[PROJ] CRS for small Island (Saba), conversion of known projection and transformation parameters (Trimble) into proj4 string

[Michel Ruijter]

Ls,
For a small Caribbean Island (Saba) I am trying to get the proper proj4 CRS
(for Qgis) in order to use GPS based coordinates on local grid related
system
The following projection and datum parameters are used in a TRimble
software package (and used in the RTK equipment) in local "Kadaster"
coordinates  to set out benchmarks etc

Ellipsoid
Ellipsoid Name   : (WGS 84)
Flattening 1/f   : 297.000
Semi Major Axis  : 6378388.000m


Datum Transformation : Seven Parameter
WGS84 to (WGS 84) (sounds a little bit confusing since ellipsoid seems to
be the international ellipsoid
Translation X    :   194.245m           Rotation X :  0°05'51.504629"
Translation Y    :  -154.530m           Rotation Y : -0°11'41.841439"
Translation Z    :   102.676m           Rotation Z :  0°04'11.988863"
Scale Factor     : 6.2965571264 ppm


Transverse Mercator Projection
Projection Origin                       False Origin
Latitude      :   17°38'10.36749"NFalse Northing  :       1967.190m
Longitude     :   63°14'15.07247"WFalse Easting   :       4714.870m
Height        :          N/A            False Elevation    :             N/A
Scale Factor  :   1.00000000

Test coordinates:
WGS84 in°N         WGS84 in°E         z(ellips)       LocalE in m
LocalN in m   Z(msl)
1 17.61578594    -63.25156367       -41.19          3215.38
-287.59            2.065
2 17.62323214    -63.23827421       290.27          4629.098
 530.823       333.55

These coordinates have been verified with pctrans (software of the dutch
navy) and the conversion (Trimble) seems to be good to within 2 cm

I have tried to convert the translation rotation and projection into a
proj4 structure within Qgis
I converted the rotation into arcseconds:

Rotation X :  0°05'51.504629"  (351.504629")
Rotation Y : -0°11'41.841439" (-701.841439")
Rotation Z :  0°04'11.988863" (251.988863")

+proj=tmerc +lat_0=17.63621319 +lon_0=-63.23752013 +k=1 +x_0=4714.870 +y_0=
1967.19  +ellps=intl
+towgs84=194.245,-154.53,102.676,-351.5046,701.841,-251.9889,6.296557
+units=m +no_defs

(note all signs of of rotation  have been changed compared to Trimble
notation  )

application of this proj4 string in Qgis results in the following two local
grid positions:
1  3250.9 mE    -209.59mN
2  4658.157mE   620.26 mN

I also tried to use OS4GEO installed on a win10 machine in many variants
e.g.

echo -63.25156367 17.61578594 |cs2cs +proj=latlong +ellps=WGS84
+towgs84=0,0,0 +no_defs +to +proj=tmerc +ellps=WGS84 +lat_0=17.63621319
+lon_0=-63.23752013 +k=1 +x_0=4714.87 +y_0=1967.19
+towgs84=-194.245,154.53,-102.676,-351.5046,701.841,-251.9889,-6.296557
+units=m +no_defs

 with as a result x=3458.54 y=-202.09 z=286.19

I have tried to use the pipeline option as well however, in one of the
first steps OSgeo seems not to convert coordinates properly:
e.g. with the statement below I expect to get 17.00 17.00 as an answer but
I get 17.00 0.00 !!!

echo 17.0 17.0 | proj +proj=pipeline +step +proj=cart +ellps=intl +step
+proj=cart +inv +ellps=intl


I have tried a number of versions of this transformation (changing signs in
the towgs string string but this does  not result in proper coordinates.

What is wrong with this proj4 string based on the rotation and projection
information from the Trimble software and how in general can we use the
translation and projection information into a valid proj4 string?

Kind regards,

Michel Ruijter

-- 
Michel Ruijter
MNRengineering
de Kempenaerstraat 82, 2341GP, Oegstgeest
mob: +31638944484, tel: +31718897137

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