[Proj] +towgs84 approximation error

Stefanos Beligiannis smpel at yahoo.com
Wed Mar 22 19:48:25 EST 2017

Hi Jochem,
if I understood well you need a method to transform your coordinates from one system to another.7 parameters transformation (or Bursa-Wolf) is a geodetic coordinates transformation method, so the first question you must answer is what type of coordinates do you have on both systems and you must describe these systems.A second issue that arises is the accuracy. Martin already explained you that 7 param. method gives transformations with errors of even >10 m big. So big errors are expected when we deal with datum (ellipsoids) that have parameters with big differences between them. There is a confuse also, if I got the point, on the proj.4 calculation rounding errors that you say are 0.1 mm and the standard deviation of your transformed coordinates which you say are 4.5 cm.In turn we can't help you unless you explain clearly : "what you have" and "what you need".
regards Stefanos Beligiannis   

      From: Martin Desruisseaux <martin.desruisseaux at geomatys.com>
 To: proj at lists.maptools.org 
 Sent: Thursday, March 23, 2017 12:33 AM
 Subject: Re: [Proj] +towgs84 approximation error
Hello Jochem

The 7 parameter coordinate transformations are for datum shifts, which
are themselves approximative operations by nature. They have stochastic
error unrelated to the Proj.4 accuracy, much greater than the sine
approximation. For example the "NAD27 to WGS 84 (4)" transformation over
USA (EPSG:1173) has an accuracy of 10 metres. So in this context I
wonder what would be the purpose of aiming for an "accuracy" of 0.1 mm.
It can not be a positional accuracy (in the geodetic sense) at least,
but maybe the intend was something else?


Le 22/03/2017 à 22:41, Jochem a écrit :
> Hello, 
> I joined the mailing list because I noticed that the PROJ.4 library uses
> approximate formulas for the 7 parameter coordinate transformation defined
> by +towgs84 (technical details: The elements of the rotation matrix are the
> rotation angles instead of the product of sines and cosines of the angles).
> For really small rotation angles this gives the same result, but not for
> larger rotations. 
> For my current application I want to transform a map in QGIS with 1 mm
> accuracy. However, the approximation causes an error of 4 cm. Since PROJ.4
> normally gives results within 0.1 mm accuracy, I did not expect such
> approximation.
> What can I do to help to fix this?
> Regards, Jochem

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