Levelling using the Global Positioning System

This report was produced for the Urban Water Research Association of Australia, a now discontinued research program.

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Report no. UWRAA 47

November 1992

Synopsis

The Global Positioning System (GPS) is a constellation of high-orbit satellites established by the United States Department of Defence for military purposes. However, civilian use of the system is currently unrestricted, providing surveyors and geodesists with a means of directly measuring the relative three dimensional position vector between points to a high degree of accuracy and without the limitation of having inter-visibility between those points. The potential applications of GPS technology are therefore many and one of the obvious and frequent questions that is asked is: Can GPS surveying techniques be used to replace traditional spirit levelling ? The research project described in this report was carried out to address and provide an answer to this question.

It is apparent that the use of GPS for establishing height information is not as straight forward as it may at first appear. The reason for this complication is due to that fact that a space vector measured by GPS techniques is independent of the gravity field. In other terms, the height component of a GPS vector is purely geometric and is referenced to a mathematical figure of the earth in the form of a mean-earth ellipsoid. Accordingly, these height differences(otherwise known as GPS heights) do not describe the direction of flow under the influence gravity, making them of limited use in surveying and engineering applications. Height differences measured by conventional levelling techniques on the other hand, are related to the earth’s gravity field and do allow the direction of flow to be determined. Such height differences are called orthometric heights and are referenced to an equipotential of the earth’s gravity field known as the geoid or more commonly as Mean Sea Level.

It follows that to use GPS technology to provide useful (orthometric) height information, the height differences derived from GPS observations must be transformed from the ellipsoidal to the geoidal reference surface. It is also apparent that this transformation must be carried out to a high degree of accuracy to avoid compromising the inherent accuracy of the GPS data. Essentially then, the problem of using GPS for levelling reduces to one of determining the shape of the geoid with respect to the ellipsoidal reference frame used in GPS positioning.

This project investigated a number of geoid modelling techniques with a view to establishing a convenient and accurate method of deriving orthometric height information from GPS. For this purpose, a pilot project was undertaken in the eastern suburbs of Melbourne, the results of which reveal that the more sophisticated geoid modelling techniques allow orthometric heights to be deduced from GPS observations with accuracies comparable to third-order levelling standards.

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