邱卫宁, 齐公玉, 田丰瑞. 整体最小二乘求解线性模型的改进算法[J]. 武汉大学学报 ( 信息科学版), 2010, 35(6): 708-710.
引用本文: 邱卫宁, 齐公玉, 田丰瑞. 整体最小二乘求解线性模型的改进算法[J]. 武汉大学学报 ( 信息科学版), 2010, 35(6): 708-710.
QIU Weining, QI Gongyu, TIAN Fengrui. An Improved Algorithm of Total Least Squares for Linear Models[J]. Geomatics and Information Science of Wuhan University, 2010, 35(6): 708-710.
Citation: QIU Weining, QI Gongyu, TIAN Fengrui. An Improved Algorithm of Total Least Squares for Linear Models[J]. Geomatics and Information Science of Wuhan University, 2010, 35(6): 708-710.

整体最小二乘求解线性模型的改进算法

An Improved Algorithm of Total Least Squares for Linear Models

  • 摘要: 针对观测方程中观测向量和数据矩阵均有误差的情况,提出了整体最小二乘的改进算法,利用附有限制条件的平差模型,导出了观测向量和数据矩阵精度不等情况下的计算公式。该算法满足拟合方程应有的条件,提高了整体最小二乘递推算法的逼近精度,为整体最小二乘应用于测量数据处理提供了可行的方法。

     

    Abstract: Aiming at the condition that among observation equations there are errors in both observation vector and structure matrix,we propose an improved algorithm of total least squares(TLS).Meanwhile,when observation vector and structure matrix are with unequal precision,we deduce the calculation formula using an adjustment model with constraints.Analysis and calculation show that the algorithm that improves approximation accuracy of recursive TLS effectively,can satisfy the conditions needed by fitting equation.

     

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