基于Householder变换的贪婪正交最小二乘辨识算法

针对含有未知时滞的多输入受控自回归系统模型的时滞与参数辨识问题,基于Householder变换探讨一种贪婪正交最小二乘辨识算法.首先,由于各输入通道的时滞未知,通过设置输入数据回归长度对系统模型进行过参数化,得到一个含有稀疏参数向量的高维辨识模型;其次,为了避免最小二乘算法中对高维协方差矩阵的求逆运算,利用Householder变换对信息矩阵进行正交分解,推导基于Householder变换的正交最小二乘算法;然后,为了提高辨识效率,降低辨识成本,推导基于Householder变换的贪婪准则,进而得到基于Householder变换的贪婪正交最小二乘辨识算法,该算法能够在少量采样数据的条件下获得稀疏参数向量的估计值;最后,根据估计的稀疏参数向量的结构得到系统时滞估计.仿真结果表明了所提出算法的有效性.

Greedy orthogonal least squares identification algorithm based on Householder transformation

For the identification of the multiple-input controlled autoregressive systems with unknown time-delays, a greedy orthogonal least squares identification algorithm based on the Householder transformation is discussed. Since the time-delays are unknown, an over-parameterization identification model with a sparse parameter vector can be obtained by setting an input regression length. In order to avoid computing the inverse of the high-dimensional covariance matrix in the least squares algorithm, an orthogonal least squares algorithm based on the Householder transformation is derived and a greedy criterion based on the Householder transformation is derived to improve the identification efficiency and reduce the identification cost. The proposed algorithm can effectively estimate the sparse parameter vector with a small amount of sampled data. Finally, the time-delays are estimated according to the structure of the sparse parameter vector. A simulation example is used to illustrate the effectiveness of the proposed algorithm.