混合结构总体最小二乘参数估计

ON MIXED STRUCTURED TOTAL LEAST SQUARES FOR PARAMETERS ESTIMATION

为解决当系数矩阵由常数列和非常数列组成,非常数列含有重复元素时传统混合总体最小二乘估计理论不够严密的问题,提出混合结构总体最小二乘参数平差模型,根据非线性最小二乘平差理论推导了混合结构总体最小二乘参数平差的迭代计算公式,并分别模拟计算了观测向量元素所受误差干扰量等于、大于和小于非常数列中非重复元素误差干扰量三种情况。实验结果表明:混合结构总最小二乘法不仅能够同时估计出系数矩阵常数列和非常数列所对应的参数值,而且能够对常数元素赋予零改正值,不同位置的同一元素赋予相同的改正值,单位权中误差估计值更接近模拟值;在系数矩阵非常数列中非重复元素所受误差干扰量大于观测矢量所受误差干扰量时,混合结构总体最小二乘参数平差法的参数和单位权中误差估计结果明显更接近于真实值。

In this contributions we defined the model of mixed structured total least squares according to the mixed least squarestotal least squares and proposed an iterative algorithm for the mixed structured total least squares problems, which solving by the nonlinear least squares adjustment theory. Three numerical examples are given at last, where assumes the errors of elements in observation vector equal , greater and lesss than the error of in dependent elements in coefficient matrix , respectively. It＇ s shown that the method represented in this paper would be able to estimate the parameters theoretically closer to the true value and attain the more precise mean square er ror of weight unit than least squares and mixed least squarestotal least squares, especially when the coefficient ma trix which holds more errors than observation vector.