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Journal of Applied Geodesy

Editor-in-Chief: Kahmen, Heribert / Rizos, Chris

CiteScore 2018: 1.61

SCImago Journal Rank (SJR) 2018: 0.532
Source Normalized Impact per Paper (SNIP) 2018: 1.064

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Volume 11, Issue 4


Congruence analysis of geodetic networks – hypothesis tests versus model selection by information criteria

Rüdiger Lehmann
  • Corresponding author
  • University of Applied Sciences Dresden, Faculty of Spatial Information, Friedrich-List-Platz 1, D-01069 Dresden, Germany. +49 351 462 3146, +49 351 462 2191
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  • De Gruyter OnlineGoogle Scholar
/ Michael Lösler
  • Frankfurt University of Applied Sciences, Faculty of Architecture, Civil Engineering and Geomatics Laboratory for Industrial Metrology, Nibelungenplatz 1, D-60318 Frankfurt am Main, Germany. +49 69 1533-2784, +49 69 1533-2058
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Published Online: 2017-09-15 | DOI: https://doi.org/10.1515/jag-2016-0049


Geodetic deformation analysis can be interpreted as a model selection problem. The null model indicates that no deformation has occurred. It is opposed to a number of alternative models, which stipulate different deformation patterns. A common way to select the right model is the usage of a statistical hypothesis test. However, since we have to test a series of deformation patterns, this must be a multiple test. As an alternative solution for the test problem, we propose the p-value approach. Another approach arises from information theory. Here, the Akaike information criterion (AIC) or some alternative is used to select an appropriate model for a given set of observations. Both approaches are discussed and applied to two test scenarios: A synthetic levelling network and the Delft test data set.

It is demonstrated that they work but behave differently, sometimes even producing different results. Hypothesis tests are well-established in geodesy, but may suffer from an unfavourable choice of the decision error rates. The multiple test also suffers from statistical dependencies between the test statistics, which are neglected. Both problems are overcome by applying information criterions like AIC.

Keywords: Deformation analysis; Congruence model; Model selection; Hypothesis test; p-value approach; Information criterion; Akaike information criterion


  • [1]

    Abdi H (2007) The Bonferonni and Šidák corrections for multiple comparisons. In: Neil Salkind (ed) Encyclopedia of measurement and statistics. Sage, Thousand Oaks.Google Scholar

  • [2]

    Akaike H (1974) A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19: 716–723.CrossrefGoogle Scholar

  • [3]

    Antonopoulos A, Niemeier W (1983) Formulierung und Test impliziter linearer Hypothesen bei der geodätischen Deformationsanalyse. In: Welsch W (ed.) Deformationsanalysen ’83 – Geometrische Analyse und Interpretation von Deformationen geodätischer Netze. Beiträge zum Geodätischen Seminar, 22. April 1983. Wissenschaftlicher Studiengang Vermessungswesen, Hochschule der Bundeswehr München, 9, 13–27.Google Scholar

  • [4]

    Aydin C (2012) Power of Global Test in Deformation Analysis. J Surv Eng, 138(2): 51–56, DOI .CrossrefWeb of ScienceGoogle Scholar

  • [5]

    Baarda W (1968) A testing procedure for use in geodetic networks, Vol. 2, Number 5, Netherlands Geodetic Commission, Publication on Geodesy, Delft, Netherlands. http://www.ncgeo.nl/phocadownload/09Baarda.pdf.Google Scholar

  • [6]

    Blais JAR (1991) On some model identification strategies using information theory. Manuscripta Geodaetica, 16(5): 326–332.Google Scholar

  • [7]

    Böhm S, Kutterer H (2006) Modeling the Deformations of a Lock by Means of Neuro-Fuzzy Techniques. XXIII FIG Congress Munich, Germany, October 8–13. http://www.fig.net/pub/fig2006/papers/ps06/ps06_03_boehm_kutterer_0597.pdf.Google Scholar

  • [8]

    Burnham KP, Anderson DR (2002) Model Selection and Multimodel Inference: A Practical Information-theoretic Approach. Springer, Berlin.Google Scholar

  • [9]

    Burnham KP, Anderson DR (2004) Multimodel inference: understanding AIC and BIC in Model Selection. Sociological Methods and Research, 33: 261–304, DOI .CrossrefGoogle Scholar

  • [10]

    Caspary W, Welsch W (1979) Seminar über Deformationsanalysen, Schriftenreihe des wissenschaftlichen Studiengangs Vermessungswesen, Hochschule der Bundeswehr München, 4, ISSN: 0173-1009.Google Scholar

  • [11]

    Felus YA, Felus M (2009) On choosing the right coordinate transformation method. In: Proceedings of FIG working week 2009: surveyors key role in accelerated development. Eilat, Israel, May 3–8, http://www.fig.net/pub/fig2009/papers/ts04c/ts04c_felus_felus_3313.pdf.Google Scholar

  • [12]

    Hahn M, Heck B, Jäger R, Scheuring R (1989) Ein Verfahren zur Abstimmung der Signifikanzniveaus für allgemeine Fm,n-verteilte Teststatistiken – Teil I: Theorie. zfv – Zeitschrift für Vermessungswesen, 114: 234–248.Google Scholar

  • [13]

    Hahn M, Heck B, Jäger R, Scheuring R (1991) Ein Verfahren zur Abstimmung der Signifikanzniveaus für allgemeine Fm,n-verteilte Teststatistiken – Teil II: Anwendungen. zfv – Zeitschrift für Vermessungswesen, 116: 15–26.Google Scholar

  • [14]

    Hahn M, van Mierlo J (1987) Die Abhängigkeit der Ausgleichungsergebnisse von der Genauigkeitsänderung einer Beobachtung. zfv – Zeitschrift für Vermessungswesen, 112: 105–115.Google Scholar

  • [15]

    Harmening C, Neuner H-B (2014) Raumkontinuierliche Modellierung mit Freiformflächen. In: DVW – Gesellschaft für Geodäsie Geoinformation und Landmanagement e.V.: Beiträge zum 139. DVW-Seminar: Terrestrisches Laserscanning 2014 (TLS 2014), Wissner, 78: 105–122.Google Scholar

  • [16]

    Heunecke O, Kuhlmann H, Welsch WM, Eichhorn A, Neuner H (2013) Handbuch Ingenieurgeodäsie: Auswertung geodätischer Überwachungsmessungen. 2nd edn., Wichmann, Heidelberg.Google Scholar

  • [17]

    Jäger R, Müller T, Saler H, Schwäble R (2005) Klassische und robuste Ausgleichungsverfahren – Ein Leitfaden für Ausbildung und Praxis von Geodäten und Geoinformatikern. Wichmann, Heidelberg.Google Scholar

  • [18]

    Klees R, Ditmar P, Broersen P (2003) How to handle colored observation noise in large least-squares problems. J Geod, 76(11): 629–640, DOI .CrossrefGoogle Scholar

  • [19]

    Koch KR (1999) Parameter Estimation and hypothesis testing in linear models. 2nd edn., Springer, Heidelberg, DOI .CrossrefGoogle Scholar

  • [20]

    Kullback S, Leibler RA (1951) On information and sufficiency. Annals of Mathematical Statistics, 22(1): 79–86, DOI .CrossrefGoogle Scholar

  • [21]

    Kutterer H-J (1999) On the sensitivity of the results of least-squares adjustments concerning the stochastic model. J Geod, 73(7): 350–361, DOI .CrossrefGoogle Scholar

  • [22]

    Lehmann R (2014) Transformation model selection by multiple hypothesis testing. J Geod, 88(12): 1117–1130, DOI .CrossrefGoogle Scholar

  • [23]

    Lehmann R (2015) Observation error model selection by information criteria vs. normality testing. Stud. Geophys. Geod, 59(4): 489–504, DOI .CrossrefWeb of ScienceGoogle Scholar

  • [24]

    Lehmann R, Attrodt A (2016) Epochenvergleiche von Präzisions-EDM-Messungen zur Untersuchung der Punktstabilität auf einer EDM-Basislinie. Schriftenreihe des Instituts für Markscheidewesen und Geodäsie an der Technischen Universität Bergakademie Freiberg 2016-1. http://nbn-resolving.de/urn:nbn:de:bsz:520-qucosa-204058.Google Scholar

  • [25]

    Lehmann R, Lösler M (2016) Multiple Outlier Detection: Hypothesis Tests Versus Model Selection by Information Criteria. J Surv Eng, 142(4), DOI .CrossrefWeb of ScienceGoogle Scholar

  • [26]

    Lehmann R, Neitzel F (2013) Testing the compatibility of constraints for parameters of a geodetic adjustment model. J Geod, 87(6):555–566, DOI .CrossrefGoogle Scholar

  • [27]

    Lösler M, Haas R, Eschelbach C (2016) Terrestrial monitoring of a radio telescope reference point using comprehensive uncertainty budgeting – Investigations during CONT14 at the Onsala Space Observatory. J Geod, 90(5): 467–486, DOI .CrossrefGoogle Scholar

  • [28]

    Lösler M, Eschelbach C, Haas R (2017) Congruence analysis using original observations (in German). zfv – Zeitschrift für Geodäsie, Geoinformation und Landmanagement, 142(1): 41–52, DOI .CrossrefGoogle Scholar

  • [29]

    Lösler M, Lehmann R, Eschelbach C (2017) Model Selection via Akaike Information Criterion – Application in Congruence Analysis (in German). avn – Allgemeine Vermessungs-Nachrichten, 124(5): 137–145.Google Scholar

  • [30]

    Luo X, Mayer M, Heck B (2011) Verification of ARMA identification for modelling temporal correlations of GNSS observations using the ARMASA toolbox, Stud. Geophys. Geod., 55: 537–556.CrossrefWeb of ScienceGoogle Scholar

  • [31]

    Luo X, Mayer M, Heck B (2012) Analysing time series of GNSS residuals by means of AR(I)MA processes. In: N. Sneeuwet al.(eds.), VII Hotine-Marussi Symposium on Mathematical Geodesy, International Association of Geodesy Symposia 137, Springer, Berlin.Google Scholar

  • [32]

    Neumann I, Kutterer H (2006) Geodetic Deformation Analysis with Respect to Observation Imprecision. XXIII FIG Congress Munich, Germany, October 8–13. http://www.fig.net/pub/fig2006/papers/ts68/ts68_05_neumann_kutterer_0573.pdf.Google Scholar

  • [33]

    Neumann I, Kutterer H (2007) Congruence Tests and Outlier Detection In Deformation Analysis With Respect To Observation Imprecision. Journal of Applied Geodesy, 1(1): 1–7, DOI .CrossrefGoogle Scholar

  • [34]

    Niemeier W (2008) Ausgleichungsrechnung, Statistische Auswertemethoden. 2nd edn., de Gruyter, Berlin.Google Scholar

  • [35]

    Pelzer H (1971) Zur Analyse geodätischer Deformationsmessungen. Deutsche Geodätische Kommission, Reihe C, Nr. 164, München.

  • [36]

    Pope AJ (1976) The statistics of residuals and the detection of outliers. NOAA Technical Report NOS65 NGS1, US Department of Commerce, National Geodetic Survey Rockville, Maryland. http://www.ngs.noaa.gov/PUBS_LIB/TRNOS65NGS1.pdf.Google Scholar

  • [37]

    Teunissen PJG (2000) Testing theory; an introduction. 2nd edn., Series on Mathematical Geodesy and Positioning, Delft University of Technology, The Netherlands.Google Scholar

  • [38]

    Velsink H (2015) On the deformation analysis of point fields. J Geod, 89(11): 1071–1087, DOI .CrossrefGoogle Scholar

  • [39]

    Welsch WM (1983) Deformationsanalysen ’83 – Geometrische Analyse und Interpretation von Deformationen geodätischer Netze. Beiträge zum Geodätischen Seminar, 22. April 1983. Wissenschaftlicher Studiengang Vermessungswesen, Hochschule der Bundeswehr München, 9, ISSN 0173-1009.Google Scholar

About the article

Received: 2016-12-21

Accepted: 2017-08-25

Published Online: 2017-09-15

Published in Print: 2017-12-01

Citation Information: Journal of Applied Geodesy, Volume 11, Issue 4, Pages 271–283, ISSN (Online) 1862-9024, ISSN (Print) 1862-9016, DOI: https://doi.org/10.1515/jag-2016-0049.

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