[Proj] +towgs84 approximation error

Martin Desruisseaux martin.desruisseaux at geomatys.com
Thu Mar 23 06:23:25 EST 2017

Hello Jochem

Le 23/03/2017 à 01:48, Jochem a écrit :

> WGS84 is just a hub for many users.
Right, but this is an issue. There is today 6 versions of WGS84: WGS
84(Transit), WGS 84(G730), WGS 84(G873), WGS 84(G1150), WGS 84(G1674),
WGS 84(G1762). The difference between them can more than 1 metre.
Furthermore - maybe not in your case but usually -, a transformation
from A to WGS84 involves stochastic errors and a transformation from
WGS84 to B involve additional stochastic errors that could be avoided
when defining the transformation directly from A to B (e.g. from NAD27
to NAD83). For those reasons, the use of a hub ("early-binding") is not
the preferred approach. In Well Known Text (WKT), the TOWGS84 keyword
has been removed in the new WKT 2 format (ISO 19162); another mechanism
(BOUNDCRS) is defined for those who really want early-binding.

Implementing the recommended approach ("late-binding") in Proj.4
requires access to a more complete EPSG dataset, which has been the
discussed in another thread a few months ago. The proposal was to use
SQLite. But I understand that the time frame may not fit your needs.

> I think these are 3 reasons why the approximation is not good enough
> and should be improved.
But EPSG guidance notes that you referred [1] also said that whether
there is an error or not depend on how the 7 parameters were derived. If
they were derived by an algorithm that itself used the small angle
approximation, then the current Proj.4 implementation is exact and the
proposed improvement would introduce errors. Unfortunately there is no
way as far as I know to said how the 7 parameters were derived. The
standard way would have been to define 2 separated operation methods
depending how the 7 parameters were derived, but this has not been done
(I presume because the errors were considered too small compared to
stochastic errors). However I admit that those who derived the 7
parameters using the small angle approximation probably care less about
errors than those who derived the 7 parameters using the full formulas.


[1] http://www.iogp.org/pubs/373-07-2.pdf (page 135)

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