快速广义最小二乘法及其仿真

在线性系统辨识中,由于输入/输出间存在着量测噪声等,致使系统方程的残差是相关的,应用普通最小二乘法求取模型得到的将是有偏估计。为克服这一缺点,常采用广义最小二乘法,但它要求确定的残差方程和进行数据滤波、具有存储量大、计算速度慢等缺点。本文介绍另一种无偏估计的新算法—快速广义最小二乘法,通过理论推导和仿真研究,给出算法框图、选择参数方法以及仿真运行中的有关问题。

FGLS Method and Its Emulation

In linear system identification, the error of system equations will usually be correlative because of existance of the noice produced in measuring the input and the output. Therefore, the obtained estimate will be biased if using the ordinary least square method. Usually a generalized least squar syuare method is used to eliminate the deturbing of this noice. But, generliged least square method requires that error equations must be determinisiic and the data must be filtered. Moreover, this method needs large memory and has lower calculating speed. Using both of theoretical derivation and emulation, this paper introduced another kind of qeneralized method With unbiased estimate—FGLS method and discussed how to determine parameters, listed the questions related to this method simulation and gave an algorithm flowchart.