带不等式约束的最小二乘方法比较  

Comparison of Least Squares Methods with Inequality Constraints

作　　者：彭英豪 余代俊[1] PENG Yinghao;YU Daijun(Chengdu University of Technology Academy of Geosciences,Chengdu Sichuan 610059,China)

机构地区：[1]成都理工大学地球科学学院

出　　处：《北京测绘》2019年第12期1470-1473,共4页Beijing Surveying and Mapping

摘　　要：解决带不等式约束的平差问题已有较多方法,但不同方法之间的对比分析不足。本文讨论三种带不等式约束的最小二乘算法:简单迭代算法、虚拟误差方程法、迭代乘子法,三种算法都是基于有效约束理论将不等式约束转换为等式约束,通过迭代求解。采用同一组数据和蒙特卡罗仿真实验方法对三种算法计算结果进行对比分析,实验结果分析表明:迭代乘子法算法效率最高,推荐使用该算法。There are many ways to solve the problem of adjustment with inequality constraints,but the comparative analysis between different methods is insufficient.This paper discusses three least squares algorithms with inequality constraints:simple iterative algorithm,virtual error equation method,and iterative multiplier method.All three algorithms transform inequality constraints into equality constraints based on effective constraints theory and solve them iteratively.The same set of data and Monte Carlo numerical simulation experiment method are used to compare and analyze the results of the three algorithms.The results show that the iterative multiplier method has the highest efficiency.This algorithm is recommended.

关 键 词：不等式约束 有效约束 简单迭代算法 虚拟误差方程法 迭代乘子法 

分 类 号：P207[天文地球—测绘科学与技术]