混合总体最小二乘法在平面坐标转换中的相对有效性
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摘要
在平面四参数坐标转换中,除经典最小二乘法和总体最小二乘法解算之外,新兴的混合总体最小二乘也可以消除或减弱随机误差对坐标转换参数估计的影响。以不同观测值个数、不同类型的随机误差的四参数坐标转换为例,运用算例和仿真实验的方法,通过比较这三种方法所估计出的参数和观测向量的相对比较指标,证明:在平面四参数坐标转换中混合总体最小二乘法和最小二乘法基本等价并且均优于总体最小二乘法。
In the coordinate transformation of planar four-parameter,the new LS-TLS method can eliminate or reduce the effect of random error on the estimation of coordinate transformation parameters,except the classical LS method and TLS method. Based on different number of observations,the different types of random error of four coordinate conversion parameters,this paper uses the method of calculation and simulation experiment,by comparing the relative parameters and the observation vector index,proved that the four parameters in plane coordinate transformation in LS-TLS method and LS method and were superior to TLS method.
In the coordinate transformation of planar four-parameter,the new LS-TLS method can eliminate or reduce the effect of random error on the estimation of coordinate transformation parameters,except the classical LS method and TLS method. Based on different number of observations,the different types of random error of four coordinate conversion parameters,this paper uses the method of calculation and simulation experiment,by comparing the relative parameters and the observation vector index,proved that the four parameters in plane coordinate transformation in LS-TLS method and LS method and were superior to TLS method.
引文
[1]鲁铁定,周世建,王乐洋.混合总体最小二乘的迭代解算算法[J].数据采集与处理,2015(7):802-809.
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[3]汪奇生,杨德宏.顾及系数矩阵常数列的总体最小二乘迭代解法[J].测绘工程,2014(7):38-45.
[4]孙同贺,闫国庆,燕志明.基于稳健估值的混合总体最小二乘直线拟合[J].测绘地理信息,2016(2):11-13.
[5]赵旭,周拥军.平行直线拟合的混合LS-TLS平差及精度评定方法[J].北京测绘,2015(4):89-92.
[6]葛永慧.再生权最小二乘法稳健估计[M].北京:科学出版社,2015:7-78.
[7]刘珺.总体最小二乘法在七参数坐标转换中的探讨[J].测绘通报,2015(S0):136-138.
[8]赵晓囡,姜佃高,贾宁宁,等.常用稳健估计方法应用于水准网的相对增益比较[J].测绘科学技术学报,2014,31(3):244-248.
[9]陶叶青,高井祥,姚一飞.平面坐标转换的稳健总体最小二乘算法[J].中国矿业大学学报,2014,43(3):534-539.
[2]鲁铁定.总体最小二乘平差理论及其在测绘数据处理中的应用[D].武汉:武汉大学,2010:43-48.
[3]汪奇生,杨德宏.顾及系数矩阵常数列的总体最小二乘迭代解法[J].测绘工程,2014(7):38-45.
[4]孙同贺,闫国庆,燕志明.基于稳健估值的混合总体最小二乘直线拟合[J].测绘地理信息,2016(2):11-13.
[5]赵旭,周拥军.平行直线拟合的混合LS-TLS平差及精度评定方法[J].北京测绘,2015(4):89-92.
[6]葛永慧.再生权最小二乘法稳健估计[M].北京:科学出版社,2015:7-78.
[7]刘珺.总体最小二乘法在七参数坐标转换中的探讨[J].测绘通报,2015(S0):136-138.
[8]赵晓囡,姜佃高,贾宁宁,等.常用稳健估计方法应用于水准网的相对增益比较[J].测绘科学技术学报,2014,31(3):244-248.
[9]陶叶青,高井祥,姚一飞.平面坐标转换的稳健总体最小二乘算法[J].中国矿业大学学报,2014,43(3):534-539.