Complementing and Validating Uncertainty of Terrestrial Laser Scanning via Interval Analysis

Abstract. Terrestrial laser scanning (TLS) enables dense spatial sampling. However, the analysis of millimeter-level deformations is limited by uncertainty rather than resolution. Inter-epoch differences can arise from actual changes or systematic effects. Classical stochastic models address random variability based on certain distributional assumptions, but they do not offer deterministic bounds for persistent effects that remain even after calibration and correction. This paper presents a complementary interval-based framework for bounding such effects and integrating them into least-squares workflows. Starting from measurement and instrumental correction models for high-end panoramic scanners, bounded deviations of influence parameters are propagated to TLS observations and represented as observation-level interval radii. These radii are then mapped via an interval-extended least-squares adjustment to obtain conservative bounds on residuals and parameter estimates, along with stochastic covariances. To validate the interval description without a trusted nominal reference, we propose a residual-domain strategy based on two-face (Face 1/Face 2) acquisitions. In this strategy, the model parameters are first estimated from Face 1 observations and then kept fixed when evaluating the corresponding Face 2 observations. This prevents the adjustment from absorbing remaining systematic effects into the model parameters. The resulting averaged face-combined residuals are then compared with the propagated interval bounds. The approach is demonstrated on real TLS data from the Bonn reference wall. The results show that the propagated bounds generally enclose the averaged face-combined residuals and reveal station-dependent residual structures that motivate extending the current instrument-only interval budget to include geometry, registration, and surface-interaction effects.