引用本文: 王乐洋, 许才军, 鲁铁定. 病态加权总体最小二乘平差的岭估计解法[J]. 武汉大学学报 ( 信息科学版), 2010, 35(11): 1346-1350.
WANG Leyang, XU Caijun, LU Tieding. Ridge Estimation Method in Ill-posed Weighted Total Least Squares Adjustment[J]. Geomatics and Information Science of Wuhan University, 2010, 35(11): 1346-1350.
 Citation: WANG Leyang, XU Caijun, LU Tieding. Ridge Estimation Method in Ill-posed Weighted Total Least Squares Adjustment[J]. Geomatics and Information Science of Wuhan University, 2010, 35(11): 1346-1350.

## Ridge Estimation Method in Ill-posed Weighted Total Least Squares Adjustment

• 摘要: 采用岭估计法处理加权总体最小二乘平差的病态性问题,推导了相应的求解公式及均方误差评定精度的方法,定义了病态加权总体最小二乘平差中的模型参数分辨矩阵,并讨论了岭参数的含义及其作用,给出了确定病态加权总体最小二乘岭估计中岭参数的岭迹法、广义交叉核实法和L曲线法。算例计算了普通最小二乘、普通总体最小二乘的结果,并比较了三种确定岭参数的方法在处理病态加权最小二乘岭估计和病态加权总体最小二乘岭估计中的优缺点。

Abstract: The method of ridge estimation to treat ill-posed and weighted total least squares adjustment(TLSA) is put forward.The solution equation and evaluating precision by mean square error are deduced.The model parameter discernable matrix in ill-posed and weighted TLSA is defined,then the meaning and effect of the ridge parameter is discussed.For the case that the ridge parameter is difficult to determine in ridge estimation to treat ill-posed and weighted TLSA,the L-curve method,generalized cross-validation(GCV) and the ridge mark method are introduced and given.At last,through some cases,the comparisons are carried out among the L-curve method,GCV and the ridge mark method,also the results of common least squares(LS) and total least squares are given,and some conclusions are obtained.

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