整体最小二乘法与最小二乘法的差异性分析

Difference analysis and comparison between total least squares and least squares

加权整体最小二乘法(WTLS)估计变量误差模型(EIV)参数需要进行大量的矩阵运算,为了提升估计EIV模型参数的计算效率.本文以WTLS的平差准则为出发点,运用矩阵运算定理,研究了WLS与WTLS平差准则之间的联系,从理论上证明了最小二乘法(不加权)与整体最小二乘法(不加权)估计EIV模型参数的等价性;同时分析了在EIV模型参数是微小量的条件下,用加权最小二乘法(WLS)直接代替WTLS估计EIV模型参数的可行性.模拟结果表明,在坐标转换参数是微小量的情况下WLS和WTLS的解算结果基本一致,验证了理论分析的正确性.

Because weighted total least squares(WTLS)method has a great amount of matrix operations,the computing efficiency of WTLS is lower than that of weighted least squares WLS.To improve the computational efficiency,this paper theoretically analyses the relationship between WLS and WTLS based on the adjustment criterion of WTLS.When the coefficient matrix and the observation vector are given unit weight matrix,the equivalence of the least squares(unweighted)and the total least squares(unweighted)for estimating the parameters of EIV model is proved.At the same time,the feasibility of using WLS instead of WTLS to estimate the parameters of EIV model is discussed under the small parameter conditions.Finally,a simulation experiments of coordinate transformation is provided.The simulation results show that the solution results of WLS and WTLS are basically the same when the coordinate transformation parameters are small.