Sect_11.2.1

11.2.1 GPS Network Transformations

INTRODUCTION

Geodetic datums permit station coordinates to be related within a rigorous framework. The coordinate sets may be stated as either Cartesian components ( X,Y,Z ), or ellipsoidal values (,,h ), and can be converted from one coordinate system to the other using closed formulae such as those given in section 11.1.6. In either case there is an implied origin, as well as three graduated axes.

An adjusted survey network on a specific datum will result in a unique coordinate set for all stations in the network. A readjustment of the same network, but with different constraints or an updated data set, will result in another coordinate set. Nevertheless the datum remains unchanged. The AGD66 and AGD84 coordinate sets are examples of this, both are realisations of the Australian Geodetic Datum. However, the differences in the two coordinate sets can be accommodated within a transformation model.

In the case of GPS results, the datum is nominally that of WGS84. There is therefore often the need to transform the GPS results into another datum, such as that implied by the local terrestrial control coordinate set. Hence, there are two important roles for transformation models in the context of GPS surveying:

To relate two datums, for example the GPS satellite datum to a local geodetic datum.
To relate two coordinate sets, either two GPS networks or two local geodetic networks, both nominally on the same datum.

To maintain generality in the following discussions it will be assumed that the transformation models are used to relate reference systems, and only where it is important will the distinction be made between transforming datums and transforming coordinate sets.

There are a number of questions relating to this transformation process:

What is the exact functional model that relates one reference system to another?

Are the parameters of the model available?

Must the precision of the transformation parameters be taken into account?

If transformation parameters had to be determined, what software is available and what operational procedures should be followed?

Are the transformation parameters so determined "universal", that is, are they applicable to other networks?

Can the transformation process alter the relative disposition of points in the network, hence in effect being indistinguishable from another network "adjustment"?

Useful references for further reading on the topic of transformation models are HARVEY (1986) and HARVEY (1994), with valuable hints on procedures for the reliable estimation of transformation parameters. STEED (1990) is a good reference for transformation procedures appropriate for Australian surveys.

In section11.1.4, the transformation model based on the similarity transformation was described, realisable in the two forms: the Bursa-Wolf model, and the Molodensky-Badekas model. Where the transformation parameters are available, these can be applied to transform a set of Cartesian coordinates in one datum to those of another datum (using eqn (11.1-1) or eqn (11.1-2)).

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