[OSRS-PROJ] Datum Shifting

cjmce at lsu.edu cjmce at lsu.edu
Wed Jul 5 11:53:57 EDT 2000

When Atef Elassal wrote GCTP, his objective was to translate John P. Snyder
to FORTRAN 77.  He did a superb job for the needs of the U.S. Geological
Survey at the time.

In regard to expanding PROJ4 to geodetic-type manipulation:

The inclusion of the MadTran algorithms is actually incomplete for
3-parameter and 7-parameter methods.  In actuality, there is a Bursa-Wolf
model and there is a Molodensky-Badekas model.  The NIMA implementation in
MadTran was actually the Americanized version of the Bursa-Wolf 7-parameter
model.  The European version (such as found in LEICA's "SKI" software for
geodetic-quality differential GPS solutions), uses the opposite sign for
the infinitesimal rotations.  Whopping errors will result if you confuse
the two.  (The only way to avoid errors is to always provide a test point
in both coordinate systems).

Furthermore, the Molodensky-Badekas model allows the use of the classical
Datum Origin to be used in the solution such that the scale factor is
changed substantially to account for the much-reduced magnitude of the
translation components.  (Of course, this also has two flavors of rotations
- the American/Australian version and the European version.)

Unbeknownst to some people is that if presented with a set of parameters
for a 7-parameter model, one CANNOT truncate the rotations just because
"they are so small."  In the least-squares solution for the seven
parameters, the rotations are solved first, then scale factor, then
translations.  The "tiny" rotations amount to quite a bit at the surface of
the ellipsoid and have a direct and specific effect on the magnitude of the
translation components (and the scalar).  When performing a least-squares
solution with the identical co-located points, the magnitude of the
translation-only components in a 3-parameter solution will be entirely
different than the magnitude of the translation components in a 7-parameter

When you talk about "elevations" being used in a "datum shift," are you
going to take into account the EGM96 Geoid when going to the WGS 84 Datum?
What about NIMA's Multiple Regression Equation (MRE) solutions for
continental areas?

Note that the NADCON algorithm is great for the U.S., but what about Canada
& Mexico?  I believe "Geomatics Canada" has a hefty price tag on their
transformation package for Maple Leaf applications.  Have you seen the
eye-popping prices charged by the Norwegians for their datum shift package?
I think only the U.S. and Australia give their stuff out for free.  South
Africa's solution is privately marketed by Prof. Charles Merry at the
University of Capetown.

Going 3-D "geodetic" is a big chunk to bite off ...

I write a monthly column on this stuff with a different country featured
each month in "Photogrammetric Engineering and Remote Sensing."  If you
have an interest in this type of stuff, look under "GRIDS & DATUMS" at the
society's web site:


There's over a dozen past columns of mine available in .pdf format for
downloading and printing with Adobe Acrobat Reader.  This month is on the
Kingdom of Spain, last month was on the Republic of Ghana.


Clifford J. Mugnier (cjmce at LSU.edu)
Surveying, Geodesy, and Photogrammetry
12408 CEBA Building
Baton Rouge, Louisiana  70803
Voice and Facsimilie: (225) 388 - 8536

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