Sect_11.3.10

11.3.10 GPS Heighting

GPS LEVELLING

GPS levelling has the following characteristics:

Involves relative geoid heights.
Is independent of any reference system, as it involves determining the separation of two physical surfaces: the topographic surface and the geoid. Requires geoid heights on a reference ellipsoid to which the GPS heights are also referred (either a local ellipsoid if GPS heighting process applied after GPS transformation to local datum, or a global ellipsoid if GPS results are not first transformed).
GPS levelling can be considered a by-product of the GPS survey process. GPS heighting may therefore be a more economical heighting technique than standard levelling procedures.
The resulting relative orthometric height accuracy is dependent on the accuracy of both the (relative) GPS-derived ellipsoid heights and the (relative) geoid heights. The accuracy can be expressed in terms of the length of the baseline, that is, in "parts per million".
Relative (ellipsoidal) heighting by GPS survey is generally a factor of 2-3 times less precise than the horizontal components. Residual atmospheric biases are the source of the greatest uncertainty.
GPS levelling involves additional calculations for geoid height determination, of which only the geometric method is relatively simple.
Software can be purchased for computing geoid heights from geopotential models. Different models can then be used.
Geoid heights from gravimetry, in Australia, can be obtained from the Australian Survey and Land Information Group (AUSLIG) through their web site (this is referred to as AUSGEOID98). In Canada, the geoid data is precomputed on a grid, and a program is available for purchase to interpolate to any point.

GPS Levelling Accuracy

GPS levelling is more economical than standard levelling techniques, but the accuracy is generally lower. The allowable misclose for spirit levelling is:

1st order: 4 (mm) or 4cm in 100km 2-way levelling (0.4ppm), or 1.2cm in 10km (1.2ppm).
2nd order: 8 (mm) or 8cm in 100km (0.8ppm), or 2.5cm in 10km (2.5ppm).
3rd order: 12 (mm) or 12cm in 100km (1.2ppm), or 3.8cm in 10km (3.8ppm).

Note that the accuracy of spirit levelling is a function of the of the distance, and not just of the distance itself (as in the case of GPS accuracy). This is illustrated in the Figure below.

Comparison of accuracies of ellipsoidal height differences from GPS and from spirit levelling.
(a) GPS heighting (2ppm), (b) 3rd order levelling, (c) 2nd order levelling, (d) 1st order levelling.
(MITCHELL, 1990)

The following comments can be made concerning GPS levelling accuracy:

GPS accuracies appear to be of the order of 2-10ppm. At best, GPS levelling can provide 3rd order levelling standard for short distances (<20-30km), even if the geoid height computation is error-free.
Geopotential models can provide relative geoid height data to an accuracy of the order of 3-10ppm.
Geoid heights determined from gravimetry, in Australia, are considered to be accurate at the 2-6ppm level.
The accuracy of geoid heights derived from simple interpolation techniques varies considerably, from several ppm to 10 or more ppm.
GPS orthometric heights obtained from gravimetrically-derived geoid heights can be used to independently check (for blunders in) spirit levelled data. This is particularly feasible in Australia where the AHD is only of third order (MITCHELL, 1990).

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