[Proj] +towgs84 approximation error

Jochem jochem.lesparre at kadaster.nl
Sat Mar 25 08:18:31 EST 2017

Hi Noel,

You mean you would like to see less rapid, but more cheery responses? I am
Sorry. I really do find the discussion with you and the others very
interesting en enjoyable. But, I notice we both tend to repeat ourselves,
which is not getting us somewhere. I'll try to break with that.

I am happy you support my suggestion of having the strict formulas as an
option. You are totally right that it would not be more accurate in a
geodetic sense, in most cases. However, are cases where the strict formulas
are more accurate, also geodetically. I'll explain.

The country where I was working this week has an imprecise (20 cm errors)
old triangulation network with large (40 arc-seconds) rotation parameters to
ITRF2008 at 2005.0=WGS84(G1762). They installed a continuously operating GNSS
reference station (CORS). Using that, they corrected the coordinates of
their first order triangulation points and changed the false Northing and
Easting to not mix corrected and uncorrected coordinates. By that they
introduced a new precise reference frame, but with the same large rotation
parameters to WGS84. The precise values of these parameters are still
unknown. But they started to log the GNSS observations of their CORS. As
soon as they acquired a full year of data, I will compute the precise
coordinates of their CORS relative to the IGS network and estimate the
transformation parameters to ITRF2014 using adjustment software that happens
to use the strict formulas. And I will continue to do that yearly. The
precision of this transformation to ITRS will be definitely be better than
the 4 cm approximation error of the default +towgs84 formulas. Does that
explain why I say I need the strict formulas also for geodetic precision? 

As I said I agree totally with your point that the 7 parameters are often
highly correlated, but I am doubting if that influences the precision of
transformed coordinates. All the other things you say are correct, no
doubts. An experiment (or challenge if you wish) would be very interesting. 

However, the challenge you suggest makes no sense to me. We both know that
old triangulation frames have a too low accuracy to make the strict formulas
necessary  (unless it would have enormous > 1 arc-minute rotations). So I
would like to alter the experiment on two points: use a GNSS corrected old
frame (like pseudo-RD of the Netherlands) with 1 cm relative standard
deviations, but with rotation angles to ETRS89 up to 40 arc-seconds (I can
just shift the Netherlands 1 km to the north to accomplish that, to simulate
an error of 1 km in the astronomical observations of the central point)... 

Kind regards, Jochem 


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