School
of Surveying and Spatial Information Systems University of New South Wales
CRITICAL ANALYSIS OF GPS
HEIGHTING
By Stuart
Bracken Supervised
by Chris Rizos October 2006 Abstract Geoid/ Ellipsoid Relationship Results Geoid Comparison Conclusion 


Abstract The Global Positioning System (GPS) is an effective tool for establishing high precision geodetic control networks. While GPS has the ability to provide accurate horizontal coordinates, vertical control is generally 23 times less accurate. The aim of this thesis is to study the accuracy of converting GPSderived ellipsoidal heights to orthometric height, i.e. those suitable for practical use in surveying applications. A comparison will be made between published height values in the Australian Height Datum (AHD) and height values derived from a GPS survey between Bathurst and Cowra, using both Ausgeoid 93 and Ausgeoid 98. Geoid/ Ellipsoid Relationship The height derived from GPS observations does not relate to a physical surface such as MSL, but to a mathematical (ellipsoidal) surface. The ñreference ellipsoidî used in Australia for GPSderived heights is the World Geodetic System 1984 (WGS 84) ellipsoid, which for practical purposes is coincident with the Geodetic Reference System of 1980 (GRS80). It is the relationship between the ellipsoid and the geoid that allows the derivation of GPS heights that approximate AHD71 (Featherstone et.al, 1998). In 1991 the Australian Surveying and Land Information Group (AUSLIG) (now Geoscience Australia) released a gravimetric geoid model that referred to the WGS 84 ellipsoid. This geoid model is known as Ausgeoid 91. Subsequent geoid models, Ausgeoid 93 and Ausgeoid 98, have been introduced using more recent global geopotential models; different computational procedures, updated gravimetric data, and the recently derived Digital Elevation Model for Australia. An accurate geoid model is vital if GPS is to be used to generate heights that are physically meaningful (Featherstone et.al, 2001). h = H  N (1) Where H = height above the ellipsoid h = height above the geoid N = geoid minus ellipsoid separation (N value) The Australian Height Datum AHD71 was developed for mapping purposes, and is considered a 3^{rd} order height datum. It is a network of relatively low order optical levelling benchmarks covering 97230 km across Australia. (Roelse et.al, 1975). There are known systematic errors in the Australian Height Datum due to, for example, the omission of orthometric corrections based on observed gravity data, the systematic errors involved in the levelling observations themselves, and the fixing of the 30 tide gauges situated around the coast of Australia to ñzero orthometric heightî. GPS Survey The NSW Department of Lands (DoL) in Bathurst supplied the equipment used in this thesis project. DoL is responsible for the maintenance of the geodetic infrastructure, such as high quality survey marks, throughout the state of New South Wales. The GPS receivers they used to perform these tasks were dualfrequency Trimble receivers, along with Zephyr geodetic antennas The GPS survey was carried out using dualfrequency receivers operated in the fast static mode. This technique is well suited to such a survey as the baselines are relatively short (<7km). http://www.trimble.com/trimbler7_spec.shtml Results The graph below is an indication, although on a relatively small scale, of the improvement in Ausgeoid 98. The average allowable misclose based on 12Ìk is 0.024m. The average allowable misclose in a relative sense using Ausgeoid 98 is 0.020m, which falls within the specifications. Using Ausgeoid 93 data however the average misclose is 0.027m, which is just outside the third order levelling specifications. The large errors in opposite directions between benchmarks have a compensating effect along the level route and would therefore give a misleading conclusion as to the overall accuracy of either geoid. A clearer understanding of the differences between the geoid models can be gained by looking at the RMS values for the relative miscloses, which are tabulated below



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Geoid Comparison 


The geoid height minus ellipsoid height, or N
value, was computed using both the ï93 and ï98 geoid models and the resulting
values compared with a derived N value. As expected the heights derived using
Ausgeoid 98 were generally more favorable in their comparison with the
published data. Figure 10 illustrates the differences in N values for both
Ausgeoid 93 and Ausgeoid 98. Conclusion The use of GPS to derive height is extremely efficient however in evaluating its accuracy, even at third order specifications; it is obvious further discussion is required. Although the results obtained in this project suggest we could not rely entirely on GPS for determining height in the AHD71 it is certainly by no means unachievable. Any compatibility between GPS derived heights and the AHD71 are negated by the inconsistencies between the geoid and the AHD. Therefore any improvement in accuracy is dependant upon a recomputation or redefinition of one or both of these vertical reference surfaces. References:Featherstone, W.E, Johnston, G.M. 1998. Ausgeoid 98: A New Gravimetric Geoid for Australia. 24^{th} National Surveying Conference of the Institution of Engineering and Mining Surveyors, 27^{th} September Ü 3^{rd} October 1998, Australia. AUSLIG. Featherstone, W.E, Kirby, J.E, Kearsley, A.H.W., Gilliland, J.R., Johnston, G.M., Steed, J., Forsberg, R., Sideris, M.G. 2001. The Ausgeoid98 geoid model of Australia: data treatment, computations and comparisons with GPSlevelling data. Journal of Geodesy, 75, 313330. Roelse, A., Granger, H.W., Graham, J.W., 1975 The adjustment of The Australian Levelling Survey 19701971. Technical Report 12, 2^{nd} ed. Division of National Mapping. Further InformationFor more
information, please contact: Chris Rizos
(Supervisor) Email: c.rizos@unsw.edu.au Mail: School of
Surveying and Spatial Information Systems University of
New South Wales UNSW SYDNEY NSW
2052 Australia Phone:
+61293854202 Fax:
+61293137493 WWW: http://www.gmat.unsw.edu.au/ 