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势函数解决附不等式约束平差问题的研究

发表时间:2008-03-31  浏览量:1469  下载量:671
全部作者: 欧阳文森,欧为林,朱建军
作者单位: 长沙县国土资源局;湖南省第一测绘院;中南大学信息物理工程学院
摘 要: 测量数据处理中经常会有些先验信息可以利用,这些先验信息可以总结成等式或不等式。附等式约束的平差理论目前已经十分成熟,因而如果是等式约束,则可用附等式约束的间接平差方法来处理。但如果是不等式约束,即附不等式约束的平差问题在直接求解时有所困难,FRISCH(1955)和CARROLL(1961)提出了将不等式约束转化为无约束的罚函数算法并在求解优化问题上取得了非常好的效果,然而这种经典的罚函数随着惩罚因子的增大,其Hessian矩阵会出现病态,收敛速度会变的很慢。本文试图运用罚函数的思路,尝试引入一种势函数算法并结合最小二乘平差模型来解决附不等式约束的平差问题;文中通过分析基于最优性条件(K-T条件)下该势函数具有的四个性质和拉格朗日函数法来推导平差结果及其统计特征的显式表达式,通过编程可知算法过程简单、易推广,从数值算例的结果也证明该算法具有可行性。
关 键 词: 大地测量;线性不等式约束;势函数;最小二乘平差;显式表达式
Title: Solving the LICA problem by a potential function method
Author: OUYANG Wensen, OU Weilin, ZHU Jianjun
Organization: The Bueau of Land and Resources Changsha Town;The First Surveying and Mapping institute of Hunan Province;Info-physics Geomatics Engineering Colleg, Central South University
Abstract: In survey data processing, sometimes there is prior information that can be used. This prior information can be expressed by equality or inequality constraints on the parameters. The equality-constrained adjustment theory has been maturated and comprehended, so if the constraints are equality the problem can be solved by the equality-constrained indirect adjustment theory. However, if the constraints are linear inequality, the problem become linear inequality constrained adjustment (LICA) and the computation will be very difficult. FRISCH(1955) and CARROLL(1961) proposed that penalty function which transformed constrained-unequation into unstrained function obtain good result, but the Hessian matrix will be sick and the convergence speed will be slow with the penalty factorial's accretion. So the paper tries to adopt the thought of penalty and combines one new potential function (PF) method and least-square method to solve the LICA problem. It analyses the PF’s four characteristics based on the K-T principle and Lagrange function method and then educates the explicit expression of adjustment result and thus the statistical properties can be easily determined. A numerical example is given to show the interesting method.
Key words: geodetic survey; LICA; potential function; least-square adjustment; explicit expression
发表期数: 2008年7月第6期
引用格式: 欧阳文森,欧为林,朱建军. 势函数解决附不等式约束平差问题的研究[J]. 中国科技论文在线精品论文,2008,1(6):622-627.
 
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