ARMAX模型参数估计的新两步法

 本文提出了一种ARMAX模型参数估计的新两步法。这种方法与其它递推估计方法（如增广矩阵法,极大似然法,Durbin两步法、三步法等）比较,具有较好的收敛特性,对参数的估计,特别是对C参数的估计比较精确,这是利用其它方法,一直未能很好解决的一个难题。

A NEW TWO STAGE RECURSIVE ESTIMATION FOR ARMAX PROCESSES

ARMAX model is a very important model in practice. It has been used for describing the stochastic processes extensively. It represents the general form for popular time-series and digital-filter models. Therefore, many research work have been carried out and different estimate methods have been presented.Professor K. J. Astrom and D. Q. Mayne showed in their work that the three stage least square method, which is a new algorithm for recursive parameter estimation in ARMAX processes, was a good method.It is shown that the algorithm under reasonable condition always converges and has a good convergent performance.Based on the multistep(three steps)methods the author proposed a new two stage recursive estimation method in this paper.This method is different from the first two stage of the multistep method, namely, this method is different from Durbin's two stage recursive estimation.With this new method,a recursive estimation of parameters in ARMAX process was implemented, and a better computer simulation result was obtained. For the computational stability, the square root algorithm was used. In comparison with other recursive estimation method, such as the extended matrix method, the general recursive least square method, the recursive maximum likelihood method, and the three stage recursive estimation method, etc, this new two stage method has good convergence to the true parameters, especially for the parameter C, which has not been solved with other estimation methods up to now, and still is a very difficult problem. The simulation of the application of this method to self-turning control also provided a satisfactory result.