一种基于改进外点法的多项式拟合解法  

A Polynomial Fitting Method Based on Improved Exterior Point Method

作　　者：吴桐[1] 张阳阳[1] 孙妍艳 张万栋[1] 刘翠芝[1] WU Tong;ZHANG Yangyang;SUN Yanyan;ZHANG Wandong;LIU Cuizhi(School of Resources and Civil Engineering, Northeastern University, Shenyang 110819,China)

机构地区：[1]东北大学资源与土木工程学院,沈阳市文化路3号巷11号110819

出　　处：《大地测量与地球动力学》2019年第1期57-60,共4页Journal of Geodesy and Geodynamics

摘　　要：针对多项式模型拟合的参数求解问题,依据最优化方法理论,将其转化为有约束的非线性规划问题进行求解,采用最速下降法进行迭代,从而在不线性化的情况下解决非线性问题。首先通过分析外点法的罚因子、目标函数和迭代初值,说明对外点法改进的合理性;再通过算例,说明该方法的可行性,并与常规方法比较,显示出其精度高、多解性等优点,为研究非线性模型空间数据处理理论提供一种新的思路。This paper considers the problem of parameter fitting for polynomial models.Based on the theory of optimization method,we transform the problem into a constrained nonlinear programming problem,using the fastest descent method to iterate in the calculation to solve the nonlinear problems without linearization.Firstly,the rationality of the improvement of the external point method is illustrated by analysis of the penalty factor,the objective function,and the initial value of the external point method.Secondly,using an example we explain the feasibility of the method;compared with the traditional method,this method possesses high precision and multi-solution,and provides a new idea for studying the spatial data processing theory of nonlinear models.

关 键 词：多项式拟合 最优化方法 约束非线性规划 参数求解 最速下降法 

分 类 号：P207[天文地球—测绘科学与技术]