Home Congruence analysis of geodetic networks – hypothesis tests versus model selection by information criteria
Article
Licensed
Unlicensed Requires Authentication

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

  • Rüdiger Lehmann EMAIL logo and Michael Lösler
Published/Copyright: September 15, 2017
Become an author with De Gruyter Brill

Abstract

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.

References

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

[2] Akaike H (1974) A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19: 716–723.10.1109/TAC.1974.1100705Search in Google 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.Search in Google Scholar

[4] Aydin C (2012) Power of Global Test in Deformation Analysis. J Surv Eng, 138(2): 51–56, DOI 10.1061/(ASCE)SU.1943-5428.0000064.Search in Google 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.10.54419/t8w4sgSearch in Google Scholar

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

[8] Burnham KP, Anderson DR (2002) Model Selection and Multimodel Inference: A Practical Information-theoretic Approach. Springer, Berlin.Search in 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 10.1177/0049124104268644.Search in Google Scholar

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

[16] Heunecke O, Kuhlmann H, Welsch WM, Eichhorn A, Neuner H (2013) Handbuch Ingenieurgeodäsie: Auswertung geodätischer Überwachungsmessungen. 2nd edn., Wichmann, Heidelberg.Search in 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.Search in 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 10.1007/s00190-002-0291-4.Search in Google Scholar

[19] Koch KR (1999) Parameter Estimation and hypothesis testing in linear models. 2nd edn., Springer, Heidelberg, DOI 10.1007/978-3-662-03976-2.Search in Google Scholar

[20] Kullback S, Leibler RA (1951) On information and sufficiency. Annals of Mathematical Statistics, 22(1): 79–86, DOI 10.1214/aoms/1177729694.Search in Google 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 10.1007/s001900050253.Search in Google Scholar

[22] Lehmann R (2014) Transformation model selection by multiple hypothesis testing. J Geod, 88(12): 1117–1130, DOI 10.1007/s00190-014-0747-3.Search in Google Scholar

[23] Lehmann R (2015) Observation error model selection by information criteria vs. normality testing. Stud. Geophys. Geod, 59(4): 489–504, DOI 10.1007/s11200-015-0725-0.Search in Google 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.Search in 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 10.1061/(ASCE)SU.1943-5428.0000189.Search in Google 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 10.1007/s00190-013-0627-2.Search in Google 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 10.1007/s00190-016-0887-8.Search in Google 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 10.12902/zfv-0147-2016.Search in Google 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.Search in 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: 537–556.10.1007/s11200-011-0033-2Search in Google 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.10.1007/978-3-642-22078-4_19Search in 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.Search in 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 10.1515/jag.2007.001.Search in Google Scholar

[34] Niemeier W (2008) Ausgleichungsrechnung, Statistische Auswertemethoden. 2nd edn., de Gruyter, Berlin.10.1515/9783110206784Search in Google Scholar

[35] Pelzer H (1971) Zur Analyse geodätischer Deformationsmessungen. Deutsche Geodätische Kommission, Reihe C, Nr. 164, München.Search in Google Scholar

[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.Search in Google Scholar

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

[38] Velsink H (2015) On the deformation analysis of point fields. J Geod, 89(11): 1071–1087, DOI 10.1007/s00190-015-0835-z.Search in Google 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.Search in Google Scholar

Received: 2016-12-21
Accepted: 2017-8-25
Published Online: 2017-9-15
Published in Print: 2017-12-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 26.10.2025 from https://www.degruyterbrill.com/document/doi/10.1515/jag-2016-0049/html?lang=en
Scroll to top button