一种基于高阶累积量的复共轭四阶系统辨识方法

Identification of the Fourth-Order System with Two Pairs of Conjugate Poles Based on Higher-Order Cumulants

研究了利用高阶累积量方法对复共轭四阶系统进行辨识的问题 ,分析讨论了这种四阶系统的特点 ,给出了由连续系统到离散系统的转换公式 ,并利用基于累积量表示的修正尤勒 沃克方程对该四阶系统进行了辨识 .针对估计精度不高的问题 ,提出了前滤波的方法 .在各种不同条件下的仿真对比实验表明 ,在SNR (SignalNoiseRatio)比较低和两对共轭极点距离相距较近时 ,基于高阶累积量的复共轭四阶系统辨识方法比普通自相关方法具有更好的辨识结果 .

The fourth-order system with two pairs of conjugate poles is more difficult to be identified than an ordinary one. The identification of such system is discussed when applying higher-order cumulants. The special fourth-order system is identified by using the modified Yule-Walker equation based on higher-order cumulants. A pre-filtering is used in order to improve the estimation accuracy. Simulations have shown that the proposed method is robust, and the estimation results are much better than the conventional parameter estimators (via second-order statistics). The comparison shows that when SNR decreases, the advantage of the algorithm becomes even more evident. Different inherent harmonious frequencies of the fourth-order system will lead to different estimation accuracy. It is relatively easier to identify the system when one pair of the conjugate poles is far from the other. However, the problem becomes more involved when they get closer.