Measurement Uncertainty: Determining generalized variance-covariance matrices of terrestrial laser scans considering all relevant error sources

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

Knowledge about the measurement uncertainty of an instrument is of vital importance in engineering tasks, such as deformation analyses. The corresponding stochastic information is needed to provide the answer if a geometric change is significant or just reasoned by errors of the instrument. Hence, a realistic stochastic model, usually defined by a variance-covariance-matrix (VCM), avoids the misinterpretation of errors in general, and correlations in specific, as deformations of the object. However, correct stochastic information about the measurement uncertainty of a terrestrial laser scanner (TLS) is still missing. Hence, differences between point clouds are possible to detect, but the testing for significance based upon a rigorous error assessment is currently realistic only in special cases. The project defines three main objectives. Firstly, we aim at setting up realistic and, thus, fully-populated VCMs including all relevant error sources of the measurement uncertainty of TLSs. Those error sources comprise the combined influence of object properties, geometry, atmosphere and imperfections of the laser scanner calibration, all depending on the laser scanner settings (rotation frequency, point density). Secondly, the VCMs need to be generalizable meaning that they rely on forward models parameterizing the dependencies between error sources and resulting uncertainty. Thirdly, the derivation of the VCMs needs to be adaptable to different spatial scales, i.e., the spatial density and the spatial extent of the underlying TLS point cloud. Hence, dense and local point clouds are handled differently than sparse and global point clouds. We will develop methodologies to empirically quantify and mathematically parameterize relevant error sources and the corresponding uncertainties. In sense of the listed objectives, we will step-by-step increase the VCM’s complexity by dividing the error sources into the ones that only act on individual observations (variances), the ones that are mainly relevant for neighbored points in a local vicinity (short-scale correlations) and the ones that are mainly relevant for points that have a large spatial distance, thus being outside of this local neighborhood (long-scale correlations). Herein, short-scale effects are mainly governed by geometry- and object-related phenomena – proportional to overlapping laser spots – and the high-frequent sampling of the laser scanner. Long-scale effects are mainly due to imperfections of the laser scanner calibration and atmospheric effects since the corresponding errors vary only to a small amount on short scale. All methodologies will be developed and evaluated based on various scanned structures that account for different complexity levels: small reference objects, a large wall made out of exposed concrete and a water dam made out of rubble stones. In the end, the derived VCMs can be used to perform strict geodetic deformation analyses.

• DFG Programme: Research Units
• Subproject of: FOR 5455: Deformation analysis based on terrestrial laser scanner measurements (TLS-Defo)
• International Connection: Austria
• Co-Investigator: Professor Dr.-Ing. Volker Schwieger
• Cooperation Partner: Professor Dr.-Ing. Hans-Berndt Neuner