加权总体最小二乘在曲面拟合中的应用  

Application of Weighted Total Least-squares in Surface Fitting

作　　者：袁豹[1] 岳东杰[1] 许义[1] 孙腾科[1] 

机构地区：[1]河海大学测绘科学与工程系,南京市210098

出　　处：《勘察科学技术》2013年第3期47-50,共4页Site Investigation Science and Technology

基　　金：国家自然科学基金资助项目(51079053)

摘　　要：曲面拟合是一种常用的数学方法并被广泛应用于测绘领域,针对常规曲面拟合时采用最小二乘法没有考虑系数矩阵中数据含有的偶然误差,引入加权总体最小二乘这种严密的平差方法,分析了加权总体最小二乘的模型以及解法,讨论了加权总体最小二乘方法在几种典型曲面拟合(平面拟合,球面拟合,二次曲面拟合)中的应用。分析表明,加权总体最小二乘法更加精确。Surface fitting is a commonly used mathematical method and being widely used in surveying and mapping field, for least-squares method used in traditional surface fitting does not consider the acci- dental errors of data in coefficient matrix, the rigorous adjustment method for weighted total least-squares is introduced, the model and solution of weighted total least-squares is analyzed, and the application of weighted total least-squares is discussed in several typical surface fitting including plane fitting, spherical fitting and quadratic surface fitting. The analysis results show that the weighted total least-squares method is more accurate.

关 键 词：加权总体最小二乘 曲面拟合 奇异值分解 迭代解法 权阵 

分 类 号：P207[天文地球—测绘科学与技术]