New non-linear adjustment methods for application in geodesy and related fields

新的非线性平差方法在大地测量学及相关领域的应用

• 批准号: 242160557
• 负责人: Professor Dr.-Ing. Frank Neitzel
• 金额: --
• 依托单位: Fachgebiet Geodäsie und Ausgleichungsrechnung
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/242160557?language=en
• 关键词: New; non; linear; adjustment; methods

A common problem in engineering or other technical sciences is that oftentimes desired target val-ues cannot be determined directly. Hence the unknown parameters need to be connected to corre-sponding measurements by applying a functional model. An example is the determination of 3D coordinates of an object based on observed distances and directions.In order to ensure accuracy and reliability always more measurements are conducted than needed for the unique determination of the unknown parameters. In such cases an adjustment problem arises which leads to the best possible result under consideration of inevitable random measurement errors.Based upon scientific efforts that have been carried out from 1980 onwards within the field of mathematical statistics not only random measurement errors but also errors in the parameters of the functional model have been considered, a case which is referred to as "Errors-In-Variables (EIV) Model".In order to solve the resulting non-linear adjustment problem the "Total Least-Squares (TLS)" approach has been developed. This approach transfers, under certain conditions, the determination of desired parameters into an eigenvalue problem for which efficient solution methods are available.This approach, however, fails in case of special structures regarding the functional and/or stochastic model. Within the proposed project new non-linear adjustment methods should be developed that enable a generalised solution of the EIV-model.The general methodology is based on setting up appropriate non-linear normal equations for gen-eralised problems in order to obtain the best possible solution regarding numerical efficiency and convergence behaviour. The new methods should also be applied for regularisation of ill-posed problems, robust parameter estimation in presence of outliers and consideration of dispersion matrices of arbitrary structure. A problem which previously has not been treated is the EIV-model with prior information which should yield to TLS collocation.These novel adjustment methods should be applied in Geodesy (e.g. for coordinate transformation), geostatistics (e.g. kriging) and computer vision (e.g. 3D surface matching). The adaptation to challenges in other subject areas should be possible due the generalised formulation of the new non-linear adjustment methods.

工程或其他技术科学中的一个常见问题是，通常无法直接确定所需的目标值。因此，需要通过应用函数模型将未知参数连接到相应的测量。例如，根据观察到的距离和方向确定物体的三维坐标。为了确保准确性和可靠性，总是进行比唯一确定未知参数所需的更多的测量。在这种情况下，出现了调整问题，该调整问题在考虑不可避免的随机测量误差的情况下导致最好的可能结果。基于从1980年起在数理统计领域内进行的科学努力，不仅考虑了随机测量误差，而且考虑了函数模型参数中的误差，为了解决由此产生的非线性平差问题，发展了“总体最小二乘”方法。在一定条件下，这种方法将期望参数的确定转化为特征值问题，并给出了有效的求解方法，但在函数模型和随机模型的特殊结构情况下，这种方法就失效了。在建议的项目中，应开发新的非线性调整方法，以实现EIV模型的一般化解决方案。一般方法基于为一般化问题建立适当的非线性正规方程，以获得关于数值效率和收敛行为的最佳可能解决方案。新的方法也应适用于正则化不适定的问题，鲁棒参数估计存在的离群值和考虑色散矩阵的任意结构。这些新的平差方法应应用于大地测量学（如坐标变换）、地质统计学（如克里金）和计算机视觉（如三维表面匹配）。由于新的非线性调整方法的普遍制定，适应其他学科领域的挑战应该是可能的。