Distribution-free Uncertainty Description for TLS-based Areal Deformation Analysis

• Applicant: Professor Dr.-Ing. Steffen Schön
• Subject Area: Geodesy, Photogrammetry, Remote Sensing, Geoinformatics, Cartography
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 490989047

We usually assume that (a) systematic errors in the deformation analysis only evolve out of the measurement process and that (b) these errors can be reduced by calibrating the instrument or by applying adequate measurement strategies. However, for geodetic terrestrial laser scanning (TLS), this is not always the case: the measurements are internally preprocessed with functions unknown to the user, calibration parameters might not describe the misalignments accurately enough, the laser beam interacts unpredictably with the measured surface, the surface model uncertainty exists, and laser scans are transformed in a combined geodetic datum. Subsequently, systematics remains, and the total uncertainty budget for the deformation analysis must be completed in order to deliver sound statements about the occurrence of a potential deformation. We propose to enclose the observation uncertainties due to remaining systematics by the most natural approach, i.e., deterministic intervals. We will use concepts from interval mathematics for their treatment. This approach is thus free of any assumption about the statistical distribution of the observations or their stochasticity. Thanks to their intrinsic linear uncertainty propagation, intervals are especially suited to treat remaining systematic errors. The objective of this project is the development, implementation, testing, and validation of concepts and strategies based on interval mathematics on how to treat the uncertainty about remaining systematics through all necessary steps of the observation analysis in TLS-based areal deformation analysis. In phase I of this research unit, we will focus on developing (i) concepts to enclose the remaining observation uncertainty of terrestrial laser scanners by intervals, thus being free of any assumption about the stochastic error distribution, (ii) approaches to transfer the observation uncertainty to point uncertainty of the TLS point cloud and (iii) strategies to assess the uncertainty of the areal approximations in the framework of interval fields. This project will contribute to complete the uncertainty budget of geodetic TLS measurements and to derive deterministic uncertainty bounds for TLS-derived surfaces as steps towards area-based deformation analysis.

• DFG Programme: Research Units
• Subproject of: FOR 5455: Deformation analysis based on terrestrial laser scanner measurements (TLS-Defo)
• Co-Investigator: Professor Dr.-Ing. Ingo Neumann