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# Error Propagation in Geodetic Networks Studied by FEMLAB

Authors:
Editor:
, , ,
DOI:
10.1007/978-3-642-22078-4
Abstract:
Geodetic networks can be described by discrete models. The observations may be height differences, distances, and directions. Geodesists always make more observations than necessary and estimate the solution by using the principle of least squares. Contemporary networks often contain several thousand points. This leads to so large matrix problems that one starts thinking of using continous network models. They result in one or more differential equations with corresponding boundary conditions. The Green’s function works like the covariance matrix in the discrete case. If we can find the Green’s function we also can study error propagation through large networks. Exactly this idea is exploited for error propagation studies in large geodetic networks. To solve the boundary value problems we have used the FEMLAB software. It is a powerful tool for this type of problems. The M-file was created by Daniel Bertilsson. Modifying the code is so simple that a student can do it. We demonstrate some results obtained this way.Geodetic networks can be described by discrete models. The observations may be height differences, distances, and directions. Geodesists always make more observations than necessary and estimate the solution by using the principle of least squares. Contemporary networks often contain several thousand points. This leads to so large matrix problems that one starts thinking of using continous network models. They result in one or more differential equations with corresponding boundary conditions. The Green’s function works like the covariance matrix in the discrete case. If we can find the Green’s function we also can study error propagation through large networks. Exactly this idea is exploited for error propagation studies in large geodetic networks. To solve the boundary value problems we have used the FEMLAB software. It is a powerful tool for this type of problems. The M-file was created by Daniel Bertilsson. Modifying the code is so simple that a student can do it. We demonstrate some results obtained this way.
ISBN:
3642220770, 9783642220777, 9783642220784
Type:
Conference paper
Language:
English
Published in:
International Association of Geodesy Symposia: Proceedings of the Symposium in Rome, 6-10 June, 2009, 2012, p. 239-244
Main Research Area:
Science/technology
Publication Status:
Published
Series:
International Association of Geodesy Symposia
Review type:
Peer Review
Conference:
VII Hotine-Marussi Symposium on Mathematical Geodesy, 2012
Publisher:
Springer
Submission year:
2012
Scientific Level:
Scientific
ID:
254845998