A detailed study of the duality relation for the least squares adjustment in euclidean spaces |
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| Authors: | József Ádám |
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| Institution: | (1) Satellite Geodetic Observatory, Pf. 546, H-1373 Budapest, Hungary |
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| Abstract: | The Euclidean spaces with their inner products are used to describe methods of least squares adjustment as orthogonal projections
on finite-dimensional subspaces. A unified Euclidean space approach to the least squares adjustment methods “observation equations”
and “condition equations” is suggested. Hence not only the two adjustment solutions are treated from the view-point of Euclidean
space theory in a unified frame but also the existing duality relation between the methods of “observation equations” and
“condition equations” is discussed in full detail. Another purpose of this paper is to contribute to the development of some
familiarity with Euclidean and Hilbert space concepts. We are convinced that Euclidean and Hilbert space techniques in least
squares adjustment are elegant and powerful geodetic methods. |
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