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Progress Towards A Centimeter Level Orthometric Heights Using a Single GPS Receiver
Y. Al Marzooqi, H. Fashir & Syed Iliyas Ahmed
Dubai, United Arab Emirates
R. Forsberg & G. Strykowski
National Survey and Cadastral Denmark
SUMMARY
A high-resolution and high-precision detailed gravimetric geoid has been computed for Dubai Emirate, ranging from 240 35'N to 250 21'N in latitude and 540 52'E to 560 13' E in longitude. The EGM96 geopotential model complete to degree and order 360 was combined with surface gravity data and Fast Fourier Transformation (FFT) algorithm to generate the geoid file. The surface data consists of 1km x 1 km gravity data and 20m X 20m Digital Terrain Elevation Model as well as GPS and leveling data. The method of least square collocation has also been used for an alternative preliminary geoid computation. The computed geoid has an estimated error of 2cm rms.
Comparison of the gravimetric geoid with the GPS/ leveling derived geoidal heights of 3750 stations all over Dubai Emirate shows that the absolute agreement with respect to the GPS/ leveling datum is generally better than 3-4 cm rms. Results show that combining both GPS heights and the Dubai geoid model can give orthometric heights accurate to 2-5 cm. The method can thus work as a good alternative to traditional levelling, particularly for third order levelling in large areas.
1. Introduction
The positions of points derived from Global Positioning System (GPS) measurements are usually computed in a terrestrial three-dimensional Cartesian frame. The resulting X, Y and Z co-ordinates of the GPS points are then transformed, using a reference ellipsoid, into geodetic co-ordinates in terms of latitude( ), longitude ( ), and ellipsoidal height (h). The GPS recovers the latitude and longitude differences to about 1 ppm and ellipsoidal height differences to about 1-2 ppm Ayhan (1993). Ellipsoidal heights (h) are heights measured from a defined reference ellipsoid. However, orthometric heights which are useful in most Surveying and Engineering applications are measured from the geoid. The difference between the two heights depends on the separation between the geoid and the reference ellipsoid, that is geoidal height (N). If the geoid undulation (N) of station is known, and the ellipsoidal height (h) is determined from GPS observations, then the absolute orthometric height (H) of the station can be determined directly from: . Also in a relative mode, the orthometric height differences between two stations can be obtained without levelling by combining the computed and determined by GPS interferometry from: .
The determination of the geoid has been one of the prime objectives of geodesy. The knowledge of the geoid with respect to some reference ellipsoid, either on a global or local scale is valuable to geodesy, surveying and geophysics for a number of purposes such as the reduction of measured distances to a reference surface and the processing of satellite observations. The geoid represents the datum to which height differences and the gravity potentials are referred. The geoid heights are essential for verification of global datums and transformation of local datums to the world datum. Also the combination of an accurate geoid model with GPS co-ordinates plays a dominant role in achieving high accuracy levelling results. Spirit levelling is tedious, time consuming and costly in conventional surveying exercise. The knowledge of the geoid is also essential in geophysical explorations (reconnaissance survey), in control surveys, in large scale mapping, in engineering surveys, in height control and in understanding of the Earth's crustal structure.
The geoid solution was base on EGM96 model coefficient set complete to degree and order 360, 1 km x 1 km point gravity anomalies and 20m x 20m mean height blocks. Our intention is to generate a more accurate geoid file for Dubai Emirate by combining the above data set with EGM96 model coefficients set, to satisfy current geodetic requirements in the Emirate.
The lack of gravity measurement over much of the earth surface is still the major problem in gravimetric geodesy. Various methods do exist to compute geoid undulations from surface gravity data, namely, Stokes's integration, Fast-Fourier Transform (FFT) and Least Squares Collocation (LSC). The combination of spherical harmonics potential coefficient set with terrestrial gravity data in order to reduce the latter requirement to a localised region for geoid height computation has been carried out by many researchers (e.g Molodenskii et al, 1960;Paul, 1973;Rapp, 1981; Jekeli, 1981; Sjoberg, 1985;Vanicek et al, 1986). In this investigation, the combination of spherical harmonics potential coefficient set with terrestrial gravity data is used to compute the geoid. The modified spheroidal Stokes's kernel is used in the geoid computation instead of the conventional ellipsoidal Stokes's kernel. It is found that spheroidal function tapers off more rapidly than the ellipsoidal function for increasing spherical distances. Thus we can expect that a truncation of the spheroidal (modified) integration at a certain spherical distance lead to smaller truncation errors compared to the truncation of the ellipsoidal (original) Stokes's integration.
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