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I have a .DWG file of a series of survey points that has no associated projection file with it. The surveying group I received the data from states that the system they use is a local coordinate system in a "modified UTM 20N". The data are located on St. Kitts in the Caribbean. Here are some of the points in WGS84 DMS, WGS84 DD, and in the local coordinate location Easting and Northing (meters):

    Point_Id    Latitude    Longitude   Ellip_Height    Lat_DD  Long_DD CustomX CustomY CustomZ GRS
1   17° 16' 53.25342" N 62° 40' 43.25561" W 63.148  17.281459   -62.678682  2796138.580 -5412477.224    1882617.923 WGS84
2   17° 17' 58.85760" N 62° 41' 43.83679" W 82.806  17.299683   -62.695510  2794282.417 -5412782.257    1884549.473 WGS84
3   17° 20' 08.90031" N 62° 42' 26.74262" W -17.577 17.335806   -62.707429  2792566.808 -5412220.661    1888336.213 WGS84
4   17° 23' 29.53690" N 62° 46' 26.37868" W 6.196   17.391538   -62.773994  2785445.293 -5413844.723    1894230.305 WGS84
5   17° 24' 22.92018" N 62° 47' 54.72740" W -21.295 17.406367   -62.798535  2782889.824 -5414577.508    1895788.138 WGS84

Here is the info from the Leica File that the surveyor gave me:

 Ellipsoid A: WGS 1984
    Ellipsoid B - GRS 1980
    Type: Classical 3D
    Transformation type: Molodensky Badekas

    dx: 18.2922m
    dy: -35.5306m
    dz: 12.4868m
    Rx: -1.69221"
    Ry: -1.69378"
    Rz: -1.92504"
    SF: 5.7362 ppm
    x0: 2787863.0804
    y0: -5414455.175
    z0: 1888935.4451

Here is a screenshot I received from the surveyor enter image description here

How do I define the reference system in ArcGIS Desktop with those given parameters?

I have seen the custom projection tool in ArcGIS, but I don't see any entry fields for the rotations he gave me (Rx, Ry, Rz):

Here is the screenshot from ArcMap enter image description here

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    Seems to me a 3D Cartesian transformation, instead of a projection. See: proj.org/operations/transformations/molobadekas.html
    – Gabriel De Luca
    Nov 13, 2019 at 3:59
  • Thanks for your response @GabrielDeLuca. I think you're right. What do I do with it then?
    – BenW
    Nov 13, 2019 at 4:06
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    Question edited for clarification and reduced to one question. I'd like the answer in ArcGIS primarily as I'm the most accustomed to it, but QGIS as well if possible.
    – BenW
    Nov 13, 2019 at 4:17
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    You are welcome. In QGIS you can add a custom CRS with the PROJ string. There is a parameter of which I am not sure: +convention. For others, the following chain seems appropriate: +proj=molobadekas +x=18.2922 +y=-35.5306 +z=12.4868 +rx=-1.69221 +ry=-1.69378 +rz=-1.92504 +s=5.7362 +px=2787863.0804 +py=-5414455.175 +pz=1888935.4451.
    – Gabriel De Luca
    Nov 13, 2019 at 4:27
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    I was told those parameters are for changing from GCS in WGS84 to their modified UTM 20N. He gave me both the Northing and Easting of the coordinates in their system as well as the DMS of the coordinate in WGS84. Here's an example: Ellip_Height Lat_DD Long_DD CustomX CustomY CustomZ 63.148 17.281459 -62.678682 2796138.580 -5412477.224 1882617.923 82.806 17.299683 -62.695510 2794282.417 -5412782.257 1884549.473 -17.577 17.335806 -62.707429 2792566.808 -5412220.661 1888336.213 6.196 17.391538 -62.773994 2785445.293 -5413844.723 1894230.305
    – BenW
    Nov 13, 2019 at 18:48

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