姚宜斌, 孔建. 顾及设计矩阵随机误差的最小二乘组合新解法[J]. 武汉大学学报 ( 信息科学版), 2014, 39(9): 1028-1032. DOI: 10.13203/j.whugis20130030
引用本文: 姚宜斌, 孔建. 顾及设计矩阵随机误差的最小二乘组合新解法[J]. 武汉大学学报 ( 信息科学版), 2014, 39(9): 1028-1032. DOI: 10.13203/j.whugis20130030
YAO Yibin, KONG Jian. A New Combined LS Method Considering Random Errors of Design Matrix[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9): 1028-1032. DOI: 10.13203/j.whugis20130030
Citation: YAO Yibin, KONG Jian. A New Combined LS Method Considering Random Errors of Design Matrix[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9): 1028-1032. DOI: 10.13203/j.whugis20130030

顾及设计矩阵随机误差的最小二乘组合新解法

A New Combined LS Method Considering Random Errors of Design Matrix

  • 摘要: 目的 提出了一种顾及设计矩阵随机误差的最小二乘组合解法(combined least square,CLS),该算法适用于整体最小二乘(TLS)的参数估计。给出了整体最小二乘平差新算法下的精度评定公式,解决了传统TLS解算方法难以进行严密的精度评定的难题,并通过算例验证了新算法的可行性和正确性。

     

    Abstract: Objective A new combined LS(CLS)method is proposed which considers the random error in a designmatrix after a brief introduction of TLS and its iteration algorithm and the SVD algorithm.The newalgorithm can be applied for TLS parameter estimation,so that TLS can be integrated with classicalLS in theory.By proposing rigorous accuracy assessment formulas for TLS under the new algorithm,this paper solves the bottleneck problem which restricts the application of TLS,and then shows thefeasibility and correctness of the new method through examples.The research results are meaningfulnot only for TLS theory,but also for the whole data processing theory.

     

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