摘要
通过理论推导,发现总体最小二乘解是最小二乘解的线性变换;当系数矩阵含有误差时最小二乘解是有偏的,而总体最小二乘解是无偏的;总体最小二乘解的条件数大于最小二乘解的条件数,总体最小二乘解更容易受到数据误差的影响。通过进一步推导给出了总体最小二乘与最小二乘在解、残差、单位权方差估值等方面的关系式。
Through theory derivation and proof,some properties of the total least squares estimation are found.The total least squares estimation is the linear transformation of the least squares estimation.When the coefficient matrix contains error,the least squares is biased.The total least squares estimation is unbiased.The condition number of the total least squares estimation is bigger than that of the least squares estimation,so the total least squares estimation is more easier to be affected by the data error than the least squares estimation.Through further derivation,the relation of solutions,residuals,unit weight variance estimations between the total least squares and the least squares are given.
出处
《大地测量与地球动力学》
CSCD
北大核心
2012年第5期48-52,57,共6页
Journal of Geodesy and Geodynamics
基金
国家自然科学基金(41204003)
东华理工大学博士科研启动基金(DHBK201113)
江西省数字国土重点实验室开放研究基金(DLLJ201207)
关键词
总体最小二乘
最小二乘
奇异值分解
残差
单位权方差
total least squares（TLS）
least squares（LS）
singular value decomposition（SVD）
residual
unit weight variance
