采用联合平差法处理附有病态等式约束的反演问题

Solving Equality Constraint Inversion with Ill-posed Constraint Matrix Using United Method

探讨了附有病态等式约束的反演问题,尝试用降秩处理方法解这类病态约束问题,通过算例验证了此种方法与截断奇异值方法是等价的。然后提出了一种联合平差方法,它不仅能解病态的约束问题,而且能解决主模型秩亏或病态同时约束模型病态的问题,增强了应用性。最后设计了多种方案进行计算和比较,验证了联合平差法的有效性和可行性。

Solving method to equality constraint inversion with ill-posed constraint matrix is discussed,and rank-reducing processing method,which is proved equivalent to truncated singular value decomposition method（SVD）,is proposed to solve this kind of problem.Further more,a united adjustment method with enhanced usability is also put forward,which can not only solve inversion with ill-posed constraint matrix,but also solve problems with master model ill-conditioned or rank-deficient when constraint model is ill-conditioned.Finally,through some well-designed cases,the methods are discussed,and some conclusions are obtained.