[OSRS-PROJ] datum shift Gauss Krueger

Frans de Roos (EPL) Frans.de.Roos at epl.ericsson.se
Thu Jun 13 01:24:30 EDT 2002

Hello All

I got the same problem as Harald Wehr when tranforming from wgs84 to Gauss-Krueger (zone 4) . My transformation will also be about 55 meters wrong.

I use cs2cs as follow
cs2cs +proj=latlong +datum=WGS84 +to +proj=tmerc +ellps=bessel
+lat_0=0 +lon_0=12 +x_0=4500000 +towgs84=583,68,399

What I know from some other program I should use 

Gauss Krueger 4, Bessel, Potsdam_IST_V2_0 
583.00     - Translation dx in meter to WGS84
68.0       - Translation dy in meter to WGS84
399.50     - Translation dz in meter to WGS84
0          - Rotation ro (omega) in Radiant to WGS84
0          - Rotation rf (phi) in radiant to WGS84
13.6e-06   - Rotation rk (Kappa) in Radiant to WGS84
11.3e-06   - Mapscale factor in ppm (parts per million) to WGS84

And tranformation should calculate

ID  lon (WGS84)  lat (WGS84)    X (GK4)      Y (GK4)
1   11.60608768  48.25167084    4470860.075  5346044.934
2   10.96510029  50.25949478    4426313.445  5569780.810
3   7.46         51.57          4185407.951  5724830.919

When I use cs2cs I get the X-value to be about 55 meters wrong! The Y-value will just differ 0 - 3 meter.
I think that I should in some way add the rotation kappa in the calculation! Does anyone know how how I should do this?

If I change the dy value from 68 to 18 I got some better values. Now the X and Y values will differ about 8 meters but I don't think I should do this.


		Dear Frank,

		The Europeans like to do their rotations in an opposite direction from the
		rest of the world when doing 7-parameter Datum Shifts.  Translation and
		Scale Factors remain the same.  e.g., you will get weird and unexplainable
		results if you rotate in the wrong direction.

		A Helmert transform done with geocentric coordinates in three dimensions is
		called a Helmert Direct from Geodetic to Geocentric, and is called a
		Helmert Inverse from Geocentric to Geodetic.

		Molodensky-Badekas does a 3-d Helmert direct to geocentric coordinates,
		subtracts the geocentric coordinates of the classical Datum origin, then
		does the 7-parameter, then finally does the Helmert inverse back to the new
		Datum's geodetic coordinates.

		Bursa-Wolf does a 3-d Helmert direct to geocentric coordinates, does NOT
		subtract the geocentric coordinates of the classical Datum origin, then
		does the 3-parameter, or 4-parameter, or 7-parameter, then finally does the
		Helmert inverse back to the new Datum's geodetic coordinates.

		How do you tell which direction to rotate?  It is impossible unless you
		have a test point.  Since Harald does have a test point ...

		So now you know.


		Prof. Clifford J. Mugnier (cjmce at LSU.edu)
		Chief of Geodesy
		Department of Civil Engineering
		Baton Rouge, LA  70803
		Voice and Facsimile:  (225) 578-8536
		Pager:              1-(888) 365-5180

		Harald Wehr wrote:
		> Hi Frank,
		> first i apologize, that i contact you directly.
		> In the PROJ.4-mailing-list no one answered to my problem. Attached you
		> find my mail from february 26th that I send to the list.

		> I want to convert some data from latlong/wgs84 to tmerc/bessel with
		> datum shift from wgs84 to potsdam-datum here in germany.  How do i have
		> to use the function? Are helmert-7-parameter as well as
		> molodenski-3-parameter implemented? I tried the following:


		I didn't answer because I am always getting confused about the terminology
		for some of the different transforms.  There is a three and seven
		parameter transform implemented; however, I am not certain that the
		interpretation of the parameters (sign, handedness, etc) is exactly what
		is defined for helmert and molodenski.  I think it is though.

		> --------
		> cs2cs -v +proj=latlong +to +proj=tmerc +ellps=bessel +lat_0=0 +lon_0=12
		> +x_0=4500000 +towgs84=-586,-87,-409 <<EOF
		> 10.69079E 51.86134N
		> EOF
		> --------
		> As result i get the following:
		> ---------
		> # ---- From Coordinate System ----
		> #Lat/long (Geodetic)
		> #
		> # +proj=latlong +ellps=WGS84
		> # ---- To Coordinate System ----
		> #Transverse Mercator
		> # Cyl, Sph&Ell
		> # +proj=tmerc +ellps=bessel +lat_0=0 +lon_0=12 +x_0=4500000
		> # +towgs84=-586,-87,-409
		> #--- following specified but NOT used
		> # +ellps=WGS84
		> 4409820.23 5748070.07 698.769
		> ---------
		> The result is not good enough. I expect something like that:
		> 4409920 5748280.
		> Whats wrong here? I got the "towgs"-parameters from a another
		> helmert-calculation i found in the internet which work in another
		> program i have here and show the results i expected.

		First, no actual datum shift is being applied in this case because PROJ
		doesn't equate +ellps=WGS84 with the WGS84 datum automatically.  I realized
		this when I did the conversion without the +towgs84 parameter and got the
		same results.  Please use +datum=WGS84 to force treatment of the lat/long
		coordinates as being the WGS84 datum.

		Howwever, this doesn't seem to get us any closer to your expected values.

		warmerda at gdal[355]% cs2cs +proj=latlong +datum=WGS84 +to +proj=tmerc
		+lat_0=0 +lon_0=12 +x_0=4500000 +towgs84=-586,-87,-409 < test.dat
		4409793.19      5747857.54 1386.040

		I tried reversing the sign of the offset, as this is a frequent
		and get:

		warmerda at gdal[356]% cs2cs +proj=latlong +datum=WGS84 +to +proj=tmerc
		+lat_0=0 +lon_0=12 +x_0=4500000 +towgs84=586,87,409 < test.dat
		4409847.28      5748282.64 11.504

		This is close to what you expect in the northing (2m), but no so close in
		easting - still off by 70m or so.  I am no sure what else to say.

		Best regards,

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