多项式模型方次与参数同时估计的正交化法

 本文提出多项式模型方次与参数同时估计的一种方法。利用切比雪夫多项式使矛盾方程组系数矩阵正交化,利用Householder变换直接解矛盾方程组,尽可能降低病态条件数,提高了计算精度。同时,通过对信息矩阵的适当排列,在估计参数的过程中得到各次模型所对应的最小二乘估计的残差平方和,从而实现了模型方次和参数的同时估计。

ORTHOGONALIZATION METHOD OF SIMULTANEOUS ESTIMATION OF POLYNOMIAL MODEL ORDER AND PARAMETER

Orthogonalization method of simultaneous estimation of polynomial model order and parameter is presented in this paper. The coefficient matrix is orthogonalized by using polynomial and the overdetermined equations are solved by Householder transformation. The numerical ill-condition is decreased as low as possible, hence the operational accuracy is increased. The least square cost functions of several different model order can. be obtained in the process of parameter estimation by means of specially arranging the information matrix and hence the model order and parameter can be simutaneously estimated.