基于Kalman滤波算法的Volterra级数核估计及其应用  

Volterra-kernel estimation and its application based on Kalman filtering algorithm

作　　者：彭秀艳[1] 门志国 刘长德 

机构地区：[1]哈尔滨工程大学自动化学院,黑龙江哈尔滨150001

出　　处：《系统工程与电子技术》2010年第11期2431-2435,2475,共6页Systems Engineering and Electronics

摘　　要：为了进一步提高Volterra级数模型在混沌时间序列预测中的精度以及核估计的收敛速度,提出利用自适应Kalman滤波算法对Volterra级数核进行估计的一种新方法。同时,在混沌动力系统相空间重构的基础上,采用关联维数法和最大Lyapunov指数法,对船舶运动时间序列进行混沌特性判定,并对船舶横摇运动时间序列进行多步预测。仿真表明,与归一化最小均方(normalization least-mean-square,NLMS)算法和最小二乘(recursive least-square,RLS)算法的Volterra级数模型相比,基于自适应Kalman滤波算法的Volterra模型在收敛速度与预报精度方面均优于NLMS算法和RLS算法,为实时在线预报提供了理论依据。In order to improve chaotic time series forecasted precision and convergence rate of kernels about Volterra series model.A new method is presented to estimate the Volterra series＇ kernels based on Kalman filtering algorithm.Meanwhile,based on the reconstruction of the chaotic dynamic space,the chaos characteristics of ship motion time series are identified using the correlation dimension method and Lyapunov exponent method.The experiments of ship rolling motions time series multi-step forecasts are done based on the obtained Volterra series model.The simulation results indicate this method with Kalman filtering algorithm is feasible,the convergence rate and the prediction precision are better than the recursive least-square（RLS） algorithm and normalization least-mean-square（NLMS） algorithm.The theory basis is provided for the real-time online forecast.

关 键 词：VOLTERRA级数 Kalman滤波算法 相空间重构 关联维数 最大Lyapunov指数法 多步预测 

分 类 号：TP29[自动化与计算机技术—检测技术与自动化装置]