For example if we compare the AGD84 (Australian Geodetic Datum) with GDA94 (Geocentric Datum Australia), the centre of the AGD Datum is 200 metres different to GDA, because it is a best fit to the geoid.

But how is this difference realised (implicitly) given only the Lat/Long/ Ellipsoidal Height of a Point (Johnstone), the semi-major axis (a) and the flattening (f)? I realise that (a) is different by 23 metres, but it is the angle between the 2 datums that makes the most difference, this is what I am trying to get a handle on.

Asking another way, how could I calc the ECEF coords for the centre of the AGD, to see how different it is to GDA?

Asking yet another way, how to determine the shift & angles between the axes of of AGD & GDA?

I already have the GDA manual - http://www.icsm.gov.au/gda/gdatm/gdav2.3.pdf and am working through writing C++ code for this. I also understand how AGD is not very consistent, so a conversion between the 2 datums requires the use of a model, it is just that I am trying to truly understand the mathematical difference between the two.

Sorry for the particularly nerdy question, & thanks in advance for any answers.


The difference is defined by the datum shift between the two reference ellipsoids. The shift itself is defined with a transformation (7 param. Helmert, 4 param,....) using 3D cartesian coordinates (X, Y, Z) which are calculated from ellipsoid coordinates (lat, lng, elevation).

The transformation (parameters) is usually derived from a set of points which have coordinates known in both systems, using least squares adjustment.

Heres a link how to calculate 3D cartesian coordinates from lat-lng-elevation: http://en.wikipedia.org/wiki/Geodetic_datum#Conversion_calculations

  • Cheers @U2ros, that makes sense. I can see how the transformation process would work, given some common points. It was just that the official definition of AGD never seemed to mention a shift, nor any angular tilts, or any common points for that matter. I found the value of the shifts on-line, after some extensive searching. I guess it is all a bit academic, because AGD is not consistent, so requires a model to transform. But I have an idea of the theory now (thanks to your help). My link above has some formulae for doing conversions to XYZ, but thanks again for your time & effort. 8+) – TheIdeasMan Jul 28 '13 at 13:22

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