; Hi target V.30 dual frequency GNSS receiver and its accessories, Data logger, Computer hardware and software and Computer – HP Laptop and internet facilities. Softwares used included; Arc GIS, Google map, microsoft word, Microsoft excel, Hi target Geomatic offices, CSRS – PPP website andGeoid Eval Calculator. GNSS observations were conducted on 6 station monument. The dual frequency v30 Hi target instrument was used in the static mode to make observations on all the established points at an epoch rate of 30 seconds; for a period of one hour to one hour thirty minutes (session) per station. The secondary data were the EGM 2008, obtained from Geoid eval platform in https://www.geographiclib.sourceforge.ion/cgi-bin/GeoidEval. Geoid Eval platform makes provision for the geographical coordinates to be inputed before the geoidal-ellipsoidal separation values can be provided. Geoid Eval computes the height of the geoid above the WGS 84 ellipsoid using interpolation in a grid of values for the earth gravity models. To obtain the orthometric height, the geoid value is subtracted from the ellipsoidal height obtained from the GNSS-PPP observation. The accuracy of the geoid value is 1mm and that of the GNSS-PPP was adjudged to be 3cm respectively. It was recommended that, more orthometric heights be distributed for monitoring of the earth’s dynamisms.
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Akcin, Hakan, and Cahit Tagi Celik. "Performance of artificial neural networks on kriging method in modeling local geoid." Boletim de Ciências Geodésicas 19, no. 1 (2013): 84–97. http://dx.doi.org/10.1590/s1982-21702013000100006.
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Transformation of ellipsoidal heights determined by satellite techniques into local leveling heights requires geoid heights at points of interest. However, the geoid heights at each point are not available. In order to determine them, the local geoid in the transformation area must be modeled or computed by an appropriate method, one way of doing it, is to use control points both of whose ellipsoidal and local leveling heights are available. In this study, performance of geoid by ANN compared to Kriging method in modeling local geoid was presented. Moreover, the transformation ability of the methods was investigated through a geodetic test network in Bursa Metropolitan Area of Turkey. The results suggest that the model by ANN exhibit better results than the one by Kriging Method.
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Virts, Katrina S., and William J. Koshak. "Mitigation of Geostationary Lightning Mapper Geolocation Errors." Journal of Atmospheric and Oceanic Technology 37, no. 9 (2020): 1725–36. http://dx.doi.org/10.1175/jtech-d-19-0100.1.
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AbstractThe geolocation of lightning flashes observed by spaceborne optical sensors depends upon a priori assumptions of the cloud-top height (or, more generally, the height of the radiant emitter) as observed by the satellite. Lightning observations from the Geostationary Lightning Mappers (GLMs) on Geostationary Operational Environmental Satellite 16 (GOES-16) and GOES-17 were originally geolocated by assuming that the global cloud-top height can be modeled as an ellipsoidal surface with an altitude of 16 km at the equator and sloping down to 6 km at the poles. This method produced parallax errors of 20–30 km or more near the limb, where GLM can detect side-cloud illumination or below-cloud lightning channels at lower altitudes than assumed by the ellipsoid. Based on analysis of GLM location accuracy using a suite of alternate lightning ellipsoids, a lower ellipsoid (14 km at the equator, 6 km at the poles) was implemented in October and December 2018 for GLM-16 and GLM-17, respectively. While the lower ellipsoid slightly improves overall GLM location accuracy, parallax-related errors remain, particularly near the limb. This study describes the identification of optimized assumed emitter heights, defined as those that produce the closest agreement with the ground-based reference networks. Derived using the first year of observations from GOES-East position, the optimal emitter height varies geographically and seasonally in a manner consistent with known meteorological regimes. Application of the optimal emitter height approximately doubles the fraction of area near the limb for which peak location errors are less than half a GLM pixel.
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Eteje, S. O., O. F. Oduyebo, and M. N. Ono. "Comparison of Three Gravimetric-Geometric Geoid Models for Best Local Geoid Model of Benin City, Nigeria." International Journal of Advanced Engineering Research and Science (IJAERS) 6, no. 12 (2019): 261–72. https://doi.org/10.22161/ijaers.612.23.
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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.
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Raufu, Ibrahim Olatunji, Herbert Tata, and Solihu Olaosegba. "GEODESY, CARTOGRAPHY, AND AERIAL PHOTOGRAPHY." GEODESY, CARTOGRAPHY, AND AERIAL PHOTOGRAPHY 98,2023, no. 98 (2023): 63–75. http://dx.doi.org/10.23939/istcgcap2023.98.063.
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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.
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Łyszkowicz, Adam, Joanna Kuczyńska-Siehień, and Monika Biryło. "Preliminary Unification of Kronsztadt86 Local Vertical Datum with Global Vertical Datum." Reports on Geodesy and Geoinformatics 97, no. 1 (2015): 103–11. http://dx.doi.org/10.2478/rgg-2014-0015.
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AbstractThe study concerns computation of the gravity potential difference between the Kronsztadt86 datum and the global vertical datum. This method is based on the use of ellipsoidal heights from satellite observations, normal heights obtained from the conducted leveling campaign and quasigeoid/ellipsoid separations computed based on the EGM2008 model. The obtained results indicate that there are substantial differences in the estimated value of the parameter ΔW, computed from three different satellite networks: POLREF, EUVN-DA and ASG-EUPOS. The parameter was determined with sufficient accuracy and the applied systematic error model has low efficiency. The computations reveal that the best value of ΔW for the territory of Poland is 0.43 m2s-2.
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Ijaware, V. A. "Comparative Analysis of Ellipsoidal Height and Shuttle Radar Topographic Mission Elevation." Journal of Applied Sciences and Environmental Management 24, no. 8 (2020): 1397–402. http://dx.doi.org/10.4314/jasem.v24i8.14.
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Ellipsoidal elevation represents a precise geospatial data type within the analysis and modelling of various hydrological and ecological phenomenon required in preserving the human environment. Likewise, Shuttle Radar Topographic Mission (SRTM) has created an unparalleled data set of global elevations that are freely available for modelling ubiquitous environmental applications. This research aims to carry out a comparative analysis of ellipsoidal heights and SRTM heights with the following objectives: downloading DEM’s (SRTM) data covering the study area, determining the spot heights within the boundary in conventional method, extract DEM’S heights within the boundary of the study area, and compared the heights in the conventional method with DEM’S heights. South GPS and Leica Total Station were used to acquire data for control extension and spot heightening respectively while the elevation of SRTM data was obtained by transforming the X and Y data from GPS observationto Longitude and Latitude before using ArcGIS 10.6 to extract the elevation of the boundary pillar and all the spot heights which were relatively compared in terms of its products- heights, contour, 3-D wireframe, 3-D surface model, and overlaid of contour on shaded relief. The results of the study showed that vertical difference using conventional method and SRTM dataset ranges between -2.345m to 11.026m. Also, the hypothesis tested using a two-tail student t-test and F-test revealed that one mean is not significantly different from the other at 95% confidence level. The research recommends that the products obtained for the two systems can be used interchangeably.
 Keywords: Shuttle radar topographic mission, Ellipsoidal elevation, contour, 3D wireframe, 3D surface model
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Ligas, Marcin, and Piotr Banasik. "Conversion between Cartesian and geodetic coordinates on a rotational ellipsoid by solving a system of nonlinear equations." Geodesy and Cartography 60, no. 2 (2011): 145–59. http://dx.doi.org/10.2478/v10277-012-0013-x.
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Conversion between Cartesian and geodetic coordinates on a rotational ellipsoid by solving a system of nonlinear equationsA new method to transform from Cartesian to geodetic coordinates is presented. It is based on the solution of a system of nonlinear equations with respect to the coordinates of the point projected onto the ellipsoid along the normal. Newton's method and a modification of Newton's method were applied to give third-order convergence. The method developed was compared to some well known iterative techniques. All methods were tested on three ellipsoidal height ranges: namely, (-10 - 10 km) (terrestrial), (20 - 1000 km), and (1000 - 36000 km) (satellite). One iteration of the presented method, implemented with the third-order convergence modified Newton's method, is necessary to obtain a satisfactory level of accuracy for the geodetic latitude (σφ < 0.0004") and height (σh< 10-6km, i.e. less than a millimetre) for all the heights tested. The method is slightly slower than the method of Fukushima (2006) and Fukushima's (1999) fast implementation of Bowring's (1976) method.
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Kyamulesire, B., P. D. Oluyori, and S. O. Eteje. "COMPARATIVE ANALYSIS OF THREE PLANE GEOMETRIC GEOID SURFACES FOR ORTHOMETRIC HEIGHT MODELLING IN KAMPALA, UGANDA." FUDMA Journal of Sciences (FJS) 4, no. 3 (2020): 43–51. https://doi.org/10.33003/fjs-2020-0403-255.
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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.
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Fazilova, Dilbarkhon, Aziz Kazakov, and Ilkhom Alimukhamedov. "Improving global Geoid by GPS and leveling data over the Fergana valley territory." InterCarto. InterGIS 28, no. 1 (2022): 568–79. http://dx.doi.org/10.35595/2414-9179-2022-1-28-568-579.
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The Republic of Uzbekistan currently uses the Baltic normal system of heights associated with the quasi-geoid surface. The introduction of innovative technologies of global navigation satellite systems (GNSS) made it possible to determine with high accuracy the geometric heights related to the Earth model — an ellipsoid. For a complex representation of spatial data and analysis of information about the territory, natural resources, man-made objects, their dynamics in the National Geographic Information System (NGIS), first of all, it is necessary to solve the problem of refining the reference vertical coordinate system and ensuring its connection with the global ones, namely, to ensure adjustment of these two height systems. The task is complicated by the fact that for the territory of the country there is no information about the quasi-geoid determined by modern methods, which are necessary for the transition from geometric ellipsoidal heights obtained using GPS measurements to normal heights which are used for solving a wide range of practical problems in various fields of environmental sciences. In recent years, global geopotential models of the Earth (GGM) calculated using various satellite missions has become an alternative solution to the problem. The study considers two high order GGMs (EGM2008 and GECO) to create a system of normal heights for the territory of the Fergana Valley. The height anomaly values for them reach the maximum for the region — about −49 m. The method of constructing parametric models (or corrective surfaces) using leveling and GPS measurements at “common points” was used to refine them. The range of corrections made was from −0.28 m to 0.29 m. Moreover, the GECO model was significantly improved compared to EGM2008 in the flatland part of the study area, which has large geoid anomalies. The Krasovsky ellipsoid and the corresponding Baltic height system were chosen as a reference surface to create in the future a grid for converting heights between local and geocentric coordinate systems. The results of a comprehensive statistical analysis made it possible to reveal that GECO gives a more accurate representation of the region’s relief and is recommended for solving practical problems in the Fergana Valley.
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Brown, N. J., W. E. Featherstone, G. Hu, and G. M. Johnston. "AUSGeoid09: a more direct and more accurate model for converting ellipsoidal heights to AHD heights." Journal of Spatial Science 56, no. 1 (2011): 27–37. http://dx.doi.org/10.1080/14498596.2011.580498.
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Lukoševičius, Viktoras. "DFHRS-BASED COMPUTATION OF QUASI-GEOID OF LATVIA." Geodesy and Cartography 39, no. 1 (2013): 11–17. http://dx.doi.org/10.3846/20296991.2013.788827.
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In geodesy, civil engineering and related fields high accuracy coordinate determination is needed, for that reason GNSS technologies plays important role. Transformation from GNSS derived ellipsoidal heights to orthometric or normal heights requires a high accuracy geoid or quasi-geoid model, respectively the accuracy of the currently used Latvian gravimetric quasi-geoid model LV'98 is 6–8 cm. The objective of this work was to calculate an improved quasi-geoid (QGeoid) for Latvia. The computation was performed by applying the DFHRS software. This paper discusses obtained geoid height reference surface, its comparisons to other geoid models, fitting point statistics and quality control based on independent measurements.
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Eteje, S. O., B. Kyamulesire, and P. D. Oluyori. "Establishment of local geometric geoid model for Busoga, Uganda." World Journal of Advanced Research and Reviews 8, no. 3 (2020): 139–48. https://doi.org/10.30574/wjarr.2020.8.3.0468.
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The importance of the local geoid model for the computation of accurate geoid heights, as well as orthometric heights used for engineering constructions, necessitated its establishment in areas, regions or countries. Consequently, this study establishes the local geometric geoid model of Busoga, Uganda, using the geometric method. A total of 26 points were used in the study, 20 points for the development of the model and 6 test points. GNSS observations were acquired with Trimble GNSS dual-frequency receivers and processed with Bernese (V5.2) and Spectra Precision Survey Office (v4.1) software to obtain the coordinates and ellipsoidal heights of the points. Differences between the existing orthometric and ellipsoidal heights were computed to obtain the geoid heights. The Least squares adjustment technique was applied to determine the fit, as well as the Bicubic and Multiquadratic models’ parameters. The Root Mean Squares Error (RMSE) index was used to compute the accuracy of the models. The geoid models were compared with their RMSE, as well as accuracy to determine which of them is more suitable for application in the study area. The comparison result shows that the Multiquadratic geoid model is more suitable for implementation in the study area. A Microsoft Excel program was developed for the application of the model in the study area.
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Bruno, Kyamulesire, Okiemute Eteje Sylvester, and Dare Oluyori Paul. "Establishment of local geometric geoid model for Busoga, Uganda." World Journal of Advanced Research and Reviews 8, no. 3 (2020): 139–48. https://doi.org/10.5281/zenodo.4421199.
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The importance of the local geoid model for the computation of accurate geoid heights, as well as orthometric heights used for engineering constructions, necessitated its establishment in areas, regions or countries. Consequently, this study establishes the local geometric geoid model of Busoga, Uganda, using the geometric method. A total of 26 points were used in the study, 20 points for the development of the model and 6 test points. GNSS observations were acquired with Trimble GNSS dual-frequency receivers and processed with Bernese (V5.2) and Spectra Precision Survey Office (v4.1) software to obtain the coordinates and ellipsoidal heights of the points. Differences between the existing orthometric and ellipsoidal heights were computed to obtain the geoid heights. The Least squares adjustment technique was applied to determine the fit, as well as the Bicubic and Multiquadratic models’ parameters. The Root Mean Squares Error (RMSE) index was used to compute the accuracy of the models. The geoid models were compared with their RMSE, as well as accuracy to determine which of them is more suitable for application in the study area. The comparison result shows that the Multiquadratic geoid model is more suitable for implementation in the study area. A Microsoft Excel program was developed for the application of the model in the study area.
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Phillips, Helen A., Ian Allison, R. Coleman, G. Hyland, Peter J. Morgan, and N. W. Young. "Comparison of ERS satellite radar altimeter heights with GPS-derived heights on the Amery Ice Shelf, East Antarctica." Annals of Glaciology 27 (1998): 19–24. http://dx.doi.org/10.3189/1998aog27-1-19-24.
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In the spring of 1995 an extensive global positioning system (GPS) survey was carried out on the Amery Ice Shelf, East Antarctica, providing ground-truth ellipsoidal height measurements for the European remote-sensing satellite (ERS) radar altimeters. GPS- and altimeter-derived surface heights have been compared at the intersecting points of the ERS ground tracks and the GPS survey. The mean and rms height difference for all ERS-1 geodetic-phase tracks across the survey region is 0.0 + 0.1 m and 1.7 m, respectively. The spatial distribution of the height differences is highly correlated with surface topographic variations. Comparisons of GPS-derived surface-elevation profiles along ERS ground tracks show that the ERS altimeters can closely follow the GPS representation of the actual surface.
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Bruno Kyamulesire, Sylvester Okiemute Eteje, and Paul Dare Oluyori. "Establishment of local geometric geoid model for Busoga, Uganda." World Journal of Advanced Research and Reviews 8, no. 3 (2020): 139–48. http://dx.doi.org/10.30574/wjarr.2020.8.3.0468.
Full textAbstract:
The importance of the local geoid model for the computation of accurate geoid heights, as well as orthometric heights used for engineering constructions, necessitated its establishment in areas, regions or countries. Consequently, this study establishes the local geometric geoid model of Busoga, Uganda, using the geometric method. A total of 26 points were used in the study, 20 points for the development of the model and 6 test points. GNSS observations were acquired with Trimble GNSS dual-frequency receivers and processed with Bernese (V5.2) and Spectra Precision Survey Office (v4.1) software to obtain the coordinates and ellipsoidal heights of the points. Differences between the existing orthometric and ellipsoidal heights were computed to obtain the geoid heights. The Least squares adjustment technique was applied to determine the fit, as well as the Bicubic and Multiquadratic models’ parameters. The Root Mean Squares Error (RMSE) index was used to compute the accuracy of the models. The geoid models were compared with their RMSE, as well as accuracy to determine which of them is more suitable for application in the study area. The comparison result shows that the Multiquadratic geoid model is more suitable for implementation in the study area. A Microsoft Excel program was developed for the application of the model in the study area.
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Tata, H., and G. P. Dare. "Determination of Orthometric Heights for Enhancing Built-Up Expansion in an Urban Flood Plain on Parts of Lokoja, Kogi State, Nigeria." Journal of Spatial Information Sciences 2, no. 1 (2025): 127–43. https://doi.org/10.5281/zenodo.14811884.
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Elevation is crucial for determining the location of points on or beneath the Earth's surface, particularly in flood-prone areas. In Lokoja, many residents live in low-lying regions and river floodplains, attracted by natural resources and agricultural opportunities. However, this rapid urban growth often leads to flooding, which damages infrastructure, livelihoods, and public services. This study aimed to acquire coordinates, determine orthometric heights, and identify flood-prone areas to guide urban expansion. Researchers selected 234 points at 25-meter intervals and recorded Easting, Northing coordinates, and ellipsoidal heights using a South Galaxy Differential GPS, while with a benchmark of known orthometric height, orthometric heights were measured using a spirit levelling instrument. Various maps were generated using Surfer 13 and ArcGIS software, including contour, digital terrain, watershed, shaded relief, vector, and flood vulnerability maps. Findings indicated that areas with orthometric heights between 49m and 61m are especially vulnerable to flooding and unsuitable for development, posing significant risks to human safety. Development in these regions is deemed unsustainable and threatens the well-being of the local population.
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Grafarend, Erik W., and Johannes Engels. "A global representation of ellipsoidal heights — geoidal undulations or topographic heights — in terms of orthonormal functions." manuscripta geodaetica 17, no. 1 (1992): 59–64. http://dx.doi.org/10.1007/bf03655435.
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Grafarend, Erik W., and Johannes Engels. "A global representation of ellipsoidal heights - geoidal undulations or topographic heights - in terms of orthonormal functions." manuscripta geodaetica 17, no. 1 (1992): 52–58. http://dx.doi.org/10.1007/bf03655434.
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Pepe, M., and G. Prezioso. "A MATLAB GEODETIC SOFTWARE FOR PROCESSING AIRBORNE LIDAR BATHYMETRY DATA." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-5/W5 (April 9, 2015): 167–70. http://dx.doi.org/10.5194/isprsarchives-xl-5-w5-167-2015.
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The ability to build three-dimensional models through technologies based on satellite navigation systems GNSS and the continuous development of new sensors, as Airborne Laser Scanning Hydrography (ALH), data acquisition methods and 3D multi-resolution representations, have contributed significantly to the digital 3D documentation, mapping, preservation and representation of landscapes and heritage as well as to the growth of research in this fields. <br><br> However, GNSS systems led to the use of the ellipsoidal height; to transform this height in orthometric is necessary to know a geoid undulation model. The latest and most accurate global geoid undulation model, available worldwide, is EGM2008 which has been publicly released by the U.S. National Geospatial-Intelligence Agency (NGA) EGM Development Team. Therefore, given the availability and accuracy of this geoid model, we can use it in geomatics applications that require the conversion of heights. Using this model, to correct the elevation of a point does not coincide with any node must interpolate elevation information of adjacent nodes. <br><br> The purpose of this paper is produce a Matlab® geodetic software for processing airborne LIDAR bathymetry data. In particular we want to focus on the point clouds in ASPRS LAS format and convert the ellipsoidal height in orthometric. The algorithm, valid on the whole globe and operative for all UTM zones, allows the conversion of ellipsoidal heights using the EGM2008 model. Of this model we analyse the slopes which occur, in some critical areas, between the nodes of the undulations grid; we will focus our attention on the marine areas verifying the impact that the slopes have in the calculation of the orthometric height and, consequently, in the accuracy of the in the 3-D point clouds. This experiment will be carried out by analysing a LAS APRS file containing topographic and bathymetric data collected with LIDAR systems along the coasts of Oregon and Washington (USA).
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Ferrara, G., and C. Parente. "ADAPTATION OF THE GLOBAL GEOID MODEL EGM2008 ON CAMPANIA REGION (ITALY) BASED ON GEODETIC NETWORK POINTS." International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLVI-4/W4-2021 (October 7, 2021): 145–50. http://dx.doi.org/10.5194/isprs-archives-xlvi-4-w4-2021-145-2021.
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Abstract. The knowledge of the geoid undulation, the height of the geoid relative to a given ellipsoid of reference, is fundamental to transform the ellipsoidal heights into orthometric heights. Global geoid undulation models developed from satellite gravity measurements appropriately integrated with other data, are free accessible in internet, but their accuracy may be inadequate for specific applications. Earth Gravitational Model 2008 (EGM2008) is one of those: usually available in grid form 2.5’ × 2.5’ (a geotif is developed by Agisoft with resolution 1’ × 1’), it defines the difference between the WGS84 ellipsoid height and the mean sea level, but in some areas the discrepancies between these geoid undulations and local correspondent measured values are on the order of various decimetres. For consequence, more accurate models are necessary. This article aims to determine a geoid undulation model suitable for Campania Region (Italy), starting from the global model EGM2008 (1’ × 1’) that is locally adjusted by using geodetic network points (GNPs) and GIS interpolation functions. Three different datasets are considered including respectively 20, 40 and 60 GNPs and three deterministic interpolators are applied in global way to generate geoid undulation grids: Inverse Distance Weight (IDW), Global Polynomial 1st order (GP1), Global Polynomial 2nd order (GP2). The resultant 9 models are tested on 20 additional GNPs. The experiments demonstrate that local geoid can be produced on a little area adapting global geoid by means of GNPs: the model obtained using GP2 and 60 GNPs, the most accurate one, fits the data with ±3.2 cm root mean square error (RMSE).
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Breaban, Ana-Ioana, Valeria-Ersilia Oniga, Constantin Chirila, et al. "Proposed Methodology for Accuracy Improvement of LOD1 3D Building Models Created Based on Stereo Pléiades Satellite Imagery." Remote Sensing 14, no. 24 (2022): 6293. http://dx.doi.org/10.3390/rs14246293.
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Three-dimensional city models play an important role for a large number of applications in urban environments, and thus it is of high interest to create them automatically, accurately and in a cost-effective manner. This paper presents a new methodology for point cloud accuracy improvement to generate terrain topographic models and 3D building modeling with the Open Geospatial Consortium (OGC) CityGML standard, level of detail 1 (LOD1), using very high-resolution (VHR) satellite images. In that context, a number of steps are given attention (which are often (in the literature) not considered in detail), including the local geoid and the role of the digital terrain model (DTM) in the dense image matching process. The quality of the resulting models is analyzed thoroughly. For this objective, two stereo Pléiades 1 satellite images over Iasi city were acquired in September 2016, and 142 points were measured in situ by global navigation satellite system real-time kinematic positioning (GNSS-RTK) technology. First, the quasigeoid surface resulting from EGG2008 regional gravimetric model was corrected based on data from GNSS and leveling measurements using a four-parameter transformation, and the ellipsoidal heights of the 142 GNSS-RTK points were corrected based on the local quasigeoid surface. The DTM of the study area was created based on low-resolution airborne laser scanner (LR ALS) point clouds that have been filtered using the robust filter algorithm and a mask for buildings, and the ellipsoidal heights were also corrected with the local quasigeoid surface, resulting in a standard deviation of 37.3 cm for 50 levelling points and 28.1 cm for the 142 GNSS-RTK points. For the point cloud generation, two scenarios were considered: (1) no DTM and ground control points (GCPs) with uncorrected ellipsoidal heights resulting in an RMS difference (Z) for the 64 GCPs and 78 ChPs of 69.8 cm and (2) with LR ALS-DTM and GCPs with corrected ellipsoidal height values resulting in an RMS difference (Z) of 60.9 cm. The LOD1 models of 1550 buildings from the Iasi city center were created based on Pléiades-DSM point clouds (corrected and not corrected) and existing building sub-footprints, with four methods for the derivation of the building roof elevations, resulting in a standard deviation of 1.6 m against high-resolution (HR) ALS point cloud in the case of the best scenario. The proposed method for height extraction and reconstruction of the city structure performed the best compared with other studies on multiple satellite stereo imagery.
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Kotsakis, Christopher. "Transforming ellipsoidal heights and geoid undulations between different geodetic reference frames." Journal of Geodesy 82, no. 4-5 (2007): 249–60. http://dx.doi.org/10.1007/s00190-007-0174-9.
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Kotsakis, Christopher. "Transforming ellipsoidal heights and geoid undulations between different geodetic reference frames." Journal of Geodesy 82, no. 4-5 (2007): 261. http://dx.doi.org/10.1007/s00190-007-0179-4.
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Falchi, Ugo, Claudio Parente, and Giuseppina Prezioso. "GLOBAL GEOID ADJUSTMENT ON LOCAL AREA FOR GIS APPLICATIONS USING GNSS PERMANENT STATION COORDINATES." Geodesy and cartography 44, no. 3 (2018): 80–88. http://dx.doi.org/10.3846/gac.2018.4356.
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Orthometric heights, useful for many engineering and geoscience applications, can be obtained by GPS (Global Positioning System) surveys only when an accurate geoid undulation model (that supplies the vertical separation between the geoid and WGS84 ellipsoid) is available for the considered topic area. Global geoid height models (i.e., EGM2008), deriving from satellite gravity measurements suitably integrated with other data are free available on web, but their accuracy is often not sufficient for the user’s purposes. More accurate local models can nevertheless be acquired, but often only for a fee. GPS/levelling surveys are suitable for determining a local, accurate geoid model, but may be too expensive. This paper aims to demonstrate that GNSS (Global Navigation Satellite System) Permanent Station documents (monographs), freely available on the web and supplying orthometric and ellipsoidal heights, permit to calculate precise geoidal undulations useful to perform global geoid modelling on a local area. In fact, in this study 25 GNSS Permanent Stations (GNSS PS), located in North-Western Italy are considered: the differences between GNSS PS geoidal heights and the corresponding EGM2008 1′ × 1′ ones are used as a starting dataset for Ordinary Kriging applications. The resulting model is summed to the EGM2008 1′ × 1′, obtaining a better-performed model of the interest area. The accuracy tests demonstrate that the resulting model is better than EGM2008 grids to produce contours from a GPS dataset for large-scale mapping.
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Mosayebzadeh, M., R. Karimi, and A. A. Ardalan. "PERFORMANCE ANALYSIS OF GEOPOTENTIAL MODELS IN ESTIMATING THE GEOIDAL HEIGHT OVER IRAN." ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences X-4/W1-2022 (January 14, 2023): 545–50. http://dx.doi.org/10.5194/isprs-annals-x-4-w1-2022-545-2023.
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Abstract. Global geopotential models (GGMs) are widely used in earth sciences, especially in geodesy and geophysics. In this paper, we aim at studying GGMs' capability in the geoidal height estimation at the geographical region of Iran. This will include verification of both satellite-only and combined GGMs. To compute the geoidal height at a point, keeping the longitude and latitude constant, we change its ellipsoidal height until the GGM-derived gravity potential at the resulting height equals the geoid’s potential value. In this process, we consider the topographic bias effect once the computation of the potential is inside the topographic masses. As the benchmark for the performance analysis of GGMs, we use the known geoidal heights of 841GPS/Levelling stations with a country-wide distribution. The results indicate that the XGM2019e_2159 (n_max=2190) GGM is the best combined and the GO_CONS_GCF_2_DIR_R5 (n_max=330) GGM is the best satellite-only model for the computation of geoidal heights in the study area, Iran.
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Ameti, Perparim, and Reiner Jager. "ON THE DEFINITION OF HEIGHT REFERENCE SURFACES OVER AN ARBITRARY SELECTED AREA BY MEANS OF DFHRS APPROACH." Geodesy and cartography 42, no. 4 (2016): 115–21. http://dx.doi.org/10.3846/20296991.2016.1268431.
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The aim of this study is to analyze the best fitting geoid model for an arbitrary selected area of investigation. The Digital Finite Element Height Reference Surface (DFHRS) method, developed by Hochschule Karlsruhe has been chosen to define the height reference surface for the territory of Kosovo, which should be defined as national vertical datum. This approach allows the conversion of ellipsoidal heights determined by GPS into the standard heights, which refer to the height reference surface (HRS) of an orthometric, or normal surface system. The DFHRS is defined as continues HRS in arbitrary large areas by bivariate polynomials over an irregular grid (Jager, Schneid 2001). The DFHRS approach uses wide range of the input data (Geometric and Physical) and in our case there were 30 GPS/leveling height data as well as physical derivatives from different global geopotential models. The proposed approach has been successfully applied and results are compared to actual normal heights and in selected profiles of digital elevation reference surface calculated from the national control network. Special attention has been given to the choice of the geopotential model and the selection of the pass points in source and target surface.
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Kim, Su-Kyung, Jihye Park, Daniel Gillins, and Michael Dennis. "On determining orthometric heights from a corrector surface model based on leveling observations, GNSS, and a geoid model." Journal of Applied Geodesy 12, no. 4 (2018): 323–33. http://dx.doi.org/10.1515/jag-2018-0014.
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Abstract Leveling is a traditional geodetic surveying technique that has been used to realize a vertical datum. However, this technique is time consuming and prone to accumulate errors, where it relies on starting from one station with a known orthometric height. Establishing orthometric heights using Global Navigation Satellite Systems (GNSS) and a geoid model has been suggested [14], but this approach may involve less precisions than the direct measurements from leveling. In this study, an experimental study is presented to adjust the highly accurate leveling observations along with orthometric heights derived from GNSS observations and a geoid model. For the geoid model, the National Geodetic Survey’s gravimetric geoid model (TxGEOID16B) and hybrid geoid model (GEOID12B) were applied. Uncertainties in the leveled height differences, GNSS derived heights, and the geoid models were modeled, and a combined adjustment was implemented to construct the optimal combination of orthometric, ellipsoidal, and geoid height at each mark. As a result, the discrepancy from the published orthometric heights and the CSM (Corrector Surface Model) based adjusted orthometric heights with GEOID12B showed a mean and RMS of -8.5 mm and 16.6 mm, respectively, while TxGEOID16B had a mean and RMS of 28.9 mm and 34.6 mm, respectively. It should be emphasized that this approach was not influenced by the geodetic distribution of the stations where the correlation coefficients between the distance from the center of the surveying network and the discrepancy from the published heights using TxGEOID16B and GEOID12B are 0.03 and 0.36, respectively.
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Jackson, Kurotamuno P., and Elochukwu C. Moka. "Modelling Orthometric Heights from a Combination of Ellipsoidal Heights and Gravimetric Geoid Model in Rivers State, Nigeria." International Journal of Geosciences 11, no. 04 (2020): 184–96. http://dx.doi.org/10.4236/ijg.2020.114011.
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Manisa, Michael, Rabindra Kumar Das, Mooketsi Segobye, and Lopang Maphale. "Developing local geoid model to assess accuracy of orthometric heights from GPS-based ellipsoidal heights in Botswana." Spatial Information Research 24, no. 5 (2016): 607–16. http://dx.doi.org/10.1007/s41324-016-0057-3.
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Moussa, Hiba, and Mohammad Abboud. "Methodology of Applying Inverse Distance Weighting Interpolation Method in Determining Normal Heights." Resourceedings 4, no. 1 (2024): 01–06. http://dx.doi.org/10.21625/resourceedings.v4i1.1068.
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This article explores the application of the Inverse Distance Weighting (IDW) interpolation method in determining normal heights, utilizing a network of points with measured ellipsoidal and normal heights by the use of GNSS/levelling method. The IDW method, which assumes that points closer to each other are more alike, is employed to locate points within the correct quadrant and calculate their normal height based on the determined average height anomaly across the entire area. The accuracy of this method is validated using check points. The article further discusses the methodology of normal height determination at a country level by using generated coefficients, representing the average difference between various height-systems, which could be used as an integral to the interpolation methods used for generating a refined Digital Elevation Model (DEM) across the country. This study contributes to the ongoing discourse on the effective use of interpolation methods in geospatial analysis and DEM generation. It provides valuable insights into the practical application of the IDW method and its potential for enhancing the accuracy of normal height determination and DEM refinement. Importantly, such methods hold significant value for countries lacking gravimetric data, as they provide a viable means of determining normal heights in the absence of a local quasi geoid model.