Acta Scientiarum Polonorum

Scientific paper founded in 2001 year by Polish agricultural universities

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Administratio Locorum
(Gospodarka Przestrzenna) 7 (1) 2008     ISSN: 1644-0741
Title
THE EFFECT OF SELECTION OF MODELS FOR DETERMINING HELMERT TRANSFORMATION PARAMETERS ON CALCULATION RESULTS
Autor
Józef Beluch
Keywords
Helmert transformation, functional models of transformation, transformation with weights
Abstract
In practice, the transformation parameters are determined without taking into consideration the weights of coordinates of common points. Such practice has encouraged the author to determine the effect of disregarding such weights in the calculation procedures on determining the transformation parameters and, further on, the results of coordinate transformations. The comparative calculations have been performed for two functional models for determining the transformation parameters, provided as conditions (6) and (12). The study has been based on a numerical example of coordinates transformation. The calculation variants have been provided for various assumptions as regards the mean square errors of coordinates , and consequently, the coordinate (pseudo-observation) weights. It has been found that the selection of the functional model does not affect the calculation results, when the matrixes of secondary coordinate weights in both models are identical, while the primary coordinate weights in separated sets of adjustment points satisfy the condition Pw=kPW where: Pw – identical weights in wi set of primary coordinates, PW – weights of the same primary coordinates in the secondary set, k – proportionality factor, identical for all relations between the sets. Considerable variations in the calculation results between both models have become apparent when the above-mentioned weight relation between sets is not present, and the mean square errors of primary coordinates are greater than those of the secondary coordinates. In the opposite case, the effects of variation of mean square errors on the calculation results are very slight. The variety of weights in calculation variants in relation to variant 1, in which weights of all coordinates are identical, leads to considerable variations in the calculation results, both in the first and second functional model.
Pages
3-13
Cite
Beluch, J. (2008). THE EFFECT OF SELECTION OF MODELS FOR DETERMINING HELMERT TRANSFORMATION PARAMETERS ON CALCULATION RESULTS. Acta Sci. Pol. Geod. Descr. Terr., 7(1), 3-13.
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