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 languageEnglish
Title of host publicationVII Hotine-Marussi Symposium on Mathematical Geodesy : Proceedings of the Symposium in Rome, 6-10 June, 2009
EditorsNico Sneeuw, Pavel Novák, Mattia Crespi, Fernando Sansò
PublisherSpringer
Publication date2012
Pages239-244
Chapter36
ISBN (Print)3642220770, 978-3-642-22077-7
ISBN (Electronic)978-3-642-22078-4
DOIs
Publication statusPublished - 2012
EventVII Hotine-Marussi Symposium on Mathematical Geodesy - Rome, Italy
Duration: 6 Jun 200910 Jun 2009

Conference

ConferenceVII Hotine-Marussi Symposium on Mathematical Geodesy
CountryItaly
CityRome
Period06/06/200910/06/2009
SeriesInternational Association of Geodesy Symposia
Volume137
ISSN0939-9585

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).
@inproceedings{e40540605e074e2490b1959872ef3248,
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",
language = "English",
isbn = "3642220770",
series = "International Association of Geodesy Symposia",
publisher = "Springer",
pages = "239--244",
editor = "{ Sneeuw}, Nico and Nov{\'a}k, {Pavel } and Crespi, {Mattia } and Sans{\`o}, {Fernando }",
booktitle = "VII Hotine-Marussi Symposium on Mathematical Geodesy",
address = "Germany",

}

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

Error Propagation in Geodetic Networks Studied by FEMLAB. / Borre, Kai.

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

TY - GEN

T1 - Error Propagation in Geodetic Networks Studied by FEMLAB

AU - Borre, Kai

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84884362424&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-22078-4

DO - 10.1007/978-3-642-22078-4

M3 - Article in proceeding

SN - 3642220770

SN - 978-3-642-22077-7

T3 - International Association of Geodesy Symposia

SP - 239

EP - 244

BT - VII Hotine-Marussi Symposium on Mathematical Geodesy

A2 - Sneeuw, Nico

A2 - Novák, Pavel

A2 - Crespi, Mattia

A2 - Sansò, Fernando

PB - Springer

ER -

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