Firstly, am I correct in assuming that the process of determining the shape and the size of the spheroid is independent from the process of determining the origin and the orientation?
For example, for NAD27, it seems that the following equation -- called the Clarke 1866 ellipsoid (reference 1) -- was fitted to the surveyed points:
where the parameters to be determined were x_0, y_0, and z_0 instead of a general equation of an oblate spheroid:
Suppose we have the complete equation (with parameters already determined), and the origin and the orientation relative to some arbitrary standard coordinate system, of each different realization of all the datums. Further suppose we do not know the name of each. For example, NAD83(CORS94) may be called "1" and WGS84 (G730) perhaps "2". So they are all jumbled up. Is it possible to sort them into different groups so that each group consists of the different realizations of the same datum?
- ARSITECH "Constants for Reference Ellipsoids used for Datum Transformations" http://www.arsitech.com/mapping/geodetic_datum/