EM算法在状态空间模型参数辨识中的应用  

The Application of EM Algorithm in Parameter Identification of State-space Model

作　　者：张静[1] 张兆基[3] 周佐[2] ZHANG Jing;ZHANG Zhao-ji;ZHOU Zuo(.College of Information Technology and Communication;3.College of Physics and Electromechanical Engineering,Hexi University,Zhangye 734000,Chin;2.College of Information Engineering,Xizang Minzu University,Xianyang 712082,Chin)

机构地区：[1]河西学院信息技术与传媒学院,甘肃张掖734000 [2]河西学院物理与机电工程学院,甘肃张掖734000 [3]西藏民族大学信息工程学院,陕西咸阳712082

出　　处：《控制工程》2018年第7期1348-1354,共7页Control Engineering of China

基　　金：西藏自治区高校青年教师创新支持计划项目(QC2015-56);河西学院校长基金项目(XZ2017012)

摘　　要：针对传统辨识方法中状态变量维数不易确定和参数辨识准确率差等问题,利用EM算法实现状态空间模型参数的辨识,并使用AIC准则来确定最优的状态变量维数。在EM算法中首先利用卡尔曼滤波和卡尔曼平滑算法来实现对状态期望的估计,然后再通过对数似然函数期望的最大化来实现参数和噪声协方差的估计,如此不断迭代,直至得到最优的估计参数。通过Matlab进行仿真和分析,结果表明该方法能有效地实现状态空间模型中参数的辨识和状态的估计,并且具有比较高的准确性。Aiming at the problem of that the number of state variables is not easy to determine and the accuracy of parameters identification is poor, use EM algorithm to realize the parameters identification of state space model, and use the AIC criterion to determine the optimal dimension of state variables. In the EM algorithm, first use the Kalman filter and Kalman smoothing algorithm to realize the estimation of state expectation, and realize the estimation of the parameters and noise covariance through the maximization of the logarithmic likelihood function, then iterate until getting the optimal estimation parameters. We do simulation and analysis with Matlab, the results show that the method can effectively realize parameter identification and state estimation of state-space model, which has higher precision and accuracy.

关 键 词：状态空间模型 参数辨识 EM算法 卡尔曼滤波 AIC准则 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] N945.14[自动化与计算机技术—控制科学与工程]