广义最小二乘限定记忆参数辨识方法与仿真研究

Recursive fixed memory generalized least squares method and simulation research

最小二乘参数辨识法可用于动态系统、静态系统、线性系统、非线性系统的参数估计.可用于离线估计,也可用于在线估计.最小二乘辨识法简单、实用,其递推算法收敛可靠,并且当模型噪声为白噪声时,可得到无偏、一致和有效的估计,从而得到广泛的应用.但当模型噪声是有色噪声时,最小二乘参数估计不是无偏、一致估计,并且随着数据的增长,最小二乘递推辨识算法将出现数据饱和现象,以致递推算法慢慢失去修正的能力.广义最小二乘递推算法解决了模型噪声是有色噪声时,最小二乘参数估计的无偏性和一致性问题,并能给出噪声模型的参数估计值,但依然存在数据饱和问题.论文在广义最小二乘递推算法的基础上引入限定记忆方式,获得了广义最小二乘限定记忆参数估计递推算法(RFMGLS),解决了广义最小二乘递推算法的数据饱问题.仿真结果表明了RFMGLS算法的有效性.

The least squares method was used for parameter identification on developing, static, linear and nonlinear system. The least squares method was simple and practicable, and its reeursive algorithm converging and reliable, while equation error was white noise the estimation results was unbiased, consistent and effective. So it was used very extensively. When identified model noise was complicated noise model, the least squares method estimated results was not unbiased or consistently. The recursive algorithm appears saturated phenomenon of data followed by data increasing, which caused it losing amendatory ability slowly. Recursive Generalized Least Squares method resolved the problem that estimated results unbiased and consistency when noise was coloring, but leaved the saturated phenomenon of data. In the paper, recursive algorithm of the Recursive Generalized Least Squares method was combined with fixed memory length, so the Recursive Fixed Memory Generalized Least Squares method was obtained. It resolved the problem that saturated phenomenon of data. Simulated result had indicated algorithmic validity of RFMGLS.