多元总体最小二乘问题的牛顿解法

为提高多元总体最小二乘问题参数估值的解算效率,推导了基于牛顿法的多元加权总体最小二乘算法;分析比较了基于牛顿法的多元加权总体最小二乘解和基于拉格朗日乘数法多元加权总体最小二乘解之间的关系,根据协因数传播律给出了多元总体最小二乘平差的16种协因数阵的近似计算公式。新算法能够解决观测矩阵和系数矩阵元素具有相关性的问题,并且可以把观测矩阵和系数矩阵的随机元素和常数元素纳入到一个协因数阵中进行处理。算例结果表明,本文提出的多元总体最小二乘问题的牛顿解法可行且收敛速度更快。...

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Bibliographic Details
Published in测绘学报 Vol. 45; no. 4; pp. 411 - 417
Main Author 王乐洋 赵英文 陈晓勇 臧德彦
Format Journal Article
LanguageChinese
Published 东华理工大学测绘工程学院,江西南昌330013 2016
流域生态与地理环境监测国家测绘地理信息局重点实验室,江西南昌330013
江西省数字国土重点实验室,江西南昌330013%东华理工大学测绘工程学院,江西南昌,330013
Subjects
仿射变换
协因数传播律
多元总体最小二乘
牛顿法
牛顿法
仿射变换
多元总体最小二乘
propagation of cofactor
协因数传播律
multivariate total least squares
Newton method
affine transformation
Online AccessGet full text
ISSN1001-1595
DOI10.11947/j.AGCS.2016.20150246

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Summary:为提高多元总体最小二乘问题参数估值的解算效率,推导了基于牛顿法的多元加权总体最小二乘算法;分析比较了基于牛顿法的多元加权总体最小二乘解和基于拉格朗日乘数法多元加权总体最小二乘解之间的关系,根据协因数传播律给出了多元总体最小二乘平差的16种协因数阵的近似计算公式。新算法能够解决观测矩阵和系数矩阵元素具有相关性的问题,并且可以把观测矩阵和系数矩阵的随机元素和常数元素纳入到一个协因数阵中进行处理。算例结果表明,本文提出的多元总体最小二乘问题的牛顿解法可行且收敛速度更快。
Bibliography:11-2089/P
WANG Leyang;ZHAO Yingwen;CHEN Xiaoyong;ZANG Deyan（ 1. Faculty of Geomatics, East China University of Technology, Nanchang 330013, China; 2. Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG,Nanchang 330013, China; 3. Jiangxi Province Key Lab for Digital Land, Nanchang 330013, China）
multivariate total least squares; Newton method; propagation of cofactor; affine transformation
In order to improve calculation efficiency of parameter estimation,an algorithm for multivariate weighted total least squares adjustment based on Newton method is derived.The relationship between the solution of this algorithm and that of multivariate weighted total least squares adjustment based on Lagrange multipliers method is analyzed.According to propagation of cofactor,16 computational formulae of cofactor matrices of multivariate total least squares adjustment are also listed.The new algorithm could solve adjustment problems containing correlation between observation matrix and coefficient m
ISSN:1001-1595
DOI:10.11947/j.AGCS.2016.20150246