一种基于Partial EIV模型的多项式拟合解法

A Kind of Polynomial Fitting Method Based on Partial EIV Model

针对多项式拟合模型系数矩阵中部分元素是某一自变量的函数的特点,根据Partial EIV模型的解算思想,将系数矩阵中自变量的函数作为随机元素提取,顾及泰勒展开的二阶项,由协方差传播律计算自变量函数的协因数阵进行平差解算。实验结果表明,系数矩阵的元素不再是单独的自变量时,使用该算法可以得到与已有非线性总体最小二乘方法相近的参数结果,从构造随机向量权阵的角度提供了一种新的解算方法。

The coefficient matrix is the functions of some independent variables in the polynomial fit- ting model. According to the solution of the partial errors-in-variables（Partial EIV） model, the ran- dom elements that are the functions of independent variables of the coefficient matrix are extracted. Considering the quadratic terms of the Taylor expansion, the cofactor matrix,which is the functions of independent variables, is obtained by the law of covariance propagation. The experiments show that the results obtained by the method of this paper are similar to those obtained by the method of existed non-linear total least squares method when the elements of coefficient matrix are no more individual independent variables. This provides a method of structuring the weight matrix of random vectors.