[Proj] datum conversion, estimating parameters

Robert Jaeschke robert-j at gmx.de
Fri Mar 25 14:01:47 EST 2005


On Wed, Mar 23, 2005 at 05:53:50PM -0600, Noel Zinn wrote:

> Given ECEF coordinates in both datums, solving for the 7 parameters is just
> a least-squares problem.  Unfortunately, the 7 geocentric parameters are
> highly correlated in a small area.  For example, at a single point it's
> possible to solve for the 3 translations or for 2 rotations (any two if your
> area of interest is Germany) and the scale factor and get the same results.
> That's due to the correlations among the parameters.  It takes a large area
> to reduce those correlations geometrically.  The area of Germany is less
> than 0.1% of that of the world. Consequently, the dillution of precision
> (DOP) in solving for all 7 parameters in Germany with, say, 40 uniformly
> distributed points is about 15.  If you're familiar with the DOP concept
> from GPS, that's a big number.  Fewer points, more DOP.  In a country the
> size of Australia 40 well distributed points yields a DOP of 3.  That's
> something to work with.  And the Australians have done it!

Thank you for that explanation! I guess, I can't discover the unknown datum
just with computation. 

> In Europe NATO has been less cautious about about ill-conditioned
> least-squares problems and has published 7-parameter shifts for a number of
> countries.  This link => once
> got one to their published list, but I see it's broken at the moment.  Maybe
> it will pop back up, and maybe you'll find your unknown datum among them.
> Be cautious.

OK, I'll save that link and look for the document from time to time. 

I "proj'ed" much the last days and for locating points on a
georeferenced TK25 I use GPSman. And I don't know, if I did something
wrong again, or if this is an error in GPSman or proj:

DMS/WGS84: 12d10'27.4"E  51d41'38.3"N 
UTM/WGS84: 33U  304711 5730783  (says GPSman)
GKK/WGS84:   4 4512051 5729309  (says GPSman)

> proj +proj=utm +zone=33
12d10'27.4"E  51d41'38.3"N
304710.92       5730782.08
> proj +proj=tmerc +lat_0=0 +lon_0=12 +k=1.000000 +x_0=4500000 +y_0=0 +ellps=bessel
12d10'27.4"E  51d41'38.3"N
4512049.02      5728718.94
> cs2cs +proj=latlong +datum=WGS84 +to +proj=tmerc +lat_0=0 +lon_0=12 +k=1.000000 +x_0=4500000 +y_0=0 +ellps=bessel +datum=WGS84
12d10'27.4"E  51d41'38.3"N
4512049.17      5728654.21 698.95

I cannot explain the difference in the northing in the last two
conversions (proj does no datum shift and cs2cs shouldn't, because I
said "+datum=WGS84"). The question is: which are the correct GKK/WGS84
coordinates? The ones from GPSman or the ones from proj or from cs2cs?

Thank you again, Robert

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