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只在测量过程中产生，(B)这些误差可以通过校准仪器或应用适当的测量策略来减少。然而，对于大地激光扫描(TLS)来说，情况并不总是这样：测量数据在内部使用用户未知的函数进行预处理，校准参数可能不能足够准确地描述失调，激光光束与被测表面的相互作用不可预测，地表模型存在不确定性，激光扫描被转换为组合大地基准。随后，系统论仍然存在，必须完成变形分析的总不确定性预算，以提供关于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剩余系统学引起的观测不确定性。我们将使用区间数学中的概念来处理它们。因此，这种方法不需要任何关于观测的统计分布或其随机性的假设。由于其固有的线性不确定性传播，间隔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，即如何通过基于TLS的面形变分析中观测分析的所有必要步骤来处理剩余系统学的不确定性。在这个研究单元的第一阶段，我们将重点发展(I)按间隔封闭地面激光扫描仪的剩余观测不确定性的概念，从而摆脱任何关于随机误差分布的假设；(Ii)将观测不确定性转换为TLS点云的点不确定性的方法；以及(Iii)在间隔场框架内评估面上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，并导出TLS衍生表面的确定性不确定性界限，作为基于区域的形变分析的步骤。

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.