【作者】 冯遵德；

【导师】 卢秀山；

【作者基本信息】 山东科技大学 ， 大地测量学与测量工程， 2006， 博士

【摘要】 病态性问题是影响参数估计质量的主要因素之一，其危害是非常严重的，因此分析病态性问题产生的原因，研究病态性问题的减弱措施是测量数据处理工作中必须面对的问题。在大地测量中，同时存在着Ⅰ、Ⅱ类病态问题，而以Ⅱ类病态性问题为主，特别是随着GPS定位与导航、雷达摄影测量等先进测绘技术的应用，病态问题已经成为提高空间位置精度的主要影响因素之一，因此对Ⅱ类病态问题的分析与处理显得尤为重要。 论文在分析总结现有研究成果的基础上，针对大地测量中出现的病态问题进行剖析。 基于赋范空间、内积空间理论，H空间中的G-S正交化方法、距离度量理论、角度度量理论对观测空间的结构进行了分析。系统地推证了观测空间中观测向量间关系的度量方法，揭示了不同度量方法的区别和联系，揭示了Ⅱ类病态性问题的空间表现特征。提出了观测结构的几何表示及数值计算方法，揭示了Ⅱ类病态问题的实质。 在分析研究观测结构的基础上，提出了观测信息量度量的改进方法，借助于该方法，可以有效地度量观测向量对参数估计的作用，有利于分析观测有效性与Ⅱ类病态性的关系。 提出了Ⅱ类病态性诊断方法。针对个别观测对病态性的影响，提出了基于投影矩阵的诊断方法；对全部观测而言，提出了基于体积U的病态性诊断方法。针对GPS定位中几何精度因子的定位精度度量指标，分析了它的Ⅱ类病态性的诊断意义，揭示了GPS定位中病态性的实质，为提高定位精度采取有效措施提供了重要依据。 为了研究Ⅱ类病态性减弱措施，论文首先分析了基于最小二乘估计理论的参数估计的性质和特点，在此基础上对现有的主要病态性处理方法进行实验分析，确认了Tikhonov正则化方法是减弱病态性影响的有效方法。在认真分析和实践的基础上，提出了改进Tikhonov正则化效果的方法和措施。运用Ⅱ类病态性的分析与处理方法对数码相机检较中出现的病态问题进行诊断和分析，为提高相机检较参数的质量提供依据。初步形成了Ⅱ类病态性问题的分析与处理的理论体系。更多还原

【Abstract】 The ill-conditioned problem is one of the main factors affecting the quality of the parameters estimation, its harm is extremely serious, so analyzing the reason that the ill-conditioned produced and searching for mitigating measure is the problem which must be faced in the data processing work. In the geodetic survey, there are Ⅰ or Ⅱ two kinds ill-conditioned problems, but the Ⅱ one plays the main role, especially with the application of the GPS localization and the navigation, the radarscope photograph survey and other advanced mapping technology, the ill-conditioned have already become one of the major influence factors to improve the space position’s precision, so it is important to analysis and process Ⅱ ill-conditioned.By analyzing and summarizing the existing research, this paper discusses Ⅱ ill-conditioned in the geodetic survey.Analyzed the structures of observation spaces by use of G-S orthogonalizing method andthe measure theory on the distance or angle in H space. Deducted the measure methods of observation vector’s relation by the numbers. Pointed out the difference and relation among different measurement methods, did research on the relations of the observation subspaces thoroughly. Put forward the geometry expressing and numerical calculating methods of observation space structures. Unveiled the spatial character and the essential of Ⅱ ill-conditioned.Suggest the improving method of measuring information of observation by analyzing the structures of observation. By use of this method, we may measure the effect of observation vector to parameters estimate effectively, so this method is propitious to analyze the relation between observation validity and Ⅱ ill-conditioned.The diagnosis method of Ⅱ ill-conditioned was put forward in this paper. For the influence of individual observation to the ill-conditioned, the diagnosis method was put forward based on the projection matrix, for all observations the diagnosis method of Ⅱ ill-conditioned was suggested based on volume U that observation vectors formed. In view of the positioning accuracy measurement index of GDOP in the GPS, analyzed its diagnosis significance of Ⅱ ill-conditioned, and indicate the ill-condition essence in the GPS, and provide the important basis for taking the effective action to enhance positioning accuracy.更多还原