System identification of autoregressive processes on Stiefel and Grassmann manifolds are presented and studied. We define the system parameters as elements in the orthogonal group and we show that the system can be estimated by averaging over observations. Then we propose an algorithm on how to compute these system parameters using conjugate gradient descent on Stiefel and Grassmann manifolds, respectively.

翻译：本文提出并研究了Stiefel流形与Grassmann流形上自回归过程的系统辨识问题。我们将系统参数定义为正交群中的元素，并证明该系统可通过观测值的平均化进行估计。随后，我们分别提出在Stiefel流形和Grassmann流形上利用共轭梯度下降法计算这些系统参数的算法。