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测绘学报  2014 

附有不等式约束的加权整体最小二乘算法

DOI: 10.13485/j.cnki.11-2089.2014.0173, PP. 1013-1018

Keywords: 整体最小二乘估计,EIV模型,不等式约束,非线性算法

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Abstract:

针对现有附有不等式约束的整体最小二乘算法的缺陷,本文以partialEIV(errors-in-variables)模型[1]为基础,在整体最小二乘准则下,通过将附有不等式约束的EIV模型的求解转换为标准的附有不等式约束的最优化问题,并采用惩罚函数法等方法得到了附有不等式约束的加权整体最小二乘新算法。新算法将现有算法的特殊权阵限制条件扩展到了一般性权矩阵,将要求系数矩阵元素全部随机的限定条件扩展到了可同时包含随机和非随机元素的一般情况,并且新算法解决了现有算法计算量受制于约束方程数量的缺陷。实例计算表明,本文提出的算法简单、有效,具有普遍适用性。

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