一种Partial EIV半参数模型的系统误差处理方法

摘要

在使用总体最小二乘求解参数时,若观测值中包含系统误差,此时得到的参数估值则会受到系统误差的影响,从而得到不可靠的解,因此必须削弱系统误差对参数估计的影响,以获得相对可靠的解.本文提出在partial errors-in-variables(Partial EIV)模型的基础上给观测值增加非参数部分(系统误差),从而构建Partial EIV半参数模型;基于补偿最小二乘准则进行公式推导,并分别通过选取适当的正则化矩阵及通过L曲线法确定平滑因子.通过算例结果分析表明,与传统方法相比,本文的方法在一定程度上能够削弱系统误差的影响,得到更为可靠的参数解,从而验证了该方法的有效性和可行性.%The estimated values are affected so that they are not reliable if the observations contain systematic errors under the solution of total least squares.Thus the bad effect on the estimated values should be weakened so the relatively reliable solution can be obtained.This paper adds non parametric part (systematic errors) in the partial errors-in-variables (Partial EIV) model,building Partial EIV semiparametric model.The penalized least square criterion is introduced to derive formula,and choose the proper regularization matrix in the experiments.The smoothing factor is acquired by the method of L-curve.The results of experiments show that the algorithm of Partial EIV semi-parametric model can mitigate systematic errors to a certain extent and obtain the more reliable solution than the traditional method.So the validity of the algorithm is verified.