Abstract
In terms of high precision requested deformation analyses, evaluating laser scan data requires the exact knowledge of the functional and stochastic model. If this is not given, a parameter estimation leads to insufficient results. Simulating a laser scanning scene provides the knowledge of the exact functional model of the surface. Thus, it is possible to investigate the impact of neglecting spatial correlations in the stochastic model. Here, this impact is quantified through statistical analysis.
The correlation function, the number of scanning points and the ratio of colored noise in the measurements determine the covariances in the simulated observations. It is shown that even for short correlation lengths of less than 10 cm and a low ratio of colored noise the global test as well as the parameter test are rejected. This indicates a bias and inconsistency in the parameter estimation. These results are transferable to similar tasks of laser scanner based surface approximation.
References
[1] Ishimaru A., Wave Propagation and Scattering in Random Media, Wiley-IEEE Press, 1997.Search in Google Scholar
[2] Pesci A., Teza G., Bonali E., Casula G. and Boschi E., A laser scanning-based method for fast estimation of seismic-induced building deformations, ISPRS Journal of Photogrammetry and Remote Sensing 79 (2013), 185–198.10.1016/j.isprsjprs.2013.02.021Search in Google Scholar
[3] Harmening C., Kauker S., Neuner H. and Schwieger V., Terrestrial Laserscanning – Modeling of Correlations and Surface Deformations, FIG Working Week 2016, Chirstchurch, New Zealand (2016).Search in Google Scholar
[4] Hesse C. and Kutterer H., Automated Form Recognition of Laser Scanned Deformable Objects, Geodetic Deformation Monitoring: From Geophysical to Engineering Roles 131 (2005), 103–111.10.1007/978-3-540-38596-7_12Search in Google Scholar
[5] Holst C., Nothnagel A., Blome M., Becker P., Eichborn M. and Kuhlmann H., Improved area-based deformation analysis of a radio telescopes main reflector based on terrestrial laser scanning, Journal of Applied Geodesy 9 (2014), 1–13.10.1515/jag-2014-0018Search in Google Scholar
[6] Holst C. and Kuhlmann H., Challenges and Present Fields of Action at Laser Scanner Based Deformation Analyses, Journal of Applied Geodesy 10 (2016), 17–25.10.1515/jag-2015-0025Search in Google Scholar
[7] Holst C., Neuner H., Wieser A., Wunderlich T. and Kuhlmann H., Calibration of Terrestrial Laser Scanner, Allgemeine Vermessungs-Nachrichten 6 (2016).Search in Google Scholar
[8] Holst C., Artz T. and Kuhlmann H., Biased and unbiased estimates based on laser scans of surfaces with unknown deformations, Journal of Applied Geodesy 8 (2014), 169–183.10.1515/jag-2014-0006Search in Google Scholar
[9] Rasmussen C. and Williams C., Gaussian Processes for Machine Learning, MIT Press, Cambridge, 2006.10.7551/mitpress/3206.001.0001Search in Google Scholar
[10] Eling D., Terrestrisches Laserscanning für die Bauwerksüberwachung, Ph.D. thesis, Leibniz Universität Hannover, 2009.10.1127/0935-1221/2009/0001Search in Google Scholar
[11] Lichti D., Stewart M., Tsakiri M. and Snow J., Calibration and testing of a terrestrial laser scanner, International Archives of Photogrammetry and Remote Sensing XXXIII (2000).Search in Google Scholar
[12] Schneider D. and Maas H.-G., Integrated bundle adjustment with varicance component estimation – fusion of terrestrial laser scanner data, panoramic and central perspective image data, ISPRS Workshop on Laser Scanning (2007).Search in Google Scholar
[13] Mikhail E. and Ackermann F., Observations and least squares, Dun-Donelly, New York, 1976.Search in Google Scholar
[14] Serantoni E. and Wieser A., TLS-based Deformation Monitoring of Snow Structures, Schriftenreihe des DVW Band 85, Terrestrisches Laserscanning (2016).Search in Google Scholar
[15] Kermarrec G. and Schön S., A priori fully populated covariance matrices in least squares adjustment – case study GPS: relative positioning, Journal of Geodesy (2016), 1–20.10.1007/s00190-016-0976-8Search in Google Scholar
[16] Kermarrec G. and Schön S., Taking correlations in GPS least squares adjustments into account with a diagonal covariance matrix, Journal of Geodesy 90 (2016), 793–805.10.1007/s00190-016-0911-zSearch in Google Scholar
[17] Leica Geosystems, Leia ScanStation P20 – data sheet, Leica Geosystems (2013).Search in Google Scholar
[18] Kuhlmann H., Importance of autocorrelation for parameter estimation in regression models, 10th FIG International Symposium on Deformation Measurements (2001).Search in Google Scholar
[19] Faro Technologies Inc., Faro Products – Portable systems for measurement and 3D documentation, (2012).Search in Google Scholar
[20] Wang J., Towards deformation monitoring with terrestrial laser scanning based on external calibration and feature matching methods, Ph.D. thesis, Leibniz Universtität Hannover, 2013.Search in Google Scholar
[21] Koch K.-R., Parameter Estimation and Hypothesis Testing in Linear Models, Springer, 1999.10.1007/978-3-662-03976-2Search in Google Scholar
[22] Koch K.-R., Introduction to Bayesian Statistics, Springer, 2007.Search in Google Scholar
[23] Koch K.-R., Determining uncertainties of correlated measurements by Monte Carlo simulations applied to laserscanning, Journal of Applied Geodesy 2 (2008).10.1515/JAG.2008.016Search in Google Scholar
[24] Zamecnikova M. and Neuner H., Untersuchung des gemeinsamen Einflusses des Auftreffwinkels und der Oberflächenrauheit auf die reflektorlose Distanzmessung beim Scanning, Ingenieurvermessung 17 (2017). Wichmann, Berlin, 63–76.Search in Google Scholar
[25] Zamecnikova M., Neuner H. and Pegritz S., Influence of the Incidence Angle on the Reflectorless Distance Measurement in Close Range, INGEO – 6th International Conference on Engineering Surveying, Prague (2014).Search in Google Scholar
[26] Zamecnikova M., Neuner H., Pegritz S. and Sonnleitner R., Investigation on the influence of the incidence angle on the reflectorless distance measurement of a terrestrial laser scanner, Vermessung und Geoinformation 2+3 (2015), 208–218.Search in Google Scholar
[27] Heunecke O., Kuhlmann H., Welsch W., Eichhorn A. and Neuner H., Auswertung geodätischer Überwachungsmessungen, Handbuch Ingenieurgeodäsie, (Moser M., Müller G. & Schlemmer H.), Heidelberg: Wichmann, 2. ed., 2013.Search in Google Scholar
[28] M. Peternell, Developable surface fitting to point clouds, Comput. Aided Geom. D. 21 (2004), 785–803.10.1016/j.cagd.2004.07.008Search in Google Scholar
[29] Kauker S., Holst C., Schwieger V., Kuhlmann H. and Schön S., Spatio-temporal Correlations of Terrestrial Laser Scanning, Allgemeine Vermessungs-Nachrichten 6 (2016), 170–182.Search in Google Scholar
[30] Kauker S. and Schwieger V., First investigations for a synthetic covariance matrix for monitoring by terrestrial laser scanning, Joint International Symposium on Deformation Monitoring (2016).10.1515/jag-2016-0026Search in Google Scholar
[31] Soudarissanane S., Lindenbergh R., Menenti M. and Teunissen P., Scanning geometry: Influencing factor on the quality of terrestrial laser scanning points, ISPRS Journal of Photogrammetry and Remote Sensing 66 (2011), 389–399.10.1016/j.isprsjprs.2011.01.005Search in Google Scholar
[32] Schulz T., Calibration of a Terrestrial Laser Scanner for Engineering Geodesy, Ph.D. thesis, Technical University of Berlin, 2007.Search in Google Scholar
[33] Schwieger V., Ein Elementarfehlermodell für GPS-Überwachungsmessungen – Konstruktion und Bedeutung interepochaler Korrelationen, Ph.D. thesis, Vermessungswesen der Universität Hannover, 1999.Search in Google Scholar
[34] Schwieger V., Nicht-lineare Sensitivitätsanalyse gezeigt an Beispielen zu bewegten Objekten, Habilitation, 2005.Search in Google Scholar
[35] Niemeier W., Ausgleichungsrechnung – Statistische Auswertemethoden, Berlin, Walter de Gruyter, 2008.10.1515/9783110206784Search in Google Scholar
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