# Error Propagation in Geodetic Networks Studied by FEMLAB

Kai Borre

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

### 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.
Original language English VII Hotine-Marussi Symposium on Mathematical Geodesy : Proceedings of the Symposium in Rome, 6-10 June, 2009 Nico Sneeuw, Pavel Novák, Mattia Crespi, Fernando Sansò Springer 2012 239-244 36 3642220770, 978-3-642-22077-7 978-3-642-22078-4 https://doi.org/10.1007/978-3-642-22078-4 Published - 2012 VII Hotine-Marussi Symposium on Mathematical Geodesy - Rome, ItalyDuration: 6 Jun 2009 → 10 Jun 2009

### Conference

Conference VII Hotine-Marussi Symposium on Mathematical Geodesy Italy Rome 06/06/2009 → 10/06/2009
Series International Association of Geodesy Symposia 137 0939-9585

### Cite this

Borre, K. (2012). Error Propagation in Geodetic Networks Studied by FEMLAB. In N. Sneeuw, P. Novák, M. Crespi, & F. Sansò (Eds.), VII Hotine-Marussi Symposium on Mathematical Geodesy: Proceedings of the Symposium in Rome, 6-10 June, 2009 (pp. 239-244). Springer. International Association of Geodesy Symposia, Vol.. 137 https://doi.org/10.1007/978-3-642-22078-4
Borre, Kai. / Error Propagation in Geodetic Networks Studied by FEMLAB. VII Hotine-Marussi Symposium on Mathematical Geodesy: Proceedings of the Symposium in Rome, 6-10 June, 2009. editor / Nico Sneeuw ; Pavel Novák ; Mattia Crespi ; Fernando Sansò. Springer, 2012. pp. 239-244 (International Association of Geodesy Symposia, Vol. 137).
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title = "Error Propagation in Geodetic Networks Studied by FEMLAB",
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.",
author = "Kai Borre",
year = "2012",
doi = "10.1007/978-3-642-22078-4",
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series = "International Association of Geodesy Symposia",
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Borre, K 2012, Error Propagation in Geodetic Networks Studied by FEMLAB. in N Sneeuw, P Novák, M Crespi & F Sansò (eds), VII Hotine-Marussi Symposium on Mathematical Geodesy: Proceedings of the Symposium in Rome, 6-10 June, 2009. Springer, International Association of Geodesy Symposia, vol. 137, pp. 239-244, VII Hotine-Marussi Symposium on Mathematical Geodesy, Rome, Italy, 06/06/2009. https://doi.org/10.1007/978-3-642-22078-4
VII Hotine-Marussi Symposium on Mathematical Geodesy: Proceedings of the Symposium in Rome, 6-10 June, 2009. ed. / Nico Sneeuw; Pavel Novák; Mattia Crespi; Fernando Sansò. Springer, 2012. p. 239-244 (International Association of Geodesy Symposia, Vol. 137).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

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Borre K. Error Propagation in Geodetic Networks Studied by FEMLAB. In Sneeuw N, Novák P, Crespi M, Sansò F, editors, VII Hotine-Marussi Symposium on Mathematical Geodesy: Proceedings of the Symposium in Rome, 6-10 June, 2009. Springer. 2012. p. 239-244. (International Association of Geodesy Symposia, Vol. 137). https://doi.org/10.1007/978-3-642-22078-4