Distribution-free Uncertainty Description for TLS-based Areal Deformation Analysis

我们通常假设(a)变形分析中的系统误差仅从测量过程中演变而来，(b)这些误差可以通过校准仪器或采用适当的测量策略来减少。然而，对于大地测量地面激光扫描（TLS），情况并非总是如此：测量结果是内部预处理的，用户未知的功能，校准参数可能无法足够准确地描述失调，激光束与被测量表面不可预测地相互作用，表面模型存在不确定性，激光扫描在组合大地基准中进行转换。随后，系统分析仍然存在，必须完成变形分析的总不确定性预算，以便提供有关潜在变形发生的合理陈述。我们建议用最自然的方法，即确定性区间，来封闭由于剩余的系统性而产生的观测不确定性。我们将使用区间数学中的概念来处理它们。因此，这种方法不需要对观测值的统计分布或其随机性作任何假设。由于其固有的线性不确定性传播，区间特别适合于处理剩余的系统误差。该项目的目标是基于区间数学的概念和策略的开发、实施、测试和验证，该概念和策略是关于如何通过基于tls的面积变形分析的观测分析的所有必要步骤来处理剩余系统的不确定性。在本研究单元的第一阶段，我们将重点发展(I)将地面激光扫描仪的剩余观测不确定性以间隔封闭的概念，从而免于对随机误差分布的任何假设；（ii）将观测不确定性转移到TLS点云的点不确定性的方法；（iii）评估间隔场框架中面积近似的不确定性的策略。该项目将有助于完成大地测量TLS测量的不确定性预算，并为TLS导出的表面导出确定性不确定性界限，作为基于区域的变形分析的步骤。

We usually assume that (a) systematic errors in the deformation analysis only evolve out of the measurement process and that (b) these errors can be reduced by calibrating the instrument or by applying adequate measurement strategies. However, for geodetic terrestrial laser scanning (TLS), this is not always the case: the measurements are internally preprocessed with functions unknown to the user, calibration parameters might not describe the misalignments accurately enough, the laser beam interacts unpredictably with the measured surface, the surface model uncertainty exists, and laser scans are transformed in a combined geodetic datum. Subsequently, systematics remains, and the total uncertainty budget for the deformation analysis must be completed in order to deliver sound statements about the occurrence of a potential deformation. We propose to enclose the observation uncertainties due to remaining systematics by the most natural approach, i.e., deterministic intervals. We will use concepts from interval mathematics for their treatment. This approach is thus free of any assumption about the statistical distribution of the observations or their stochasticity. Thanks to their intrinsic linear uncertainty propagation, intervals are especially suited to treat remaining systematic errors. The objective of this project is the development, implementation, testing, and validation of concepts and strategies based on interval mathematics on how to treat the uncertainty about remaining systematics through all necessary steps of the observation analysis in TLS-based areal deformation analysis. In phase I of this research unit, we will focus on developing (i) concepts to enclose the remaining observation uncertainty of terrestrial laser scanners by intervals, thus being free of any assumption about the stochastic error distribution, (ii) approaches to transfer the observation uncertainty to point uncertainty of the TLS point cloud and (iii) strategies to assess the uncertainty of the areal approximations in the framework of interval fields. This project will contribute to complete the uncertainty budget of geodetic TLS measurements and to derive deterministic uncertainty bounds for TLS-derived surfaces as steps towards area-based deformation analysis.