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Prof. Dr.-Ing. Rüdiger Lehmann

Capacities / Funktionen

Research / Forschung

      Researchgate Score: 22.3       h-index: 9 (excluding self-citations)

      My main scientific interests are directed towards developing new estimation techniques for ever more complex geodetic observation models, to enhance the retrieval of valuable information from the measurements in terms of accuracy, reliability, and computational efficiency. Such novel techniques include outlier detection, robust estimation, advanced methods of hypothesis testing and model selection in geodetic adjustment models as well as Monte Carlo techniques for geodetic data analysis.

      18th century: C.F. Gauß invented the geodetic adjustment by least squares, which is solvable by pencil and paper (Gaussian algorithm).

      19th century: F.W. Bessel and others realized that the stochastic model of least squares adjustment often does not describe practical observations well. However, better models could not be established due to lack of computing power.

      20th century: K. Zuse and others developped the electronic computer

      21st century: Geodesists continue to use primarily Gaussian least squares.

      Currently in print / Momentan im Druck:

      Type-Constrained Total Least Squares Fitting of Curved Surfaces to 3D Point Clouds

      co-authored by: none

      abstract: We present a unified approach to curved surface fitting in the framework of total least squares. Compared to algebraic and geometric fitting of surface models to 3D point cloud, this approach is relatively new. It has the largest degree of generality, such that any conceivable surface fitting problem can be formulated within this framework. In our contribution we consider quadric surfaces, which represent a very large and most popular class of curved surfaces. We discuss aspects of parametrizations and the use of constraints to restrict the set of solutions to special types of quadrics, like planes, spheres, ellipsoids, hyperboloids, cubes, cuboids, toroids, cylinders, cones, pyramids etc. Then we propose an iterative solution using Lagrange multipliers and the Newton method. The choice of an initial guess is discussed. Finally, we present a numerical example: fitting an elliptic cylinder with oblique axis to 20 data points. The results show that the total least squares fitting using type-constraints can be generally recommended to fit curved surfaces to point clouds.

      keywords: Quadric Surfaces; Point Cloud Fitting; Newton Method; Total Least Squares; Lagrange Multipliers

      to appear in: Journal of Mathematical and Statistical Analysis

      doi: not yet assigned

      Recent publications / Aktuelle Veröffentlichungen (ab 2008)

      Hypothesis Testing in Non-Linear Models Exemplified by the Planar Coordinate Transformations
      Journal of Geodetic Science, Volume 8, Issue 1, Pages 98–114 (2018) DOI:10.1515/jogs-2018-0009 (together with M. Lösler)
      A half-century of Baarda’s concept of reliability: a review, new perspectives, and applications
      Survey Review 2018: ahead of print (together with Vinicius Francisco Rofatto, M. T. Matsuoka, I. Klein, M. R. Veronez, M. L. Bonimani)
      A universal and robust computation procedure for geometric observations
      Survey Review, Volume 50, Issue 361, Pages 364-372 (2018). DOI 10.1080/00396265.2017.1279844
      Congruence analysis of geodetic networks – hypothesis tests versus model selection by information criteria
      Journal of Applied Geodesy, Volume 11, Issue 4, Pages 271–283 (2017). DOI: 10.1515/jag-2016-0049 (together with M. Lösler)
      Modellselektion mittels Akaike-Informationskriterium – Anwendung in der Kongruenzanalyse
      Allgemeine Vermessungs-Nachrichten 05/2017 (zusammen mit M. Lösler und C. Eschelbach)
      On the statistical power of Baarda’s outlier test and some alternative
      Journal of Geodetic Science, Volume 7, Issue 1, Pages 68–78 (2017). DOI:10.1515/jogs-2017-0008 (together with A. Voß-Böhme)
      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
      Multiple outlier detection: hypothesis tests versus model selection by information criteria
      Journal of Surveying Engineering, Volume 142, Issue 4 (2016) (together with M. Lösler)
      Multiple outlier detection: hypothesis tests versus model selection by information criteria
      OPEN ACCESS of original via Qucosa (2015) (together with M. Lösler)
      Ein automatisches Verfahren für geodätische Berechnungen
      Allgemeine Vermessungs-Nachrichten 03/2015
      Ein automatisches Verfahren für geodätische Berechnungen
      OPEN ACCESS of original via Qucosa (2015)
      Observation error model selection by information criteria vs. normality testing
      Studia Geophysica et Geodetica, Volume 59, Issue 4, Pages 489-504 (2015), DOI: 10.1007/s11200-015-0725-0
      Detection of a sinusoidal oscillation of unknown frequency in a time series - a geodetic approach
      Journal of Geodetic Science, Volume 4, Issue 1, ISSN (Online) 2081-9943 (2014), DOI: 10.2478/jogs-2014-0015 (OPEN ACCESS)
      Transformation model selection by multiple hypotheses testing
      Journal of Geodesy, Volume 88, Issue 12, Pages 1117-1130 (2014), DOI:10.1007/s00190-014-0747-3
      Transformation model selection by multiple hypotheses testing
      OPEN ACCESS of postprint via Qucosa (2014)
      The usage of recursive parameter estimation in automated reference point determination
      Geophysical Research Abstracts Vol. 16, EGU2014-11215, 2014 (together with T. Lossin, M. Lösler, A. Neidhardt, S. Mähler, and Th. Klügel)
      Geodetic investigation of accuracy and reliability of INS/GNSS system iTraceRT-F200-E for navigation in tunnels
      IEEE Xplore 2014, DOI 10.1109/WPNC.2014.6843285 (together with A. Bilajbegovic)
      The usage of recursive parameter estimation in automated reference point determination
      General Meeting of the International VLBI Service for Geodesy and Astrometry (IVS) Shanghai March 2-7, 2014 (together with T. Lossin, M. Lösler, A. Neidhardt, S. Mähler)
      Langzeitmonitoring zur Überwachung des geodätischen Referenzpunktes eines VLBI2010-Radioteleskops
      Beitrag zum 129. DVW-Seminar "Zeitabhängige Messgrößen – Ihre Daten haben (Mehr-)Wert" am 26. und 27. Februar 2014 in Hannover, DVW-Schriftenreihe Band 74, Wissner Verlag (zusammen mit M. Lösler, T. Lossin, A. Neidhardt)
      Ausreißererkennung in geodätischen Zeitreihen
      Beitrag zum 129. DVW-Seminar "Zeitabhängige Messgrößen – Ihre Daten haben (Mehr-)Wert" am 26. und 27. Februar 2014 in Hannover, DVW-Schriftenreihe Band 74, Wissner Verlag
      Untersuchung zur automatisierten Bestimmung des IVS-Referenzpunktes am TWIN Radioteleskop Wettzell
      In: Wieser, A. (Hrsg): Ingenieurvermessung 14: Beiträge zum 17. Internationalen Ingenieurvermessungskurs Zürich, 14.-17. Januar 2014, Wichmann, S. 335-346, ISBN: 978-3879075355, 2014 (zusammen mit M. Lösler, T. Lossin, A. Neidhardt)
      Untersuchung zur automatisierten Bestimmung des IVS-Referenzpunktes am TWIN Radioteleskop Wettzell
      OPEN ACCESS of postprint via Qucosa (2014) (together with M. Lösler, T. Lossin, A. Neidhardt)
      The 3sigma-rule for outlier detection from the viewpoint of geodetic adjustment
      Journal of Surveying Engineering, Volume 139, Issue 4, Pages 157–165 (2013), DOI 10.1061/(ASCE)SU.1943-5428.0000112
      Testing the compatibility of constraints for parameters of a geodetic adjustment model
      Journal of Geodesy, Volume 87, Issue 6, Pages 555-566 (2013), DOI: 10.1007/s00190-013-0627-2 (together with F. Neitzel)
      Testing the compatibility of constraints for parameters of a geodetic adjustment model
      OPEN ACCESS of postprint via Qucosa (2013) (together with F. Neitzel)
      On the formulation of the alternative hypothesis for geodetic outlier detection
      Journal of Geodesy, Volume 87, Issue 4, Pages 373-386 (2013), DOI: 10.1007/s00190-012-0607-y
      Improved critical values for extreme normalized and studentized residuals in Gauss–Markov models
      Journal of Geodesy, Volume 86, Issue 12, Pages 1137–1146 (2012), DOI: 10.1007/s00190-012-0569-0
      Geodätische Fehlerrechnung mit der skalenkontaminierten Normalverteilung
      Allgemeine Vermessungsnachrichten 5/2012. VDE-Verlag Offenbach
      Monte Carlo based data snooping with application to a geodetic network (together with T. Scheffler)
      Journal of Applied Geodesy, Volume 5, Issue 3-4, Pages 123–134 (2011), DOI: 10.1515/JAG.2011.014
      Normierte Verbesserungen – wie groß ist zu groß?
      Allgemeine Vermessungsnachrichten 2/2010. VDE-Verlag Offenbach
      Conveyance of large cruise liners – Geodetic investigation of rolling and track prediction (zusammen mit B. Koop)
      Journal of Applied Geodesy, Volume 3, Issue 3, Pages 131–141 (2009), DOI: 10.1515/JAG.2009.014
      Filterung geodätischer Daten bei der Ems-Überführung von Kreuzfahrtschiffen (PDF | 460 KB)
      Beitrag zum 85. DVW-Seminar ''Zeitabhängige Messgrößen - verborgene Schätze in unseren Daten'' am 7. und 8. September 2009 in Kassel. Schriftenreihe des DVW e.V. - Gesellschaft für Geodäsie, Geoinformation und Landmanagement Band 59/2009, Seite 211-223
      Geodetic Investigation of Ship Roll Estimation for Manoeuvring Control of Cruise Liner Conveyance (PDF | 415 KB)
      In: A. Härting & J. Reinking (Eds.) Nautic Aspects of Ship Dynamics, Elsflether Schriften zur Seeverkehrs- und Hafenwirtschaft, Vol. 4, pp. 167-176, 2009 (together with B. Koop)
      Navigation of large cruise liners built by Meyer Werft, Germany (PDF | 459 KB)
      Contribution to Conference Proceedings of POSITIONs 2008, Dresden 7.-9.10.2008, pp. 313-325 (together with B. Koop)
      Das arithmetische Mittel von Mehrfachmessungen unter Wiederholbedingungen
      Allgemeine Vermessungsnachrichten 01/2008. VDE-Verlag Offenbach
      Does GNSS outperform GPS in Geodetic Applications? (PDF | 621 KB)
      Contribution to Conference Proceedings of POSITIONs 2008, Dresden 7.-9.10.2008, pp. 313-325 (together with A. Bilajbegovic)
      Aktualisiert: 23.04.2019  |  Autor: R. Lehmann