整体最小二乘法直线拟合

Methods of line-fitting based on total least-squares

针对在直线拟合中,因变量选取不同拟合的结果有差异现象,提出采用整体最小二乘法进行直线拟合。文章在分析直线方程特点的基础上,采用EIV模型描述直线方程,在解算中根据系数矩阵的特点应用QR分解分为将方程两部分,采用了混合最小二乘法求解。理论分析和实际计算结果表明,整体最小二乘法顾及了因变量和自变量的误差。拟合精度高于普通最小二乘法,采用整体最小二乘拟合直线,整体上优于普通最小二乘法。

Line fitting obtained by ordingary least square is often different if the independent variable is defferent, the reason that result in the defference is analysised in the paper. Then the method of line fitting by total least squares is proposed. We describle the line equation with errors-in-variables model, and in the parameter solution the coefficient matrix is divided into two parts by using the QR decomposition. And then the Related parameter can be achieved by the ordianary least squares and total least squares. A conclusion can be got that ling fitting by total least squares is more effective than that of ordianary least square on the whole.