复数域总体最小二乘平差  

Complex Total Least Squares Adjustment

作　　者：王乐洋[1,2,3] 于冬冬[1] 吕开云[1] 

机构地区：[1]东华理工大学测绘工程学院,江西南昌330013 [2]江西省数字国土重点实验室,江西南昌330013 [3]流域生态与地理环境监测国家测绘地理信息局重点实验室,江西南昌330013

出　　处：《测绘学报》2015年第8期866-876,共11页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(41204003;41161069;41304020);江西省自然科学基金(20132BAB216004);江西省教育厅科技项目(GJJ13456;KJLD12077;KJLD14049);地理空间信息工程国家测绘地理信息局重点实验室项目(201308);测绘地理信息公益性行业科研专项(201512026);东华理工大学博士科研启动金(DHBK201113)~~

摘　　要：在复数域最小二乘的基础上提出了复数域总体最小二乘平差方法,推导了复数域总体最小二乘和复数混合总体最小二乘的相关公式。通过算例比较分析了复数观测值的残差的模的平方和最小(平差准则1)下及残差的实部和虚部的平方和分别最小(平差准则2)下的复数最小二乘、复数观测值和系数矩阵的残差的模的平方和最小(平差准则3)下及残差的实部和虚部的平方和分别最小(平差准则4)下的复数总体最小二乘方法的优劣。试验结果表明:平差准则1下复数最小二乘较平差准则2下得到的结果更加合理,平差准则3下复数总体最小二乘较平差准则4下得到的结果更为准确;当顾及系数矩阵误差时,平差准则3下复数总体最小二乘要优于平差准则1下复数最小二乘。On the basis of complex least squares adjustment method （CLSAM）, the theory of complex total least squares adjustment method （CTLSAM） is proposed. The algorithms of complex total least squares and complex LS-TLS method are derived. Through two examples, the complex LS method under the adjustment criterions that minimize the sum of squares of the module of observation vector residual （adjustment criterion 1） and the sum of squares of the real part and imaginary part of the observation vector （adjust- ment criterion 2）, the complex TLS method under the adjustment criterions that minimize the sum of squares of the module of observation vector and coefficient matrix residual （adjustment criterion 3）and the sum of squares of the real part and imaginary part of the observation vector and coefficient matrix residual （adjustment criterion 4） are compared and analyzed respectively. The results of two examples show that the CLSAM under the adjustment criterion 1 is more reasonable than the adjustment criterion 2; the CTLSAM under the adjustment criterion 3 is more accurate than the adjustment criterion 4; the CTLSAM under the adjustment criterion 3 is better than the CLSAM under the adjustment criterion 1 when the coefficient matrix contains stochastic noise.

关 键 词：复数 总体最小二乘 混合总体最小二乘 最小二乘 平差准则 

分 类 号：P207[天文地球—测绘科学与技术]