复数域总体最小二乘平差

Complex Total Least Squares Adjustment

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.