基于复共线性诊断的正则化方法

主要研究了大地测量中不适定问题的正则化方法。根据对复共线性诊断的结果,对未受到复共线性的危害影响或受到危害影响比较小的部分未知参数附加约束,提出了基于复共线性诊断的正则化方法,并给出了正则化矩阵和正则化参数的选取方法,得到了对不适定问题未知参数的一个新的估计。数值试验表明,新的估计估值准确性较好,有效地削弱和克服了复共线性对参数估计的不良影响,优于普通的岭估计。

Regularization Based on Diagnosis of Multicollinearity

In this paper,the regularization of ill-posed problems is discussed,which usually occurs in geodesy.Based on diagnosis of multicollinearity,some constraints adds to the partial parameters which are not or less harmed by multicollinearity.A new regularization of unknown parameters estimator is given for Gauss-Markov model.Meanwhile a way to select regular matrix and regular parameter is given.Then a new estimator to unknown parameter is put forward.Computational results demonstrate its effective directed against to multicollinearity and it is superior to the ordinary ridge estimator.