整体最小二乘的迭代解法

孔建, 姚宜斌, 吴寒

孔建, 姚宜斌, 吴寒. 整体最小二乘的迭代解法[J]. 武汉大学学报 ( 信息科学版), 2010, 35(6): 711-714.
引用本文: 孔建, 姚宜斌, 吴寒. 整体最小二乘的迭代解法[J]. 武汉大学学报 ( 信息科学版), 2010, 35(6): 711-714.
KONG Jian, YAO Yibin, WU Han. Iterative Method for Total Least-Squares[J]. Geomatics and Information Science of Wuhan University, 2010, 35(6): 711-714.
Citation: KONG Jian, YAO Yibin, WU Han. Iterative Method for Total Least-Squares[J]. Geomatics and Information Science of Wuhan University, 2010, 35(6): 711-714.

整体最小二乘的迭代解法

基金项目: 国家自然科学基金资助项目(40774008,40721001);国家973计划资助项目(2006CB701301)
详细信息
    作者简介:

    孔建,硕士生,现从事测量数据处理与理论方面的研究。

  • 中图分类号: P207.2

Iterative Method for Total Least-Squares

Funds: 国家自然科学基金资助项目(40774008,40721001);国家973计划资助项目(2006CB701301)
  • 摘要: 在引入整体最小二乘平差准则的基础上,推导了整体最小二乘的迭代解法;同时,引入多元函数隐函数求导的方法以确定未知参数对观测数据的线性信息,解决了整体最小二乘下的精度评定问题。给出了运用新的解法在拟合函数确定以及坐标转换参数确定等方面的应用实例,验证了新算法的可行性。
    Abstract: The conventional solution method for TLS is based on matrix singular value decomposition.This method is rigorous in theory,but is complex and not easy to be programed.The complexity of the method is an important reason restricting TLS application in the field of Geomatics.By introducing the total least-squares adjustment standard,we derive the total least-squares iterative method,which is simple and easy to be programed.Through the introduction of multi-function derivative knowledge of the implicit function to determine the linear information of the parameters to observational data,we solve the problem of assessing the accuracy based on TLS.Finally,we apply the new method to the fitting function determination and coordinate transformation parameters determination based on measured data,and verify the feasibilities of the new method.The new method has a great significance to the popularization and application of TLS.
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出版历程
  • 收稿日期:  2010-04-27
  • 修回日期:  2010-04-27
  • 发布日期:  2010-06-04

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