Station Adjustment of Directions Using Generalized Inverses

des Instituts für Geodäsie

Heft 7/1982

Station Adjustment of Directions
Using Generalized Inverses

Uppsala and Gävle, Sweden


In: BORRE, Kai / WELSCH, Walter M. (Eds.) [1982]:
International Federation of Surveyors - FIG -
Proceedings Survey Control Networks
Meeting of Study Group 5B, 7th-9th July, 1982, Aalborg University Centre, Denmark

Schriftenreihe Wissenschaftlicher Studiengang Vermessungswesen, Hochschule der Bundeswehr München, Heft 7, Neubiberg, S. 381-399.



In a strict adjustment of directions at a triangle station no direction is arbitrarily chosen as "zero direction". Due to the unknown orientation of the set of directions the system of normal equations becomes singular, which implies that there is no unique least squares solution.

Furthermore, the directions are non-estimable in the sense of Rao. However, it is shown that all least squares estimates of directions provide identical unbiased angle estimates. The estimates and their covariance matrices are derived in the cases of directions observed in full rounds and incomplete rounds.

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