基于奇异值分解的Box-Jenkins模型参数估计算法  

Parameter Estimation Algorithm of Box-Jenkins Model Based on Singular Value Decomposition

作　　者：郭建军[1] 张端金[1] 张中华[1] 

机构地区：[1]郑州大学信息工程学院,河南郑州450001

出　　处：《郑州大学学报（工学版）》2008年第3期39-42,共4页Journal of Zhengzhou University（Engineering Science）

基　　金：河南省自然科学基金资助项目(0311011600)

摘　　要：基于奇异值分解和递推广义增广最小二乘原理,提出了Box-Jenkins模型参数估计的一种递推算法.常规的递推广义增广最小二乘算法对舍入误差较为敏感,会导致协方差矩阵失去正定性和对称性,产生病态条件问题,引起数值不稳定现象.为了改善参数估计的性能,利用协方差矩阵的奇异值分解技术,推导出Box-Jenkins模型估计算法.该算法辨识精度高,收敛速度快,数值稳定性好.仿真表明,随着噪信比的增大,新算法仍然具有良好的性能.Based on singular value decomposition （SVD） and recursive generalized extended least squares （RGELS） , a new recursive algorithm of parameter estimation for Box-Jenkins model is proposed. The traditional RGELS algorithm is sensitive to the calculation error of the covariance matrix, and is easy to cause the ill-conditioned problems. In order to improve the parameter estimation performance, SVD based Box-Jenkins model estimation algorithm is derived. Compared with the RGELS algorithm, the proposed method can obtain higher estimation accuracy, faster convergence rate, and better numerical stability. Simulation results show that with the increase of the noise signal ratio, the algorithm still has good estimation performance.

关 键 词：参数估计 奇并值分解 递推广义增广最小二乘法 Box—Jenkins模型 

分 类 号：O17[理学—数学] TP13[理学—基础数学]