利用椭球约束求解区间平差模型的正则化方法  

A regularization method for solving interval adjustment models using ellipsoid constraints

作　　者：邓伟 宋迎春[1] 李文娜 谢雪梅 DENG Wei;SONG Yingchun;LI Wenna;XIE Xuemei(School of Geosciences and Information Physics,Central South University,Changsha 410083,China;School of Civil Engineering,Central South University of Forestry and Technology,Changsha 410004,China)

机构地区：[1]中南大学地球科学与信息物理学院,长沙410083 [2]中南林业科技大学土木工程学院,长沙410004

出　　处：《测绘工程》2022年第6期13-19,26,共8页Engineering of Surveying and Mapping

基　　金：国家自然科学基金资助项目(41674009,41574005)。

摘　　要：以参数带区间约束平差模型为对象,针对传统的椭球约束算法存在平差结果可能不在约束条件内的缺点,在传统椭球约束求解方法的基础上,基于最优化理论中的二次罚函数法,提出一种改进的求解椭球约束的方法,通过对椭球特征矩阵进行加权,减小特征矩阵的半径来迭代求最优解。在模型中引入正则化项,利用L-曲线法确定正则化参数,来解决系数矩阵病态的问题。最后,通过一个反演中的模拟病态算例比较验证算法的有效性。The paper takes the parameter adjustment model with interval constraints as the object.The traditional ellipsoid constraint algorithm has the disadvantage that the adjustment results may not be within the constraints.For the traditional ellipsoid constraint solving method, based on the quadratic penalty function method in the optimization theory, an improved method for solving the ellipsoid constraint is proposed.By weighting the ellipsoid characteristic matrix, the radius of the characteristic matrix is reduced to iteratively find the optimal solution.The regularization term is introduced into the model, and the L-curve method is used to determine the regularization parameters to solve the ill-conditioned problem of the coefficient matrix.Finally, a simulated ill-conditioned case in the inversion is used to compare and analyze the effectiveness of the algorithm.

关 键 词：区间约束 椭球约束 病态问题 正则化 

分 类 号：P207[天文地球—测绘科学与技术]