Bulletin nr. 1 of the Geodetic Institute at Potsdam. Karl Reicheneder: Fehlertheorie und Ausgleichung von Rautenkeeten in der Nadirtriangulation. Theory of errors and adjustment ofradial triangulation).
✍ Scribed by A.J. van der Weele
- Publisher
- Elsevier Science
- Year
- 1949
- Weight
- 68 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0031-8663
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✦ Synopsis
Fehlertheorie und Ausgleichung von Rautenketten in der Nadirtriangulation. (Theory of errors and adjustment of radial triangulation).
The theory developped in this paper is based on a publication of Buchholtz (1934) who has treated the adjustment of a chain of rhomboids, on the assumption that the measured angles are uncorrelated and equally accurate.
Although one may admire the exhaustive way in which Reicheneder has solved the problem as he put it, there are some objections against his work, both from a point of view of photogrammetry and of the theory of errors.
It is stated on page 1 that the application of the theory of errors presupposes freedom of correlation between the direct or indirect observations. Seen in the light of theory published by Prof. Tienstra (Bulletin G6od~sique 1947. nr. 6) it is sufficient to know the tensor of cofactors or Weights of the observations. On the same page the author remarks that though the number of observations will increase if one observes angles rather than directions, this procedure will nSt yield more accurate results. Obviously this is true only for a very special way of computing the observations. Generally speaking, however, this statement is incorrect.
If one considers this question more thoroughly it is evident that correlation will occur indeed. Howfar the above-mentioned assumptions can serve as a plausible working-base is not "shown here, but, according to the experience of the undersigned, this is not very probable.
Generally speaking it is regrettable that an extensive work as the present one, is undertaken without making sure that the fundamental principles are correct. As a consequence the practical value of the results is dubious.
Similar remarks can be made regarding the choice of the weights of the directions. Distinction is only made between directions to plumb-points and auxiliary points. The lack of a base for this assumption leads also to doubts concerning the results obtained.
The mathematical methods, used by the author, give no rise to remarks. One may only ask if the application of weight symlbols (cofactors) would not have lead to a more surveyable result, the more since in this way there is no necessity to express all quantities whose mean errors must be computed, in the elements observed.
The method used induces the author to state that the mean error of a distance between two points cannot be computed from the mean errors in their coordinates (page 59). This is possible indeed if the correlation between the coordinates is taken into account. The application of the symbolic notation would have made chapter VI completely superfluous.
At some places a comparison is made between plumb-point triangulation and spatial triangulation (e.g. page 54). The remarks which are made are of doubtful value, since they are not accounted for and are hardly in accord with the practice.
Summarizing we conclude that the work of Reicheneder has little value from a photogrammetric point of view since his theory is not based on solid and approved foundations whereas from a point of view of the theory of errors it must at its best be called unelegant.
A.J. van der Weele.