灰色系统GM(n,m)模型参数的递推估计和时变估计

本文给出灰色系统GM(n,m)模型参数的递推最小二乘估计和时变参数估计,前者的优点是可以避免反复求逆矩阵,因而使计算简便,同时克服了文献1中给出的估计方法当观察数据多、矩阵线数高、分配单元增加时,微型机容量不够的弱点,而且随着新数据的到来,通过递推算法自动对系统参数加以修正,提高了模型的自适应性;时变参数估计可以缩小系统的时变性与模型参数非时变性所产生的差异。

TH ERECURSIVE ESTIMATE AND TIME VARYING ESTIMATE ON PARAMETERS OF THE GM(n,m)MODEL OF GREY SYSTEM

In this paper, we have given a recursive least square estimate and a time varying parametere estimats for the parameters that appear in grey system GM(n, m) model.The advantage of the first estimate is that, on the one hand,the process of repeatedly computing inverse matrix can be avoided, therefore time is saved. This is true particularly when the data observed are many and the matrix dimension is high, and the computation can not be easily finished in a microcomputer in the usual way.On the other hand, the parameters of the system can be modified automatically through recursive algorithm, so it enhances the adaptivity of the model.The second estimate can lessen the difference produced between time varying property of the system and non-time varying property of the model parameters,