Estimability of astronomical longitude and latitude only from theodolite observations within three-dimensional networks of terrestrial type |
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| Authors: | Erik W Grafarend |
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| Institution: | (1) Department of Geodetic Science, Stuttgart University, Keplerstr. 11, 7000 Stuttgart 1, (F.R.G.) |
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| Abstract: | Summary From a two-dimensional network adjustment it is well understood that the one orientation unknown of a theodolite frame is
estimable, once the orientation datum parameter, e.g., one azimuth, is fixed. In three-dimensional networks the problem of
estimability of three orientation unknowns inherent in a theodolite frame is more complex. Here we prove that not only the
classical horizontal orientation unknown is estimable (up to the datum degrees of freedom), but also astronomical longitude
and astronomical latitude which can be considered as two additional orientation unknowns of the theodolite frame moving with
respect to an earth-fixed equatorial frame of reference. Thus the theodolite instrument can be considered—at least theoretically—a
gradiometer measuring the variation of the directional parameters of the gravity vector from one point to another. Or up to
the datum degrees of freedom astronomical longitude and astronomical latitude can be determined from only theodolite observations
between exclusively terrestrial points. M?nicke (1982), has shown that despite the refraction problem the method works sufficiently
well in practice. |
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