基于主成分分析和噪声估计的在线子空间辨识

提出一种在线子空间辨识方法，该方法主要采用Hessenberg QR分解和特征值分解，通过对噪声项进行估计，并结合主成分分析提取子空间矩阵，获得系统的状态空间方程.引入遗忘因子机制，实现对时变系统的辨识.为了验证所提方法的适用性和有效性，分别采用数值模型和工业污水处理过程进行仿真验证.仿真结果表明，相比于其他子空间辨识方法，所提方法在辨识线性时不变系统时，能够获取很好的辨识精度；在辨识线性时变系统时，能够快速跟踪系统变化，并能够获取较好的辨识精度。

Online subspace identification based on principal component analysis and noise estimation

An online subspace identification algorithm was proposed. The underlying principles of the proposed online subspace identification method use Hessenberg QR algorithm QR factorization and eigenvalue decomposition to estimate the noise term, and then extract the subspace matrices by using principal component analysis. The state space model can be derived from the estimated subspace matrices. An exponential weight forgetting mechanism was introduced to capture the characteristics of the time-varying processes. In order to demonstrate the capability and efficiency of the proposed method, a numerical example and an industrial wastewater treatment process are used to verify the performance. The results of numerical and industrial benchmark simulations show that, compared with other subspace identification methods, the proposed method can derive good identification accuracy in the linear time invariant system, and can derive good performance in terms of system tracking and identification accuracy in the linear time variant system.