[Proj] +towgs84 approximation error

[Noel Zinn (cc)]

Jochem,

Thanks for your rapid, cheery responses that keep this interesting thread 
going.

You say, "won't be less accurate".

I do support an option (not a default) of concatenated, fully-populated 
(sines and cosines) rotation matrices for the 7-parameter transformation in 
proj4, which, for consistency in the industry, ought to be done the way 
(rotation order) ESRI do it.  Perhaps Melita can weigh in on that. 
Unfortunately, it won't be more accurate geodetically.

Having said that I need to repeat other comments made in this thread 
(notably by Martin, and paraphrasing now) about the difference between the 
numerical accuracy that you are pursuing and "geodetic accuracy".  For 
transformation between datums my ad hoc definition of "geodetic accuracy" is 
RMS error at the control points after transformation.  Unlike mathematically 
exact conversions, all transformations have error, and that's especially 
true between a world datum (your choice) and any classical, terrestrial 
(land surveying) datum such as those one comes across exploring for oil 
(which is the genesis of the EPSG dataset).

Having spent a career in oil exploration and having derived "datum shifts" 
between WGS72 and WGS84 and many local datums, I frequently had to combat 
the misperception that a 7-parameter (Bursa-Wolf of Helmert) transformation 
was more geodetically accurate than just three translations.  Folks say, "it 
has more parameters so it must be more accurate".  Well, those parameters 
are wasted in high correlations in a small-area derivation and they're not 
more accurate by my geodetic definition above.  For me this is an issue of 
appropriate geodesy versus misleading geodesy.

Jochem, I have challenge for you to illustrate this.  Share with me the 
coordinates of control points in a European country in both a world datum 
and a pre-satellite terrestrial datum.  You derive a 7-parameter shift 
between them.  I will spend my 7 parameters on multiple regression equations 
(necessarily short).  We'll see which transformation produces the lowest RMS 
error.  You can use sines and cosines in your rotation matrices.  The geoid 
is a messy complication in this.  We can limit this challenge to the 
horizontal if you wish.

Let me know.

Noel

Noel Zinn, Principal, Hydrometronics LLC
+1-832-539-1472 (office), +1-281-221-0051 (cell)
noel.zinn at hydrometronics.com (email)
http://www.hydrometronics.com (website)

-----Original Message----- 
From: Jochem
Sent: Friday, March 24, 2017 4:02 AM
To: proj at lists.maptools.org
Subject: Re: [Proj] +towgs84 approximation error

Hi Noel,

Your point on the correlations between translations and rotations was
already clear to me after your first email. However, I still don't
understand why this is so important to you. Since the coordinates
transformed with these correlated parameters won't be less accurate than the
ones with the better method you mention.

Regards, Jochem



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