Sect_11.2.2

11.2.2 GPS Network Transformations

DETERMINING TRANSFORMATION PARAMETERS

The determination of transformation parameters is the product of a Least Squares adjustment in which the coordinates of points in both networks are considered "observations". There are a number of considerations, some unique to the problem of determining transformation parameters, others shared by all Least Squares adjustments, which should be mentioned:

As the observations are the coordinates of the common points, they will be adjusted as a by-product of the estimation process. Hence the process of determining transformation parameters is a form of constrained network adjustment. The amount of constraint is controlled by the apriori VCV information. For example, if a point is to be held fixed, its coordinates can be given a very small variance, say (0.1mm)2, and set all the covariances involving this station equal to zero.
If Bayesian Least Squares (section 7.1.2 and HARVEY, 1994) is applied, the transformation parameters are treated as quasi-observables, and the apriori VCV can be assigned. Some parameters may therefore be held fixed or estimated as free parameters.
In any Least Squares adjustment the correct stochastic model (VCV matrix) must be available. As always there is a problem of discerning between precision and accuracy. (Further comments on this are made below.)
There are a number of analysis issues that need to be highlighted, such as the impact of network geometry, the effect of distortions in the networks, checking the results, and the application of statistical tests to verify the quality of the adjustment.

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