基于卡尔曼滤波的混沌系统辨识

Kalman filtering based method for identification of chaotic sequence

通过建立一种对混沌时间序列进行有效预测的方法构架,试图实现尽可能长期的混沌预测,并重构序列的主动态方程,以便于进一步的分析研究.根据非线性系统的一般框架,首先基于所观测时间序列的基本混沌特性寻找一典型混沌方程作为参考的系统动态方程;然后利用扩展卡尔曼滤波递推得到一动态方程式来逼近系统特性,重构混沌相空间吸引子.仿真结果表明,该方法可以实现较高精度的多步预测并有效地重构系统方程.

Aiming at presenting a new and effective methodology to predict chaotic time series, the authors try to make prediction as longer as possible and construct the governing system equations so that the further researches can be conducted. Based on a general nonlinear system structure, firstly, the typical chaotic equations as reference system equations that show similar chaotic characteristics with those of the observed time series are searched. Secondly, the general system equations are approximated to system characteristics using Kalman filtering based method and the attractors in phase spaces are reconstructed. Simulation results show that this method can realize multistep prediction with a higher precision, and construct the system equations effectively.