`What does this procedure accomplish?It is a Method to reduce a seven parameter geospacial  transformation to an approximate three parameter transformation.`
by Eino Uikkanen

# Sample GeoConv application "723"

In most handheld GPS-devices the datums are defined by ellipsoidal parameters DF, DA and three parameters DX, DY, DZ, which are the parameters of the so called three parameter similarity transformation. Three parameter similarity transformation defines only shifts along X-, Y- and Z-axes (=3 parameters) and is therefore less accurate than corresponding seven parameter similarity transformation, which defines shifts along X-, Y- and Z-axes (=3 parameters), rotation around X-, Y- and Z-axes (=3 parameters) and possible correction of scale (1 parameter). We could hence say, that seven parameter similarity transformation is "full similarity transformation" and three parameter similarity transformation is "poor mans similarity transformation".

When e.g. national land survey organizations calculate parameters for similarity transformation, they always calculate parameters for a seven parameter similarity transformation and very seldom for a three parameter similarity transformation.

This all leaves the ordinary GPS user with difficult problems  if there aren't any known parameters for the three parameter similarity transformation and

• Datum is not predefined in GPS or
• Datum is predefined in GPS, but the parameter values are based on old measurements or aren't accurate enough in the area where the user wants to use them.

However, with a couple of applications based on the program GeoConv, the parameters for a three parameter similarity transformation can be calculated.

The first application is based on representative set of points, from which measured coordinates are known in both coordinate systems. Unfortunately such set of points with coordinate values in both systems are rarely available. Therefore this application is not described. If you do in fact have such information available and want to make the calculations, please contact the author in address eino.uikkanen@iki.fi.

The second solution was built on the idea, that in most cases where the parameters of the three parameter similarity transformation are missing, some good parameters for a seven parameter similarity transformation are known. The basic idea is to reduce the seven parameters to three parameters. That means, that the only input needed is the parameters for a seven parameter similarity transformation. In addition to that, the user has to define a set of (ficticious) points, which very well represent the area in which the best accuracy is defined. This could be even one point in the middle of the area, e.g. in the middle of the country, city, state or region.

The method roughly described is:

• Calculate converted coordinates for a given set of points using a known seven parameter similarity transformation.
• Calculate 3D-cartesian coordinates (X,Y,Z) for both original and converted coordinates.
• Calculate average differences between the cartesian coordinates = average (converted X,Y,Z) (original X,Y,Z).
• The result, parameters for the three parameter similarity transformation, are the opposite numbers to calculated averages.

The entire documented application (batch-run), is in text-file 723.bat.txt.
If you want to use this application:

• Copy it with another name having *.bat  extension such as  <723.bat>
• Study the run and modify it to agree with your needs and computer environment
• Make the needed preparations described in the run
• And run it .. Good Luck!