部分变量误差模型的整体抗差最小二乘估计

发布时间：2019-06-09 14:24

【摘要】：部分变量误差模型(partial EIV model)的加权整体最小二乘(weighted total least-squares,WTLS)估计不具备抵御粗差的能力。鉴于粗差可能同时出现在观测值和系数矩阵中,本文在提出部分变量误差模型WTLS估计的两步迭代解法的基础上,运用抗差M估计的等价权方法,发展了一种整体抗差最小二乘(TRLS)估计方法,并采用一致最大功效统计量确定降权因子。针对WTLS估计两步迭代解法的特点,设计了两个不同的降权方案:第1个方案是在估计系数矩阵元素时,不对观测值降权,仅对系数矩阵降权;第2个方案是在估计系数矩阵元素时,既对系数矩阵降权,同时也对观测值降权。通过对模拟2D仿射变换和线性拟合实例进行计算和分析,结果表明第1方案优于第2方案,并且优于基于残差和验后单位权方差的抗差估计和现有的变量误差模型抗差估计。
[Abstract]:The weighted global least squares (weighted total least-squares,WTLS (weighted total least-squares,WTLS) estimation of partial variable error model (partial EIV model) does not have the ability to resist gross errors. In view of the fact that gross errors may appear in both observed values and coefficient matrices at the same time, based on the two-step iterative method of WTLS estimation of partial variable error model, the equivalent weight method of robust M estimation is used in this paper. In this paper, a global robust least square (TRLS) estimation method is developed, and the weight reduction factor is determined by uniform maximum efficiency statistics. According to the characteristics of two-step iterative solution of WTLS estimation, two different weight reduction schemes are designed: the first scheme is not to reduce the weight of the observed value, but only to the coefficient matrix when the element of the coefficient matrix is estimated. The second scheme is to reduce the weight of the coefficient matrix as well as the observed values when the elements of the coefficient matrix are estimated. Through the calculation and analysis of simulated 2D affine transformation and linear fitting examples, the results show that the first scheme is superior to the second scheme, and is superior to the robust estimation based on residual and post-checking unit weight variance and the existing variable error model robust estimation.
【作者单位】：信息工程大学地理空间信息学院;信息工程大学理学院;
【基金】：国家自然科学基金(41174005;41474009)~~
【分类号】：P207

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