Geometric Geoid Determination in South Korea using GPS/Levelling Data
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This paper describes the determination of geoid using height data measured by GPS and Spirit Levelling. The GPS data of the 88 stations were used to determine the geoid undulation (N) which can be easily obtained by subtracting the orthometric height(H) from the ellipsoidal height(h). From the geoid undulation (N) calculated at each station mentioned above, geoid plots with a contour interval of 0.25 m were drawn using two interpolation methods. The following interpolation methods were applied and compared with each other: Minimum Curvature Method and Least Squares Fitted Plane. Comparison between geometric geoid and gravimetric geoid undulation by FFT technique was carried out.Keywords:
Levelling
Interpolation
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In order to get the determination of quasi-geoid at the boundary of land and sea,Quasi-geoid heights derived from these geo-potential models EGM96,WDM94 and GFZ were compared with the help of the 43 GPS/leveling observations and 1 045 observed gravity anomalies respectively.The results showed EGM96 was a preferred geo-potential model for determining the high precision geoid of this area by using remove-restore approach.Since there was no GPS/leveling data on the sea,the approach of distance weighted average was better at interpolating gravimetric geoid with GPS/leveling by comparing with the polynomials.The accuracy of quasi-geoid is higher by 3cm in this area.
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This paper introduces the signif9cance of geoid refining and three methods for refining geoid, and by using the abnormal height of GPS/leveling point, sets up several mathematic models of local geoid and makes the experiments and precision analysis.
Refining (metallurgy)
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A new geoid model for Iran (IRG04) was computed based on the least squares modification of the Stokes formula. IRG04 was derived from the most recent gravity anomaly database, SRTM high resolution Digital Elevation Model (DEM) and GRACE GGM02 global geopotential model. In order to define a new height datum for Iran, we attempted to combine this high resolution gravimetric geoid model with GPS/levelling data using the corrective surface approach. The corrective surface was constructed from 224 GPS/levelling points and then evaluated with 35 independent points. Different interpolation techniques were tested for the creation of the corrective surface; among them the Kriging method was selected as it gave the smallest RMS and 'noise level' at the comparisons with GPS/levelling data. The RMS fit of the new combined geoid model versus the independent GPS/levelling data is 0.09 m, it is near four times better compared to the original gravimetric geoid model. The combined model should be more convenient and useful in definition of the new height reference surface, specifically in engineering and GPS/levelling projects.
Levelling
Interpolation
Geopotential
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Collocation (remote sensing)
Interpolation
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V okviru projekta Vzpostavljanje evropskega prostorskega referenčnega sistema v Sloveniji je bila izračunana tudi ploskev testnega geoida.V prispevku bo predstavljena primerjava določitve geoidnih višin iz geoida 2000 in testnega geoida iz leta 2010
Realization (probability)
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Geoid determination is one of the main current geodetic problems in Kenya. This is because a geoid model is required to convert ellipsoidal heights to orthometric heights that are used in practice. A local geometric geoid covering Nairobi County and its environs has been determined by a geometric approach. Nineteen points levelled by both Global Positioning System (GPS) and precise levelling techniques in the area of study have been used. Seven triangulation points have been used for the determination of transformation parameters between World Geodetic System 1984 (WGS84) and Arc‐Datum 1960 coordinates in order to express the local geoid height as a function of position. The geoid height is expressed as a function of the local plane coordinates through a biquadratic surface polynomial, using 14 GPS/levelling points. Five points have been used for testing the results. The experience with Nairobi County and its environs geometric geoid indicates that interpolation of geoid heights in a small area by a biquadratic polynomial is simple and it works well. The geoid heights obtained by biquadratic polynomial (interpolation) compare favourably on the test points with root mean square and standard deviation of 1cm in the area of study. This accuracy is sufficient for most engineering projects.
Levelling
Interpolation
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Levelling
Interpolation
Geopotential
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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.
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GPS is used more and more for height determination. Resulting ellipsoidal heights don't give information about how the water flows. Therefore traditional height systems are used. In the Netherlands this is the NAP. To perform a transformation between both height system a geoid model is needed. This theses looks at the following issues, regarding the determination of this geoid model: - Comparison between EGM96 and EIGEN-CG03C for the Dutch geoid - Computation of a height reference surface out of GPS/levelling data only - The use of variance component estimation for computation of a height reference surface out of NAP, GPS and geoid heights
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Nap
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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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