附不等式约束的病态问题求解研究

病态问题产生的原因是设计矩阵存在复共线关系,为了消除法方程奇异,我们必须附加先验信息。不等式约束是客观实际中普遍存在的一种约束,是先验信息的主要表达方式之一,因此本文提出了附不等式约束的病态问题和其求解方法。本文在Rao提出的椭球约束法的基础上导出了不等式约束条件和广义岭参数之间的转换关系,然后用传统的广义岭估计来求解附不等式约束的病态问题。该种求解思想真正实现了由附加先验信息来决定岭参数。最后用一个模拟的算例检验了本文方法的可行性。同时,算例表明:不等式约束条件越正确、越苛刻得到的结果越接近真值,精度也越高。

Study on Linear Inequality Constrained Ill-conditioned Problem

The multi-collinearity of design matrix causes ill-conditioned problems.In order to eliminate the singularity of equation,adding prior information to that is necessary.Since the inequality constraints exist extensively in real surveying and it is a main expression way of prior information,this paper puts forward inequality constraint ill-conditioned problem and its solution.This method educes the relation between inequality constraint and the generalized ridge parameters on the basis of Rao's ellipsoidal constraints.And then,it can solute the inequality constraint ill-conditioned problem by traditional generalized ridge estimation.In this method,the ridge parameters are determined by prior information.At the last part of this paper,this method is tested by a simulative example.The result shows that the more correct and strict inequality constraints can get the more exact and accurate solution.