模拟退火算法在控制网平差中的应用  

The application of simulated annealing algorithm to adjust control network

作　　者：邓兴升[1] 王新洲[1] 

机构地区：[1]武汉大学测绘学院

出　　处：《测绘工程》2008年第1期1-5,共5页Engineering of Surveying and Mapping

基　　金：国家自然科学基金资助项目(40474003);山东省泰山学者建设工程专项经费资助项目(TSXZ0502)

摘　　要：线性最小二乘估计在对非线性函数进行线性近似的过程中会产生模型误差,而一些非线性参数估计方法可能因为函数复杂而难以求导,法方程系数矩阵秩亏或呈病态矩阵时难以求解,非线性迭代解法有时对初始值的选择存在依赖性,不恰当的初始值会导致迭代无法收敛。针对这些问题,引入了模拟退火算法,介绍了该算法的基本原理、计算步骤和收敛性,并以3个控制网平差应用为例,说明该算法具有无需求导求逆,简洁实用,易于编程等优势,并能实现全局优化,获得高精度的平差结果。The linear least square estimation （LLSE） method will bring model error in the process of linear approximating to a nonlinear function. Some of the nonlinear parameter estimation methods will be difficult to compute the derivative as the function is too complex. It is difficult to solve the equation if the coefficient matrix is a rank defect one. The astringency of some nonlinear iteration methods badly depend on the choice of initial value. In order to search for the solution for above issues, the simulated annealing algorithm （SAA） is introduced in this paper. The fundamental, computation steps and the astringency of the algorithm are described. Three examples of SAA in control network adjustment show the superiorities of the SAA, such as no need to compute the derivative or inverse matrix; simple and easy to program for use; global optimisation; high computation precision and so on.

关 键 词：模拟退火算法 线性最小二乘估计 非线性模型 控制网平差 

分 类 号：P207[天文地球—测绘科学与技术]