General model for estimating range variances of terrestrial laser scanners based on (un-)scaled intensity values

2025-10-29

AI Summary

Terrestrial laser scanning (TLS) lacks accurate distance variance modeling in deformation monitoring, resulting in an incomplete stochastic model for polar-coordinate observations. Method: This paper proposes a generalized distance variance estimation method that jointly incorporates raw and scaled intensity values. For the first time, it unifies the modeling of both intensity types and explicitly characterizes the nonlinear relationship between intensity and ranging noise, thereby establishing a universal variance–covariance matrix (VCM) generation model applicable to high-end TLS systems (e.g., Z+F 5016A, Leica P50). Contribution/Results: Validated through controlled laboratory experiments and 2D dam surface scans—including both artificial targets and natural surfaces—the model significantly improves distance variance estimation accuracy and enhances the statistical reliability of TLS measurements. The approach demonstrates strong engineering applicability and robustness, providing a transferable stochastic modeling foundation for high-precision TLS-based deformation inversion.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

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• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

Abstract

Recent advancements in technology have established terrestrial laser scanners (TLS) as a powerful instrument in geodetic deformation analysis. As TLS becomes increasingly integrated into this field, it is essential to develop a comprehensive stochastic model that accurately captures the measurement uncertainties. A key component of this model is the construction of a complete and valid variance-covariance matrix (VCM) for TLS polar measurements, which requires the estimation of variances for range, vertical, and horizontal angles, as well as their correlations. While angular variances can be obtained from manufacturer specifications, the range variance varies with different intensity measurements. As a primary contribution, this study presents an effective methodology for measuring and estimating TLS range variances using both raw and scaled intensity values. A two-dimensional scanning approach is applied to both controlled targets and arbitrary objects using TLS instruments that provide raw intensity values (e.g., Z+F~Imager~5016A) and those that output scaled intensities (e.g., Leica~ScanStation~P50). The methodology is further evaluated using field observations on a water dam surface. Overall, this work introduces a comprehensive workflow for modeling range uncertainties in high-end TLS systems.

Problem

• Estimating TLS range variances using raw and scaled intensity values
• Developing stochastic model for terrestrial laser scanner measurement uncertainties
• Constructing complete variance-covariance matrix for TLS polar measurements

Innovation

• Estimating TLS range variances using intensity values
• Applying two-dimensional scanning to targets and objects
• Evaluating methodology with field observations on dam