Levellingusing the Global Positioning System

ReportNo WSAA 47


November 1992




TheGlobal Positioning System (GPS) is a constellation of high-orbit satellitesestablished by the United States Department of Defence for military purposes.However, civilian use of the system is currently unrestricted, providingsurveyors and geodesists with a means of directly measuring the relative threedimensional position vector between points to a high degree of accuracy andwithout the limitation of having inter-visibility between those points. Thepotential applications of GPS technology are therefore many and one of theobvious and frequent questions that is asked is: Can GPS surveying techniquesbe used to replace traditional spirit levelling ? The research projectdescribed in this report was carried out to address and provide an answer tothis question.


It isapparent that the use of GPS for establishing height information is not asstraightforward as it may at first appear. The reason for this complication isdue to that fact that a space vector measured by GPS techniques is independentof the gravity field. In other terms, the height component of a GPS vector ispurely geometric and is referenced to a mathematical figure of the earth in theform of a mean-earth ellipsoid. Accordingly, these height differences(otherwise known as GPS heights) do not describe the direction of flow underthe influence gravity, making them of limited use in surveying and engineeringapplications. Height differences measured by conventional levelling techniqueson the other hand, are related to the earth’s gravity field and do allow thedirection of flow to be determined. Such height differences are calledorthometric heights and are referenced to an equipotential of the earth’sgravity field known as the geoid or more commonly as Mean Sea Level.


Itfollows that to use GPS technology to provide useful (orthometric) heightinformation, the height differences derived from GPS observations must betransformed from the ellipsoidal to the geoidal reference surface. It is alsoapparent that this transformation must be carried out to a high degree ofaccuracy to avoid compromising the inherent accuracy of the GPS data.Essentially then, the problem of using GPS for levelling reduces to one ofdetermining the shape of the geoid with respect to the ellipsoidal referenceframe used in GPS positioning.


Thisproject investigated a number of geoid modelling techniques with a view toestablishing a convenient and accurate method of deriving orthometric heightinformation from GPS. For this purpose, a pilot project was undertaken in theeastern suburbs of Melbourne, the results of which reveal that the moresophisticated geoid modelling techniques allow orthometric heights to bededuced from GPS observations with accuracies comparable to third-orderlevelling standards.


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