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

Fri Aug 2 01:44:52 PDT 2019

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>
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
> de Kempenaerstraat 82, 2341GP, Oegstgeest
> mob: +31638944484, tel: +31718897137
>
>
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