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Journal of Applied Geodesy

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

CiteScore 2018: 1.61

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Source Normalized Impact per Paper (SNIP) 2018: 1.064

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Volume 11, Issue 4


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
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/ Hamza Alkhatib / Boris Kargoll / Ingo Neumann
Published Online: 2017-07-25 | DOI: https://doi.org/10.1515/jag-2017-0018


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


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About the article

Received: 2017-05-05

Accepted: 2017-07-04

Published Online: 2017-07-25

Published in Print: 2017-12-01

Citation Information: Journal of Applied Geodesy, Volume 11, Issue 4, Pages 215–230, ISSN (Online) 1862-9024, ISSN (Print) 1862-9016, DOI: https://doi.org/10.1515/jag-2017-0018.

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