附不等式约束平差模型的一种快速搜索算法  

A Fast Search Algorithm in Adjustment Model with Inequality Constraint

作　　者：谢雪梅[1,2] 宋迎春 肖兆兵[1] XIE Xuemei;SONG Yingchun;XIAO Zhaobing(School of Geosciences and Info-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,湖南长沙410083 [2]中南林业科技大学土木工程学院,湖南长沙410004

出　　处：《武汉大学学报（信息科学版）》2018年第9期1349-1354,共6页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金(41574006,41674009,41674012)~~

摘　　要：大地测量中常存在一些先验不等式约束信息,充分利用它们可以保证参数解的唯一性和稳定性。然而,现有的不等式约束平差算法主要是基于优化理论,算法通常比较复杂,需要选取有效约束或建立罚函数。在最小二乘平差准则基础上,把不等式约束看成是一个可行域,借助Fisher函数在可行域中快速搜索使误差平方和达到最小的最优解,推导出了可行解为最优解的充分必要条件。建立了基于Wolfe-Powell算法的非精确快速搜索算法,从而减小了搜索算法的计算量,得到了一种新的不等式约束平差计算方法。该算法的平差准则与最小二乘平差准则一致,不需要矩阵求逆运算,可适用于维数较大的平差问题解算。There usually exists some prior information with inequality constraint in the survey of adjustment model.The uniqueness and stability of the solution can be guaranteed by making full use of it.However,the existing adjustment algorithms with inequality constrain,which are mainly based on optimization theory,are usually complex.They need to select the effective constraint or establish penalty function.This paper mainly studies the adjustment model with inequality constraint,in which the inequality constraint is considered as a feasible region on the basis of the least squares adjustment rule and the Fisher function is used to search the optimal solution that minimizes the sum of squared errors,and sufficient necessary conditions for the optimal feasible solution are derived.A non-precise fast search based on Wolfe-Powell algorithm is given in the feasible region,which reduces the computational complexity,a new adjustment algorithm with inequality constraint is presented.The given algorithm,in which the adjustment criterion is consistent with that of the least squares adjustment criteria,does not require matrix inversion operation,and can solve some of the large dimension adjustment problem with inequality constrain.

关 键 词：先验信息 不等式约束 平差模型 二次规划 Fisher函数 

分 类 号：P207[天文地球—测绘科学与技术]