Details
| Original language | English |
|---|---|
| Pages (from-to) | 215-230 |
| Number of pages | 16 |
| Journal | Journal of Applied Geodesy |
| Volume | 11 |
| Issue number | 4 |
| Publication status | Published - 26 Oct 2017 |
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
- B-spline approximation, deformations, Gauss-Markov model, GUM, model misspecification test, model selection test, Terrestrial laser scanning, uncertainty budget
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Engineering (miscellaneous)
- Earth and Planetary Sciences(all)
- Earth and Planetary Sciences (miscellaneous)
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In: Journal of Applied Geodesy, Vol. 11, No. 4, 26.10.2017, p. 215-230.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Statistical evaluation of the influence of the uncertainty budget on B-spline curve approximation
AU - Zhao, Xin
AU - Alkhatib, Hamza
AU - Kargoll, Boris
AU - Neumann, Ingo
N1 - Publisher Copyright: © 2017 Walter de Gruyter GmbH, Berlin/Boston. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/10/26
Y1 - 2017/10/26
N2 - 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.
AB - 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.
KW - B-spline approximation
KW - deformations
KW - Gauss-Markov model
KW - GUM
KW - model misspecification test
KW - model selection test
KW - Terrestrial laser scanning
KW - uncertainty budget
UR - http://www.scopus.com/inward/record.url?scp=85030320607&partnerID=8YFLogxK
U2 - 10.1515/jag-2017-0018
DO - 10.1515/jag-2017-0018
M3 - Article
AN - SCOPUS:85030320607
VL - 11
SP - 215
EP - 230
JO - Journal of Applied Geodesy
JF - Journal of Applied Geodesy
SN - 1862-9016
IS - 4
ER -