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

Fri Aug 2 01:54:23 PDT 2019

Nick,

With the helmert [0] operation you can choose to use either the small angle approximation or the full set of equations. Enable the full equations with the +exact flag.

Michel,

I haven’t studied you email closely, but at least I can see that in your example with the pipeline you are using proj where should be using cct. The reason being that proj only works in 2D and you are asking for a 3D transformation. Generally, proj should only be used for projection of geodetic coordinates.

/Kristian

[0] https://proj.org/operations/transformations/helmert.html

From: PROJ <proj-bounces at lists.osgeo.org> On Behalf Of Nick Mein
Sent: 2. august 2019 10:45
To: Michel Ruijter <mnrengineering at gmail.com>
Cc: PROJ at lists.osgeo.org
Subject: Re: [PROJ] CRS for small Island (Saba), conversion of known projection and transformation parameters (Trimble) into proj4 string

There was a long discussion in this mailing list back in 2017 about 7 parameter transformations with large rotations. You can find the discussion at http://osgeo-org.1560.x6.nabble.com/towgs84-approximation-error-td5313738.html.

I'm not sure that there was ever a resolution to the discussion. But if PROJ is still using small-angle approximations for 7 parameter transformations then that is probably the reason that it isn't giving the expected results?

On Fri, 2 Aug 2019 at 03:39, Michel Ruijter <mnrengineering at gmail.com<mailto:mnrengineering at gmail.com>> wrote:
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
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