测绘学报

• 学术论文 •    

附有病态约束矩阵的等式约束反演问题研究

王乐洋,许才军,汪建军   

  1. 武汉大学测绘学院
  • 收稿日期:2008-11-03 修回日期:2009-06-02 出版日期:2009-10-22 发布日期:2009-10-22
  • 通讯作者: 王乐洋

Research on Equality Constraint Inversion with Ill-posed Constraint Matrix

1,Caijun XU2, 2   

  1. 1. Wuhan University
    2.
  • Received:2008-11-03 Revised:2009-06-02 Online:2009-10-22 Published:2009-10-22

摘要: 本文讨论了等式约束反演问题的求解方法,给出了约束矩阵的病态性的定义及相应的评价方法,推导了约束矩阵病态对反演结果的影响公式,通过简单的例子说明了约束矩阵病态对反演结果的影响;采用了处理约束矩阵病态的SVD方法,有效解决了约束矩阵病态造成反演结果极不稳定的问题。最后设计多个反演方案进行计算,验证了方法的有效性和可行性,得到了一些重要的结论。

Abstract: Prior information and many kinds of observations are often used in equality constraint inversion. In this thesis, solving method to equality constraint inversion is discussed, the concept and evaluate method of Ill-posed character of constraint matrix are given. The influence to adjustment results from constraint matrix Ill-posed character is deduced. Through an example, the influence to inversion result from constraint matrix Ill-posed character is analized. The SVD method is used to solve Ill-posed problem of constraint matrix. The problem that inversion result is not stable because of constraint matrix Ill-posed character is solved effectively. At last, throught some programmes of inversion, the methods are analized, and some conclusions are obtained.