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Front. Inform. Technol. Electron. Eng.  2014, Vol. 15 Issue (2): 147-152    DOI: 10.1631/jzus.C1300072
    
Stochastic gradient algorithm for a dual-rate Box-Jenkins model based on auxiliary model and FIR model
Jing Chen, Rui-feng Ding
School of Science, Jiangnan University, Wuxi 214122, China; School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China
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Abstract  Based on the work in Ding and Ding (2008), we develop a modified stochastic gradient (SG) parameter estimation algorithm for a dual-rate Box-Jenkins model by using an auxiliary model. We simplify the complex dual-rate Box-Jenkins model to two finite impulse response (FIR) models, present an auxiliary model to estimate the missing outputs and the unknown noise variables, and compute all the unknown parameters of the system with colored noises. Simulation results indicate that the proposed method is effective.

Key words： Parameter estimation      Auxiliary model      Dual-rate system      Stochastic gradient      Box-Jenkins model      FIR model     
Received: 26 March 2013      Published: 29 January 2014
CLC:  TP273  
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Cite this article:

Jing Chen, Rui-feng Ding. Stochastic gradient algorithm for a dual-rate Box-Jenkins model based on auxiliary model and FIR model. Front. Inform. Technol. Electron. Eng., 2014, 15(2): 147-152.

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http://www.zjujournals.com/xueshu/fitee/10.1631/jzus.C1300072     OR     http://www.zjujournals.com/xueshu/fitee/Y2014/V15/I2/147


基于辅助模型和有限脉冲响应模型的双率Box-Jenkins系统随机梯度辨识算法

研究目的：对具有双率特性的Box-Jenkins模型提出基于辅助模型的修正随机梯度算法。将复杂的Box-Jenkins模型简化为两个有限脉冲模型，并利用辅助模型辨识出系统损失的输出数据和未知噪声向量，接着利用修正的随机梯度算法辨识出系统的参数。仿真结果验证了方法的有效性。
研究手段：利用有限脉冲响应模型将复杂的Box-Jenkins模型转化成两个有限脉冲响应模型。双率系统的输出存在丢失情况，而传统的多项式转换技术是通过多项式转换技巧转换系统模型使其适合双率情形，但这样会导致待辨识参数维数的增大。本文通过损失数据估计方法插补丢失的输出数据，使其适合单率情形。损失数据估计方法的基本思想是，通过前一时刻参数和前一时刻信息向量辨识出当前时刻损失的输出，进而利用当前时刻信息向量刷新未知参数，两者交替进行。该方法不会增加待辨识参数维数，因而辨识效果较好。
重要结论：1. 采用有限脉冲方法，将复杂的Box-Jenkins模型转化成两个简单的有限脉冲模型。2. 利用损失数据估计方法辨识出系统丢失的数据和未知的噪声向量。3. 利用辨识出的数据能计算出带有有色噪声干扰的原系统的参数。4. 不会造成待辨识参数维数增大。

关键词： 参数估计,  辅助模型,  双率系统,  随机梯度,  Box-Jenkins模型 
[1] Ping Yang, Chao-peng Wu, Yi-lu Guo, Hong-bo Liu, Hui Huang, Hang-zhou Wang, Shu-yue Zhan, Bang-yi Tao, Quan-quan Mu, Qiang Wang, Hong Song. Parameter estimation in exponential models by linear and nonlinear fitting methods[J]. Front. Inform. Technol. Electron. Eng., 2017, 18(3): 434-444.