engleski

The Way of Solving Some Geodetic Tasks

Abstract At our Faculty, we have recently become fully aware of the expanded discussions refering to the role of mathematics in education of engineers, as well as of the necessity for cooperation between the teachers of mathematics and those of special subjects who use the mathematical methods as a tool in solving their specific problems. We stress out that there have to be the cooperation among them with the idea that in such a way, both engineers and mathematicians, can give new quality to their teaching. This paper is the result of such a mutual work. The application of the software Mathematica in solving some geodetic tasks related to "network positioning" is presented. Network positioning is the determination of the coordinates of three or more points with respect to a predefined coordinate system, and it is accomplished by making measurements that link the unknown points to points with known coordinate values. In geodetic survey there are usually more measurements than the minimum needed to determine all unknowns. These extra observations are redundant information the adjustment uses to derive optimum estimates of the coordinate parameters, as well as valuable quality information. The presentation of this information can be made either numerically or graphically - in the form of parameter standard deviations and error ellipses. The graphical and numerical capabilities of Mathematica allow survey students and engineers to work with considerably more complicated problems than in the past. In large surveying networks the number of redundant measurements can become extremely large, and the adjustment process is involved. Many different methods have been devised for making adjustment in surveying. Years ago, because of the comparatively heavy computational effort involved in adjustment, non - rigorous adjustment was most often applied. Now computers, together with corresponding software tools, eliminate the computing problems, and the most rigorous adjustment method with postadjustment statistical analyses of the results can be used. This method can also be used to plan optimal surveys. In this application, prior to conducting needed surveys, simulated surveys, using some computer software, can be run and the results analysed. It requires a sound knowledge of mathematical calculus, matrix algebra, mathematical statistics and geodesy. Although these activities have been in practice for a long time, only now the significant progress, in both theoretical development and practical applications has been made, due to the potentials of the computer technology progress.

network positioning; adjustment process; postadjustment statistical analyses

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