【作者】 张菊清；

【导师】 杨元喜； 张勤；

【作者基本信息】 长安大学 ， 大地测量学与测量工程， 2009， 博士

【摘要】 作为一种空间决策支持系统，GIS的根本任务就是分析和处理空间数据，派生和提取空间信息，而数据质量直接影响着分析结果的可靠度及应用目标的实现，从而影响着GIS产业的健康发展。因此，研究GIS数据质量控制的理论与方法具有重要的现实意义。本文主要研究了空间数据获取与分析处理过程中，几何误差纠正和空间数据插值的相关理论与算法，论文的主要内容和创新点概括如下：1、在函数模型误差控制方面，论述了空间数据几何误差纠正的函数模型拟合原理，并对各种常用的纠正模型进行了对比分析；在控制点先验随机模型误差控制方面，研究了顾及先验信息的函数模型拟合法；在异常误差影响控制方面，提出了顾及系统参数先验信息的抗差拟合法。2、在函数模型与随机模型综合影响控制方面，探讨了拟合推估在空间数据几何误差纠正中的应用，弥补了函数模型拟合法难以纠正局部随机信号的缺陷；讨论了协方差函数的拟合方法，并定量研究了协方差函数误差对拟合推估解的影响；为了抑制异常误差对拟合推估解的影响，提出了协方差函数的抗差拟合法及相应的抗差拟合推估法。3、在随机模型误差影响控制方面，提出应用方差分量估计调整先验的观测方差协方差阵与随机信号的方差协方差阵之间的不协调问题。研究了基于Helmert方差分量估计的拟合推估、基于极大似然方差分量估计的拟合推估及基于MINQUE方差分量估计的拟合推估理论；基于方差分量估计构建了自适应因子，平衡观测噪声与随机信号的贡献，从而构建了自适应拟合推估模型，并分析了自适应因子对拟合推估解的影响。4、在论述附有限制条件的函数模型拟合基础上，给出了含有随机信号约束条件、含有倾向参数的约束条件及含有倾向参数与随机信号组合约束条件的拟合推估模型，并导出了相应的解式，如此可以保证在几何误差纠正的同时能够满足各种固有的几何或物理条件。考虑到需满足的条件多且复杂，计算量大，影响误差纠正效果，于是又提出分步平差和二次误差纠正的新思路。5、提出应用BP神经网络进行空间数据几何误差的纠正，避免了因先验信息不足，函数模型、随机模型选择不当所带来的影响。同时针对BP神经网络学习训练速度慢、容易陷入局部极小等问题，对算法进行了改进。6、探讨了最小曲率插值原理及算法。通过分析发现：最小曲率插值既不需要全面了解系统误差和随机误差的特性，也不需要人为地选择函数模型、随机模型、网络结构等。由于它将研究区域格网化，再进行逐格网内插，因此具有较好的局部拟合特性，比较适合于小区域范围内的误差拟合。7、为了控制空间数据生成过程中的内插误差影响，提出了具有抗差能力的等价权平均法及能够抵制异常变异的抗差趋势面拟合分析法；分析了核函数、节点及平滑因子对多面函数拟合的影响，重点研究了节点的自适应选择问题，提出了以各节点核函数对曲面拟合贡献的大小来自适应选择节点的正交最小二乘多面函数法。更多还原

【Abstract】 As a decision-making system of spatial relation, the fundamental task of GIS is to analyze and process spatial data, derive and abstract spatial information. The quality of data influences the reliability of the analysis results and realization of application objective directly, furthermore, affect the development of GIS industry. So it has important practical significance to study the theory and method of data quality control in GIS. This dissertation mainly focuses on the theories and algorithms of geometry error compensation and spatial data interpolation in the process of spatial data acquisition and analysis. The main works and contributions are summarized as follows:1. Theory of functional model fitting for geometric error is discussed, various existing models are compared and analyzed. The fitting model considering a priori information is studied in order to control the influences of control points. A robust fitting with prior information is presented which can resist outliers of spatial datum.2. A collocation method is proposed to fit geometric error of spatial data in order to compensate the remained local random errors, since the functional model can only fit the systematic errors or trend errors. The method for covariance function fitting in collocation is discussed and influences of the uncertainty of the covariance function are analyzed. To resist the influences of outliers, robust fitting for the covariance function and robust collocation are presented.3. In collocation applications, the prior covariance matrices between signals and observations should be consistent, otherwise, the solution of collocation will be twist. The variance component estimation is introduced to adjust the disharmony between covariance matrices of observations and random signals. The collocation based on maximum likelihood estimation, MINQUE estimation and Helmert estimation of variance components are studied. To balance the covariance matrices of the signals and the observations, a new adaptive collocation estimator is also derived in which the corresponding adaptive factor is constructed by the ratio of the variance components. In addition, the influences of adaptive factor on collocation results are analyzed. 4. The inherent geometrical or physical constraints should be satisfied while in fitting of geometric errors of spatial datum, the collocation estimators, with stochastic signal constraints, trend parameter constraints, as well as the synthetic constraints of signals and trend parameters, are derived based on the functional fitting with constraints. Considering there are many conditions which will lead to excessive calculation workload, a new idea of two-step adjustment is proposed.5. BP neural network is introduced to fit the geometric errors of GIS, which can approach the systematic errors without using a fixed functional model or stochastic model. Since the neural network has the disadvantages of slow learning speed and easily arriving at local minimum, an improved neural network algorithm is put forward.6. The principle and algorithm of minimum curvature interpolation are discussed. By analyzing we find that the fitting method based on the minimum curvature does not need the comprehensive knowledge about the characteristics of system errors or random errors, either the function model, stochastic model or network structure. At first the research area is divided into grids and then unknown data is interpolated grid by grid, therefore the fitting method based on the minimum curvature has good characteristics for the local fitting. As the result, it is more suitable for error fitting in the small area.7. In order to control the influences of the outliers or abnormal variations of the interpolation data in the process of data generation, the methods of equivalent weight average and robust trend surface fitting are proposed. The influences of kernel function, nodes and smoothing factor on multiquadric fitting are analyzed. An adaptive node choosing method, which cannot only ensure the stability, but also improve the precision of fitting, is proposed based on the effect of every node to the curve fitting calculated by using the orthogonal least squares.更多还原