Deterministic uncertainty for terrestrial laser scanning observations based on intervals

authored by: Reza Naeimaei, Steffen Schön
Abstract: Terrestrial laser scanners (TLS) are well-suited for conducting area-based deformation analysis of infrastructures. Unlike common point-based geodetic sensors, TLS can measure millions of points across the environment without requiring pre-defined, signalized measurement locations. However, TLS point clouds are affected by both random variations and residual systematic errors. These uncertainty components are often addressed using only probabilistic approaches, which may inadequately or overly optimistically represent the remaining systematic errors. To overcome these limitations, this study introduces an alternative framework based on interval mathematics to bound uncertainties arising from systematic errors. The proposed methodology includes a sensitivity analysis of TLS observation correction models, examining the variability of key input parameters. Unlike the quadratic approach for variance propagation, the interval-based method enables linear uncertainty propagation, effectively characterizing residual systematic uncertainties and their maximum effects. This paper details the methodology and presents typical interval values validated through simulations and real-data experiments. The findings highlight the potential of interval-based methods to enhance the TLS uncertainty model.
Organisation(s): Institute of Geodesy
Type: Article
Journal: Journal of Applied Geodesy
ISSN: 1862-9016
Publication date: 29.04.2025
Publication status: E-pub ahead of print
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Engineering (miscellaneous), Earth and Planetary Sciences (miscellaneous)
Electronic version(s): https://doi.org/10.1515/jag-2025-0034 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{225e7735ccbf489aa3e758629aed100a,
title = "Deterministic uncertainty for terrestrial laser scanning observations based on intervals",
abstract = "Terrestrial laser scanners (TLS) are well-suited for conducting area-based deformation analysis of infrastructures. Unlike common point-based geodetic sensors, TLS can measure millions of points across the environment without requiring pre-defined, signalized measurement locations. However, TLS point clouds are affected by both random variations and residual systematic errors. These uncertainty components are often addressed using only probabilistic approaches, which may inadequately or overly optimistically represent the remaining systematic errors. To overcome these limitations, this study introduces an alternative framework based on interval mathematics to bound uncertainties arising from systematic errors. The proposed methodology includes a sensitivity analysis of TLS observation correction models, examining the variability of key input parameters. Unlike the quadratic approach for variance propagation, the interval-based method enables linear uncertainty propagation, effectively characterizing residual systematic uncertainties and their maximum effects. This paper details the methodology and presents typical interval values validated through simulations and real-data experiments. The findings highlight the potential of interval-based methods to enhance the TLS uncertainty model.",
keywords = "interval mathematics, terrestrial laser scanners, uncertainty budget",
author = "Reza Naeimaei and Steffen Sch{\"o}n",
note = "Publisher Copyright: {\textcopyright} 2025 Walter de Gruyter GmbH, Berlin/Boston 2025.",
year = "2025",
month = apr,
day = "29",
doi = "10.1515/jag-2025-0034",
language = "English",
journal = "Journal of Applied Geodesy",
issn = "1862-9016",
publisher = "Walter de Gruyter GmbH",
}