有色噪声背景下的正交子空间辨识
Orthogonal subspace identification in the presence of colored noise

针对传统子空间辨识中存在的有色噪声干扰问题, 本文提出一种正交子空间辨识方法. 首先, 根据子空间辨识算法机制构建含有色噪声的扩展状态空间模型. 然后, 结合有色噪声的相关性分析, 研究了传统子空间辨识方法的有偏性问题, 并重新设计了投影向量和正交投影方式, 用以消除有色噪声干扰. 最后, 对投影后的数据矩阵进行奇异值分解, 获取广义能观测矩阵, 进而求得系统的状态空间模型参数. 仿真结果表明该方法在有色噪声干扰下是一致无偏的, 并且具有渐进二阶统计特性. 结合陀螺仪的具体实验结果表明, 该算法在实际应用中具有比传统子空间辨识法更高的辨识精度.
To deal with the problem of colored noise in traditional subspace identification methods, this paper proposes an orthogonal subspace identification method. First, the extended state space model with colored noise is built, based on the subspace identification algorithmic mechanism. Then, with the colored noise correlation analysis, the bias problem of traditional subspace identification methods is discussed, and novel projection vector and orthogonal projection method are redesigned to eliminate the colored noise. Finally, the extended observability matrix, which is used to get the state space model parameters, is estimated through singular value decomposition of the orthogonal projection data matrix. The simulation results show this method is consistent and unbiased, and has asymptotic distribution property. The experiments with one gyroscope indicate this method can achieve better identification accuracy in practice than traditional subspace identification methods.