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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:

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where the parameters to be determined were x_0, y_0, and z_0 instead of a general equation of an oblate spheroid:

enter image description here

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?

References:

  1. ARSITECH "Constants for Reference Ellipsoids used for Datum Transformations" http://www.arsitech.com/mapping/geodetic_datum/
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    In case no-one here can answer, i've posted the question over at surveyorconnect.com
    – Martin F
    Dec 14, 2013 at 1:25
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    I do not understand the distinction you are making between those two equations: they are essentially the same, differing only in how the semiminor axis is parameterized.
    – whuber
    Dec 14, 2013 at 21:19
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    @whuber I am assuming that if I fit equation (2) to the surveyed points used for NAD27, SemiMajorAxis will not come out as 6,378,206.4 . Equation 1 is for 3 parameter fitting while equation 2 is for 5 parameter fitting.
    – user24397
    Dec 14, 2013 at 22:45

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Answered by user base9geodesy at http://surveyorconnect.com/index.php?mode=thread&id=236530#p236567

You are correct that the determination of the origin and orientation of a horizontal/geometric datum are independent of the reference ellipsoid. That being said I have never seen this solution used with respect to the determination of the ellipsoid. As per your example of NAD 27 it would be important to note that the U.S. Coast & Geodetic Survey had adopted the use of the CLARKE 1866 ellipsoid in all computations of horizontal positions in 1880, long before the development of NAD 27. In addition, the solution you show accounts for values in Earth-Center, Earth-Fixed (XYZ) coordinates which were seldom determined prior to the more contemporary capability of space-based positioning as the knowledge of true ellipsoid heights was extremely poor. Could you cite a reference source for your solution?

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  • It does state what i suspected to be the case, but as it has been so many years since i studied geodesy, i wasn't confident in my knowledge, so i cross-posted to where i thought there would be more geodesists.
    – Martin F
    Dec 14, 2013 at 19:47
  • I posted a clarification in surveyorconnect and edited the main question to add that info.
    – user24397
    Dec 14, 2013 at 20:10

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