快速同伦算法在非线性最小二乘平差中的应用  

Application of Quick Homotopy Algorithm in Non-linear Least Squares Adjustment

作　　者：欧阳全欢 

机构地区：[1]铁道第三勘察设计研究院集团有限公司,天津市岷江路10号300251

出　　处：《测绘地理信息》2012年第5期53-55,共3页Journal of Geomatics

摘　　要：针对线性化近似法模型误差大,牛顿迭代法和高斯-牛顿法局部收敛等不足,而同伦算法在非线性数据处理方面有独到优势。通过对同伦路径跟踪过程中牛顿迭代终止判据和步长控制策略进行了改进,得到了一种快速、稳定的同伦路径跟踪算法。Considering the large model error of linear approximation method,and the lack of local convergence of Newton iteration method and Gauss-Newton method,the homotopy algorithm in non-linear data processing has unique advantages.In the course of the homotopy path tracking the termination criterion of Newton iteration has been improved,and a step control strategy based on curvature ratio has been proposed.Then a fast homotopy algorithm has been acquired.

关 键 词：非线性最小二乘 同伦路径跟踪算法 迭代终止判据 步长控制策略 

分 类 号：P207[天文地球—测绘科学与技术]