基于修正量改进的递推子空间辨识算法

Recursive 4SID Subspace Identification Algorithms with Correction Method

传统的递推4SID子空间辨识算法存在对时变参数跟踪速度慢、易受噪声干扰等缺点,而基于滑窗的算法虽然提高了对时变参数的跟踪速度,但其算法实现复杂、计算量大。针对上述问题,首先运用矩阵方法从递推4SID子空间算法的数据压缩矩阵中分离出需剔除旧数据作用的修正量,并给出相关证明。在此基础上,结合固定遗忘因子方法设计了新的递推4SID子空间辨识算法。与传统遗忘因子方法相比,新的算法可以在选择较大遗忘因子的情况下,利用修正量有效隔断历史数据的作用,在降低对噪声的敏感度的同时提高了对时变参数的跟踪速度。与此同时,基于修正量的算法可以通过调整阈值大小改变对时变参数的跟踪速度。仿真结果验证了算法的有效性。

Several disadvantages are existed in traditional recursive 4SID algorithms, such as low tracking performance of time-varying systems and easily disturbed by noises. The recursive subspace identification algorithm based on moving window has large computation and complex realization. According to above problems, the eliminated correlation is separated from input and output Hankel matrices with the help of correction method, which is proved theoretically. Based on this thesis, a new recursive subspace identification algorithm is designed combining with fixed forgetting-factor method. Compared with traditional algorithms, the new method, in which larger forgetting factor is chosen, not only reduces the sensitivity with noises, but also has faster convergent rate because it can cut off the influence of old-data effectively. And the tracking convergent rate of the new algorithm can be adjusted by the threshold. Finally, the efficiency of this method is illustrated with two simulation examples.