Modeling the distribution of TLS distance related uncertainties

Accurate calibration of terrestrial laser scanners (TLSs) is essential for high-precision applications such as deformation monitoring and structural health assessment. While prior work has addressed either systematic distance deviations or measurement precision in isolation, there remains a lack of methods that jointly model both components within a probabilistic framework. This study introduces a novel approach for the simultaneous estimation and calibration of TLS distance deviation and precision by leveraging probabilistic regression. Assuming Gaussian distributed deviations, the method predicts both the mean (systematic deviation) and standard deviation (precision) using two models: NGBoost (Natural Gradient Boosting) and a deep neural network. The approach is evaluated on a dedicated benchmark data set comprising three measurement campaigns with the Z+F Imager 5016, designed to assess temporal stability and cross-device generalizability. Results reveal that while systematic deviations are temporally stable, they are unit-specific and cannot be directly transferred between devices. In contrast, the predicted precision estimates generalize successfully across different scanner units. NGBoost demonstrates superior robustness compared to the neural network, particularly in data-sparse regions. This is confirmed by an analysis of epistemic model uncertainty, where NGBoost maintains high confidence across the entire domain, whereas the neural network exhibits significant instability at intensity boundaries. The proposed method not only enables effective, instrument-specific calibration but also provides reliable, data-driven uncertainty estimates for decision-making.