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Influence of the uncertainty budget on B-Spline curve estimation

Influence of the uncertainty budget on B-Spline curve estimation

Leaders:  Ingo Neumann, Boris Kargoll, Hamza Alkhatib
Team:  Xin Zhao
Year:  2017
Date:  01-01-17
Lifespan:  since 2017

Project description

In order to guarantee the quality of a freeform curve and to get more meaningful analysis results, it is essential to be aware of all uncertainties resources and their impact on the estimation. In this work, a more sophisticated uncertainty budget is considered, that contributes to a refined covariance matrix. Uncertainties are modelled and propagated according to the “Guide to the Expression of Uncertainty in Measurements (GUM)”. Furthermore, control points of B-Spline curves are estimated by means of the least-squares methods based on the refined VCM. Comparison have been made between the B-Spline curves using identity and refined weight matrix, which reflects that the uncertainty influence within the estimation cannot be neglected for high quality results.

In the of engineering geodesy, Terrestrial Laser Scanning (TLS) has become a popular method to detect deformations and displacements. The uncertainty of TLS measurements has been studied by many authors. For this reason, this paper analysis the influence of the uncertainty budget on deduced products like the free form curves, i.e. B-Spline curves.

In many cases, the free form estimation is based on scanning thesis test that the residuals still contain random and system uncertainties caused by instrumental, object-related as well as atmospheric influence. In order to guarantee the quality of free form curve and to get more credible analysis results, it is essential to be aware of all uncertainties and their impact on the estimation.

In this project, a more detailed uncertainty budget is considered, in the context of "Guide to the Expression of Uncertainty in Measurement" (GUM), which leads to a refined covariance matrix of TLS measurements. Further, more control points of B-Spline curve are estimated by means of the least-squares methods based on the refined covariance matrix.

Comparison have been made between the B-Spline curves using identity and refined weight matrix, which reflects that uncertainty influence on estimation cannot be neglected when it became obvious. Overlapping variance component test presents a statistics support to this conclusion. Further work will quantify the range of values in the uncertainties. Additionally, recommendation will be developed that show how to take care about the statistic information within B-Spline curve estimation.