平面坐标转换模型的病态性分析与正则化算法  

Reaserch on Ill-conditioned problem in plane coordinate conversion model and its regularization algorithm

作　　者：杨娟[1] 黄淑玲[1] 戴洪宝[1] 施龙香 

机构地区：[1]宿州学院地球科学与工程学院,安徽宿州234000

出　　处：《测绘科学》2015年第6期21-24,60,共5页Science of Surveying and Mapping

基　　金：安徽省优秀青年人才基金重点项目(2013SQRL085ZD);安徽省大学生创新创业训练项目(AH201310379047);安徽省高校自然科学研究项目(KJ2013B290)

摘　　要：应用数学模型实现坐标系统的转换,转换的精度是人们关注的问题。针对平面坐标转换模型参数间的相关性可能导致的法方程系数矩阵的病态性,该文在非线性平面坐标转换模型的基础上,推导并得出线性转换模型。通过算例对线性转换模型参数的相关性、模型的病态性、及其正则化方法进行分析。结果表明法方程系数矩阵呈病态性,但病态性不是由于模型参数的相关性引起;应用参数的正则化解转换控制点的坐标,其转换精度高于最小二乘解。The accuracy of coordinate conversion is concerned when people apply mathematical model to transform different coordinate systems. For the ill-conditioned coefficient matrix of normal equation might caused by the correlation of conversion model parameters, the linear conversion model was deduced on the basis of nonlinear plane conversion model. Then, the related conclusions of conversion model parameters, the ill-conditioned problem of coefficient matrix and the regularization algorithm were analyed through an instance. Experimental results showed that the ill-conditioning problem existed in coefficient matrix of normal equation, which was not induced by the correlation of parameters; and the result of pa- rameters based on select weight fitting idea was more accurate than that of least squares.

关 键 词：平面坐标转换 线性模型 病态性 正则化 

分 类 号：P207.2[天文地球—测绘科学与技术]