EIV模型参数估计的新方法

提出了一种EIV(errors-in-variables)模型参数估计的新方法,即根据非线性最小二乘平差理论,并用构造结构矩阵的方法来顾及系数矩阵的重复元素和常数项,推导了其迭代算法和精度评定公式。新方法统一了总体最小二乘、加权总体最小二乘以及结构总体最小二乘三种算法,并给出了详细的解算步骤。新方法的推导过程及其迭代格式较为简单,易于程序实现。最后通过两个实例验证了本文方法的有效性和可行性。

A New Method of Parameter Estimation for the EIV Model

We address the problem of simplifying the algorithm of parameter estimation for EIV models. Since the EIV model is a nonlinear model, not a simple linear relationship, the traditional method is complex and hard to evaluate its precision. In this paper, a new method of parameter estimation for EIV models is presented. The iteration algorithm and accuracy evaluation formulas are deuced based on the nonlinear least squares adjustment theory and by using a structured matrix and by taking into account the repetitive elements and constant term. The new method unifys three algorithms including the total least squares, the weight total least squares and the structured total least squares, and gives a detailed solution steps. It is easy to deduce and productive to use the new method. At last, the effectiveness and applicability of the new method are verified by two experiments.