Geodetic Deformation Analysis with Respect to an Extended Uncertainty Budget

  • Hansjörg Kutterer
Living reference work entry


This chapter reports current activities and recent progress in the field of geodetic deformation analysis if a refined uncertainty budget is considered. This is meaningful in the context of a thorough system-theoretical assessment of geodetic monitoring and it leads to a more complete formulation of the modeling and analysis chain. The work focuses on three major topics: the mathematical modeling of an extended uncertainty budget, the adequate adaptation of estimation and analysis methods, and the consequences for one outstanding step of geodetic deformation analysis – the test of a linear hypothesis. The essential outcome is a consistent assessment of the quality of the final decisions such as the significance of a possible deformation.


Fuzzy Number Deformation Process Object State Kinematic Model Deformation Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Alefeld G, Herzberger J (1983) Introduction to interval computations. Academic, BostonzbMATHGoogle Scholar
  2. Bandemer H, Näther W (1992) Fuzzy data analysis. Kluwer Academic, DordrechtCrossRefzbMATHGoogle Scholar
  3. Dong D, Dickey JO, Chao Y, Cheng MK (1997) Geocenter variations caused by atmosphere, ocean and surface ground water. Geophys Res Lett 24/15:1867–1870CrossRefGoogle Scholar
  4. Drewes H, Heidbach O (2004) Deformation of the South American Crust from finite element and collocation methods. In: Sanso F (ed) A window on the future of geodesy. International association of geodesy symposia, vol 128. Springer, Berlin, pp 296–301Google Scholar
  5. Dubois DJ, Prade HM (1980) Fuzzy sets and systems: theory and applications. Academic, LondonzbMATHGoogle Scholar
  6. Eichhorn A (2007) Analysis of dynamic deformation processes with adaptive Kalman-filtering. J Appl Geod 1:9–15Google Scholar
  7. Ferson S, Kreinovich V, Hajagos J, Oberkampf W, Ginzburg L (2007) Experimental uncertainty estimation and statistics for data having interval uncertainty. Sandia National Laboratories, SAND2007-0939Google Scholar
  8. Heunecke O (1994) Zur Identifikation und Verifikation von Deformationsprozessen mittels adaptiver KALMAN-Filterung (in German). PhD thesis, University of HannoverGoogle Scholar
  9. Heunecke O, Welsch W (2001) Models and terminology for the analysis of geodetic monitoring observations-Official report of the Ad Hoc Committee WG 6.1. In: Whitaker C (ed) Proceedings of the 10th international FIG symposium on deformation measurements, OrangeGoogle Scholar
  10. Jaulin L, Kieffer M, Didrit O, Walter E (2001) Applied interval analysis. Springer, LondonCrossRefzbMATHGoogle Scholar
  11. Koch KR (1999) Parameter estimation and hypotheses tests in linear models. Springer, BerlinCrossRefGoogle Scholar
  12. Koch KR (2007) Introduction to Bayesian statistics, 2nd edn. Springer, BerlinzbMATHGoogle Scholar
  13. Kutterer H (2004) Statistical hypothesis tests in case of imprecise data. In: Sanso F (ed) V Hotine-Marussi symposium on mathematical geodesy. Springer, Berlin, pp 49–56CrossRefGoogle Scholar
  14. Kutterer H, Neumann I (2008) Multidimensional statistical tests for imprecise data, In: Xu P, Liu J, Dermanis A (eds) Vi Hotine-Marussi symposium on theoretical and computational geodesy. Springer, Berlin, pp 232–237CrossRefGoogle Scholar
  15. Kutterer H, Neumann I (2009) Fuzzy extensions in state-space filtering-some applications in geodesy. In: Proceedings of the ICOSSAR 2009. Taylor & Francis, London, pp 1268–1275. ISBN:978-0-415-47557-0Google Scholar
  16. Möller B, Beer M (2004) Fuzzy randomness. Springer, BerlinCrossRefzbMATHGoogle Scholar
  17. Näther W (2009) Copulas and t-norms: mathematical tools for modeling propagation of errors and interactions. In: Proceedings of the ICOSSAR 2009. Taylor & Francis, London, pp 1238–1245. ISBN:978-0-415-47557-0Google Scholar
  18. Neumann I (2009) Zur Modellierung eines erweiterten Unsicherheitshaushaltes in Parameterschätzung und Hypothesentests (in German). Series C 634, German Geodetic Commission, MunichGoogle Scholar
  19. Neuner H, Kutterer H (2007) On the detection of change-points in structural deformation analysis. J Appl Geod 1:63–70Google Scholar
  20. Nguyen HT, Kreinovich V (1996) Nested intervals and sets: concepts, relation to fuzzy sets, and applications. In: Kearfott B, Kreinovich V (eds) Applications of interval computations. Kluwer, Dordrecht, pp 245–290CrossRefGoogle Scholar
  21. Rawiel P (2001) Dreidimensionale kinematische Modelle zur Analyse von Deformationen an Hängen (in German). Series C 533, German Geodetic Commission, MunichGoogle Scholar
  22. Roberts G, Meng X, Meo M, Dodson A, Cosser E, Iuliano E, Morris A (2003) A remote bridge health monitoring system using computational simulation and GPS sensor data. In: Stiros S, Pytharouli P (eds) Proceedings of the 10th international FIG symposium on deformation measurements, SantoriniGoogle Scholar
  23. Saltelli A, Chan K, Scott EM (2000) Sensitivity analysis. Wiley, ChichesterzbMATHGoogle Scholar
  24. Schön S (2003) Analyse und Optimierung geodätischer Messanordnungen unter besonderer Berücksichtigung des Intervallansatzes (in German). Series C 567, German Geodetic Commission, MunichGoogle Scholar
  25. Schön S, Kutterer H (2005) Using zonotopes for overestimation-free interval least-squares-some geodetic applications. Reliable Comput 11:137–155CrossRefzbMATHGoogle Scholar
  26. Schön S, Kutterer H (2006) Uncertainty in GPS networks due to remaining systematic errors: the interval approach. J Geod 80:150–162CrossRefzbMATHGoogle Scholar
  27. Welsch W, Heunecke O, Kuhlmann H (2000) Auswertung geodätischer Überwachungsmessungen (in German). Wichmann, HeidelbergGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Bundesamt fürKartographie und GeodäsieFrankfurt am MainGermany

Personalised recommendations