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For a project of Bridge monitoring using GPS, (X,Y) GPS measurements have taken and they must be transformed into a local system (x,y) to determine the deformation as shown in the sample picture:

enter image description here

For that, many steps of calculations using some formulas in Matlab are done and summarized as follows:

  • Determination of the parameters of the transformation.
  • Transformation calculations of (X,Y) from GPS into a local system (x,y).

After getting the new coordinates (x,y), we performed new calculations to get (x,y) again but with considering the translation vector (provided by Land Authority).

The results we get for both cases are as follows:

Case 1: without translation vector:

Scale factor = (99.8 PPM), Rotation angle = (6.2 ARCSEC)
x(m) = .......,340   , y(m) = .....,992

Case 1: with translation vector:

 Scale factor = (3.2 PPM), Rotation angle = (6.18 ARCSEC)
 x(m) = .......,343   , y(m) = .....,993

From the results, we can see that both coordinates are very similar (differences in mm), but the scale factor is highly affected.

My Question: Does the translation vector does not has any effect on the coordinates in this type of transformation? Just effect the transformation parameters?

Or it has an effect on the coordinates in other types of transformation?

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