Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Applied Geodesy

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

4 Issues per year


CiteScore 2016: 1.09

SCImago Journal Rank (SJR) 2016: 0.367
Source Normalized Impact per Paper (SNIP) 2016: 0.908

Online
ISSN
1862-9024
See all formats and pricing
More options …
Ahead of print

Issues

Statistical evaluation of the influence of the uncertainty budget on B-spline curve approximation

Xin Zhao
  • Corresponding author
  • Geodetic Institute, 26555 Leibniz Universität Hannover, Nienburger Str. 1, 30167 Hannover, Germany
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Hamza Alkhatib / Boris Kargoll / Ingo Neumann
Published Online: 2017-07-25 | DOI: https://doi.org/10.1515/jag-2017-0018

Abstract

In the field of engineering geodesy, terrestrial laser scanning (TLS) has become a popular method for detecting deformations. This paper analyzes the influence of the uncertainty budget on free-form curves modeled by B-splines. Usually, free-form estimation is based on scanning points assumed to have equal accuracies, which is not realistic. Previous findings demonstrate that the residuals still contain random and systematic uncertainties caused by instrumental, object-related and atmospheric influences. In order to guarantee the quality of derived estimates, it is essential to be aware of all uncertainties and their impact on the estimation.

In this paper, a more detailed uncertainty budget is considered, in the context of the “Guide to the Expression of Uncertainty in Measurement” (GUM), which leads to a refined, heteroskedastic variance covariance matrix (VCM) of TLS measurements. Furthermore, the control points of B-spline curves approximating a measured bridge are estimated. Comparisons are made between the estimated B-spline curves using on the one hand a homoskedastic VCM and on the other hand the refined VCM. To assess the statistical significance of the differences displayed by the estimates for the two stochastic models, a nested model misspecification test and a non-nested model selection test are described and applied. The test decisions indicate that the homoskedastic VCM should be replaced by a heteroskedastic VCM in the direction of the suggested VCM. However, the tests also indicate that the considered VCM is still inadequate in light of the given data set and should therefore be improved.

Keywords: Terrestrial laser scanning; deformations; uncertainty budget; GUM; B-spline approximation; Gauss-Markov model; model misspecification test; model selection test

References

  • [1]

    Alkhatib, H. and Kutterer, H. (2013). Estimation of measurement uncertainty of kinematic TLS observation process by means of Monte-Carlo methods. Journal of Applied Geodesy, 7(2):125–134.Google Scholar

  • [2]

    Alkhatib, H., Neumann, I., and Kutterer, H. (2009). Uncertainty modeling of random and systematic errors by means of Monte Carlo and fuzzy techniques. Journal of Applied Geodesy, 3(2):67–79.Google Scholar

  • [3]

    Alkhatib, H., Schmitt, C., and Neumann, I. (2014). Spatial approximation of terrestrial laser scanner profiles by considering observations with stochastic information. In Proceedings of the XXV FIG Congress. Engaging the Challenges, Enhancing the Relevance, Kuala Lumpur.Google Scholar

  • [4]

    Baltsavias, E. P. (1999). Airborne laser scanning: basic relations and formulas. ISPRS Journal of photogrammetry and remote sensing, 54(2):199–214.Google Scholar

  • [5]

    Balzani, M., Pellegrinelli, A., Perfetti, N., and Uccelli, F. (2001). A terrestrial laser scanner: accuracy tests. In 18th International Symposium CIPA, Potsdam, Germany.Google Scholar

  • [6]

    Barrell, H. and Sears, J. (1939). The refraction and dispersion of air for the visible spectrum. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 238(786):1–64.Google Scholar

  • [7]

    Borah, D. K. and Voelz, D. G. (2007). Estimation of laser beam pointing parameters in the presence of atmospheric turbulence. Applied Optics, 46(23):6010–6018.CrossrefWeb of ScienceGoogle Scholar

  • [8]

    Bureick, J., Alkhatib, H., and Neumann, I. (2016). Robust spatial approximation of laser scanner point clouds by means of free–form curve approaches in deformation analysis. Journal of Applied Geodesy, 10(1):27–35.Google Scholar

  • [9]

    Cox, D. R. (1961). Tests of separate families of hypotheses. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics, pages 105–123, Berkeley, Calif., University of California Press.Google Scholar

  • [10]

    Eling, D., 2009 Terrestrisches Laserscanning für die Bauwerksüberwachung, Ph.D. thesis, Leibniz Universität Hannover.Google Scholar

  • [11]

    Fernández Pareja, T., García Pablos, A., and de Vicente y Oliva, J. (2013). Terrestrial laser scanner (TLS) equipment calibration. Procedia Engineering, 63:278–286.Google Scholar

  • [12]

    Gordon, B. (2008). Zur Bestimmung von Messunsicherheiten terrestrischer Laserscanner, Ph.D. thesis, Technische Universität Darmstadt.Google Scholar

  • [13]

    Gumus, K. and Erkaya, H. (2011). Analyzing the geometric accuracy of simple shaped reference object models created by terrestrial laser scanners. International Journal of Physical Sciences, 6(28):6529–6536.Google Scholar

  • [14]

    Harmening, C., Kauker, S., Neuner, H.-B., and Schwieger, V. (2016). Terrestrial laserscanning–modeling of correlations and surface deformations. In FIG Working Week 2016 Recovery from Disaster, Christchurch, New Zealand.Google Scholar

  • [15]

    Hejbudzka, K., Lindenbergh, R., Soudarissanane, S., and Humme, A. (2010). Influence of atmospheric conditions on the range distance and number of returned points in Leica Scanstation 2 point clouds. In Proceedings ISPRS Commission V Mid-Term Symposium-Close Range Image Measurement Techniques, Newcastle upon Tyne, UK, 21–24 June 2010; IAPRS, XXXVIII (5), 2010.Google Scholar

  • [16]

    ISO (2005). Optics and optical instruments–Field procedures for testing geodetic and surveying instruments–Part 5: Electronic tacheometers. International Organization of Standardization.

  • [17]

    ISO/IEC (2008a). Evaluation of Measurement Data–Supplement 1 to the “Guide to the Expression of Uncertainty in Measurement”–Propagation of distributions using a Monte Carlo method. Geneva.

  • [18]

    ISO/IEC (2008b). Uncertainty of measurement – Part 3: Guide to the expression of uncertainty in measurement (GUM:1995 with minor corrections). Geneva.

  • [19]

    Joeckel, R., Stober, M., and Huep, W. (2008). Elektronische Entfernungsmessung und ihre Integration in aktuelle Positionierungsverfahren. Wichmann.Google Scholar

  • [20]

    Kargoll, B. (2012). On the Theory and Application of Model Misspecification Tests in Geodesy. Ph.D. thesis, Deutsche Geodätische Kommission, Series C, No. 674.Google Scholar

  • [21]

    Kauker, S. and Schwieger, V. (2016). First investigations for a synthetic covariance matrix for monitoring by terrestrial laser scanning. In 3rd Joint International Symposium on Deformation Monitoring, Volume 30.Google Scholar

  • [22]

    Kauker, S. and Schwieger, V. (2017). A synthetic covariance matrix for monitoring by terrestrial laser scanning. Journal of Applied Geodesy, 11(2):77–87.Google Scholar

  • [23]

    Koch, K.-R. (1999). Parameter Estimation and Hypothesis Testing in Linear Models. Springer.Google Scholar

  • [24]

    Koch, K.-R. (2008). Evaluation of uncertainties in measurements by Monte Carlo simulations with an application for laserscanning. Journal of Applied Geodesy, 2(2):67–77.Google Scholar

  • [25]

    Koch, K.-R. (2009). Fitting free-form surfaces to laserscan data by NURBS. Allgemeine Vermessungs-Nachrichten, 116:134–140.Google Scholar

  • [26]

    Koch, K.-R. (2015). Minimal detectable outliers as measures of reliability. Journal of Geodesy, 89:483–490.Web of ScienceGoogle Scholar

  • [27]

    Lichti, D. D., Gordon, S. J., and Tipdecho, T. (2005). Error models and propagation in directly georeferenced terrestrial laser scanner networks. Journal of Surveying Engineering, 131(4):135–142.Google Scholar

  • [28]

    Lichti, D. D. and Harvey, B. (2002). The effects of reflecting surface material properties on time-of-flight laser scanner measurements. In Symposium on Geospatial Theoty, Processing and Applications, Ottawa, Canada, Vol. 2.Google Scholar

  • [29]

    Lichti, D. D., Stewart, M., Tsakiri, M., and Snow, A. (2000). Calibration and testing of a terrestrial laser scanner. International archives of Photogrammetry and Remote sensing, 33(B5/2; PART 5):485–492.Google Scholar

  • [30]

    Mazalová, J., Valentová, K., and Vlčková, L. (2010). Testing of accuracy of reflectorless distance measurement of selected Leica and Topcon total stations. GeoScience Engineering, 56(1):19–26.Google Scholar

  • [31]

    Neitzel, F. (2007). Investigation of axes errors of terrestrial laser scanners. In Fifth International Symposium Turkisch-German Joint Geodetic Days, Berlin, Germany.Google Scholar

  • [32]

    Neuner, H., Schmitt, C., and Neumann, I. (2014). Zur Bestimmung der verkehrsseitig verursachten Dehnung an einem Brückentragwerk mittels terrestrischem Laserscanning. In A. Wieser (ed.): Ingenieurvermessung’14. Beiträge zum 17. Internationalen Ingenieurvermessungskurs Zürich, pages 231–243. Wichmann.Google Scholar

  • [33]

    NTH-BAU (2010). Life Cycle Enginnering for Enginnering Structures and Buildings Strategies and Methods. Topic 6: Application of life cycle concepts to civil engineering structures, 2010–2013, www.nth-bau.de.Google Scholar

  • [34]

    Piegl, L. and Tiller, W. (1997). The NURBS book. Springer Science & Business Media.Google Scholar

  • [35]

    Reshetyuk, Y. (2006). Investigation and calibration of pulsed time-of-flight terrestrial laser scanners. Ph.D. thesis, Royal Institute of Technology (KYH).Google Scholar

  • [36]

    Rüeger, J. M. (1990). Electronic distance measurement. Springer.Google Scholar

  • [37]

    Schulz, T. (2007). Calibration of a terrestrial laser scanner for engineering geodesy. Ph.D. thesis, ETH ZURICH.Google Scholar

  • [38]

    Sommer, K. and Siebert, B. (2004). Praxisgerechtes Bestimmen der Messunsicherheit nach GUM. Technisches Messen, 71:52–60.Google Scholar

  • [39]

    Soudarissanane, S. and Lindenbergh, R. (2011). Optimizing terrestrial laser scanning measurement set-up. In ISPRS Workshop Laser Scanning 2011, Calgary, Canada, 29–31 August 2011; IAPRS, XXXVIII (5/W12), 2011.Google Scholar

  • [40]

    Soudarissanane, S., Lindenbergh, R., Menenti, M., and Teunissen, P. (2011). Scanning geometry: influencing factor on the quality of terrestrial laser scanning points. ISPRS Journal of Photogrammetry and Remote Sensing, 66(4):389–399.Google Scholar

  • [41]

    Williams, D. A. (1970). Discrimination between regression models to determine the pattern of enzyme synthesis in synchronous cell cultures. Biometrics, 26(1):23–32.CrossrefGoogle Scholar

  • [42]

    Wujanz, D., Mettenleiter, M., Burger, M., and Neitzel, F. (2016). Viewpoint planning for terrestrial laser scanning utilising an intensity based stochastic model. In 3rd Joint International Symposium on Deformation Monitoring (JISDM).Google Scholar

  • [43]

    Zámečníková, M., Neuner, H., and Pegritz, S. (2014a). Influence of the incidence angle on the reflectorless distance measurement in close range. In INGEO 2014 – 6th International Conference on Engineering Surveying, Prague, Czech Republic.Google Scholar

  • [44]

    Zámečníková, M., Neuner, H., Pegritz, S., and Sonnleitner, R. (2015). Investigation on the influence of the incidenceangle on the reflectorless distance measurement of a terrestrial laser scanner. Vermessung & Geoinformation, 2(3):208–218.Google Scholar

  • [45]

    Zámečníková, M., Wieser, A., Woschitz, H., and Ressl, C. (2014b). Influence of surface reflectivity on reflectorless electronic distance measurement and terrestrial laser scanning. Journal of Applied Geodesy, 8(4):311–326.Google Scholar

  • [46]

    Zoller+Fröhlich (2007). Technical datasheet IMAGER 5006. Zoller+Fröhlich GmbH.

About the article

Received: 2017-05-05

Accepted: 2017-07-04

Published Online: 2017-07-25


Citation Information: Journal of Applied Geodesy, ISSN (Online) 1862-9024, ISSN (Print) 1862-9016, DOI: https://doi.org/10.1515/jag-2017-0018.

Export Citation

© 2017 Walter de Gruyter GmbH, Berlin/Boston. Copyright Clearance Center

Comments (0)

Please log in or register to comment.
Log in