基于主元分析的子空间辨识算法

A New Subspace Identification Algorithm Using Principle Component Analysis

子空间辨识算法作为一种优良的多变量系统辨识算法,最近在国内发展很快。但是现在国内介绍的大多数子空间辨识算法在变量有误差(errors-in-variable)时和闭环辨识时辨识结果却是有偏的,这是因为大多数子空间辨识算法都假设输入变量是没有噪声及辨识算法中存在的一个投影过程。文中介绍了一种新的子空间辨识算法,这种算法利用主元分析(PCA)来获取系统矩阵,避免了其他算法中的投影过程,因此该算法在闭环辨识和变量有误差(errors-in-variable)的情况下,辨识结果也是无偏的。最后给出一个仿真例子说明这种辨识算法的辨识效果良好。

The subspace identification algorithm as a kind of muhivariable identification algorithm has developed quickly at home recently. But most of these algorithms at home have errors in the errors - in - variable situation and close - loop situation. The reason is that most of subspace algorithms assume the input variable to be noise free and there is a projection in the algorithm. This text introduces a new identification algorithm that uses principle component analysis （PCA） to identify the system matrices. That avoids the projection in other algorithms so it can be applied to close - loop and errors - in - variable situation. At last a simulation example is given to demonstrate the effect of this