School of Surveying and Spatial Information Systems


University of New South Wales




By Stuart Bracken


Supervised by Chris Rizos October 2006








Abstract    Geoid/ Ellipsoid Relationship    Results    Geoid Comparison    Conclusion













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 2-3 times less accurate. The aim of this thesis is to study the accuracy of converting GPS-derived 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 ˝reference ellipsoidţ used in Australia for GPS-derived 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, 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, 2001).

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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 3rd order height datum. It is a network of relatively low order optical levelling benchmarks covering 97230 km across Australia. (Roelse, 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 ˝zero orthometric heightţ.

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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 dual-frequency Trimble receivers, along with Zephyr geodetic antennas The GPS survey was carried out using dual-frequency receivers operated in the fast static mode. This technique is well suited to such a survey as the baselines are relatively short (<7km).

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The graph below is an indication, although on a relatively small scale, of the improvement in Ausgeoid 98. The average allowable misclose based on 12╠k 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



Min (m)

Max (m)

RMS (m)

Ausgeoid 98




Ausgeoid 93





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Geoid Comparison





The geoid height minus ellipsoid height, or N value, was computed using both the ´93 and ´98 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.

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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.

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Featherstone, W.E, Johnston, G.M. 1998. Ausgeoid 98: A New Gravimetric Geoid for Australia. 24th National Surveying Conference of the Institution of Engineering and Mining Surveyors, 27th September ▄ 3rd 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 GPS-levelling data. Journal of Geodesy, 75, 313-330.

Roelse, A., Granger, H.W., Graham, J.W., 1975 The adjustment of The Australian Levelling Survey 1970-1971. Technical Report 12, 2nd ed. Division of National Mapping.

Further Information

For more information, please contact:

Chris Rizos (Supervisor)



School of Surveying and Spatial Information Systems

University of New South Wales



 Phone: +61-2-9385-4202

Fax: +61-2-9313-7493


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