Junction of Control Surveys by Adjustment Compared with Coordinate Transformation

des Instituts für Geodäsie

Heft 7/1982

Junction of Control Surveys by Adjustment Compared with Coordinate Transformation

, The Netherlands

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. 115-141.


The overdetermined similarity or "Helmert" transformation is a well known and commonly applied method to connect stations coordinated in a - subsidiary - system into another - principal - system, the coordinates of which are kept fixed.

The result is a regression type "best fit" figure with remnant discrepancies at the tie points used to calculate the transformation parameters. In this process the covariance matrices of both sets of coordinates are ignored. Those discrepancies may not be of importance for certain small and medium scale mapping. However, angles and distances calculated from a combination of the principal coordinates of the tie points and those of the other transformed stations may be affected in their relative position by local jumps to such an extent that they are unfit to be used for consistent densification in respect of large scale mapping, and checking and setting out in the field for precise engineering surveys.

A method of junction by adjustment is proposed, where the remnant discrepancies are eliminated. The covariance matrices are taken into account after having been submiited to a covariance transformation in order to relate them to a common covariance reference base. This makes also possible to apply a testing procedure to the misclosures at the tie points.

The structure is shown of a substitute covariance matrix to be put into practice where the real covariance matrices are unknown or not available. This matrix - originally proposed by Alberda and Baarda - is applied to the example of a junction of two control surveys nets at the conclusion of the paper.

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