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

测绘学报 ›› 2014, Vol. 43 ›› Issue (10): 1013-1018.doi: 10.13485/j.cnki.11-2089.2014.0173

附有不等式约束的加权整体最小二乘算法

曾文宪¹,方兴¹,刘经南²,³

1. 武汉大学测绘学院
2. 武汉大学卫星定位导航技术研究中心
3. 武汉大学测绘学院

收稿日期:2013-12-16 修回日期:2014-03-19 出版日期:2014-10-20 发布日期:2014-10-24
通讯作者: 方兴 E-mail:xfang@sgg.whu.edu.cn

Weighted Total Least Squares Algorithm with Inequality Constraints

ZENG WenxianFANG Xing²,LIU Jingnan²,³

Received:2013-12-16 Revised:2014-03-19 Online:2014-10-20 Published:2014-10-24
Contact: FANG Xing E-mail:xfang@sgg.whu.edu.cn

摘要/Abstract

摘要：

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partial EIV（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。

关键词: 整体最小二乘估计, EIV模型, 不等式约束, 非线性算法

Abstract:

Since the inequality-constrained total least squares (ICTLS) is strongly limited due to the combinational difficulty, we investigate to adjust the partial errors-in-variables

(EIV) model which is equipped with inequality constraints. In this paper, we reconfigure the original ICTLS problem to a standard optimization problem, which can be

solved by existing methods such as penalty based methods. The novel ICWTLS (inequality-constrained Weighted TLS) algorithm can deal with the ICTLS problem with a

structure coefficient matrix and a general weight matrix, and successfully avoid the combinatorial difficulty. The examples illustrate that the new algorithm proposed in this 　

paper is efficient and simple, which can be used in a general case in practice.

Key words: total least squares, errors-in-variables model, inequality constraints, nonlinear program

中图分类号:

p207

曾文宪方兴刘经南. 附有不等式约束的加权整体最小二乘算法[J]. 测绘学报, 2014, 43(10): 1013-1018.

ZENG Wenxian FANG Xing LIU Jingnan. Weighted Total Least Squares Algorithm with Inequality Constraints[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(10): 1013-1018.

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附有不等式约束的加权整体最小二乘算法

Weighted Total Least Squares Algorithm with Inequality Constraints

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