[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.

Frans

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.

Cliff

Prof. Clifford J. Mugnier (cjmce at LSU.edu)
Chief of Geodesy
CENTER FOR GEOINFORMATICS
Department of Civil Engineering
LOUISIANA STATE UNIVERSITY
Baton Rouge, LA  70803
Voice and Facsimile:  (225) 578-8536
Pager:              1-(888) 365-5180
================================
http://www.ASPRS.org/resources.html
http://www.ce.LSU.edu/~mugnier/
================================

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:

Harald,

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
+ellps=bessel
+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
incompatibility,
and get:

warmerda at gdal[356]% cs2cs +proj=latlong +datum=WGS84 +to +proj=tmerc
+ellps=bessel
+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
the
easting - still off by 70m or so.  I am no sure what else to say.

Best regards,

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