基于偏差消除最小二乘估计和Durbin方法的两阶段ARMAX参数辨识

辛斌; 白永强; 陈杰

doi:10.3724/SP.J.1004.2012.00491

基于偏差消除最小二乘估计和Durbin方法的两阶段ARMAX参数辨识

doi: 10.3724/SP.J.1004.2012.00491

辛斌^1,2,3,
白永强^1,2, ,,
陈杰^1,2

1.
北京理工大学自动化学院北京 100081;
2.
复杂系统智能控制与决策教育部重点实验室北京 100081;
3.
曼彻斯特大学商学院决策与认知科学研究中心曼彻斯特 M15 6PB 英国

详细信息

通讯作者:
白永强, 博士, 北京理工大学自动化学院讲师.主要研究方向为智能控制与智能系统. E-mail:byfengyun@bit.edu.cn

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出版历程
- 收稿日期: 2010-05-20
- 修回日期: 2011-11-09
- 刊出日期: 2012-03-20

Two-stage ARMAX Parameter Identification Based on Bias-eliminated Least Squares Estimation and Durbin0s Method

XIN Bin^1,2,3,
BAI Yong-Qiang^{1,2
, ,},
CHEN Jie^1,2

1.
School of Automation, Beijing Institute of Technology, Beijing 100081, P.,R.,China;
2.
Key Laboratory of Complex System Intelligent Control and Decision, Ministry of Education, Beijing 100081, P.,R.,China;
3.
Decision and Cognitive Sciences Research Centre, Manchester Business School, The University of Manchester, Manchester M15 6PB, U.K.

摘要

摘要: 针对带有外生变量的自回归移动平均模型(Autoregressive moving average with exogenous variable, ARMAX)的参数辨识问题提出一种两阶段辨识方法. 首先通过偏差消除最小二乘方法辨识带有外生变量的自回归部分(Autoregressive part with exogenous variable, ARX),然后采用Durbin方法将移动平均部分(Moving average, MA)的参数辨识问题转换成一个长自回归模型(Long autoregressive, LAR)的参数辨识问题, 并利用MA与等价LAR的参数对应关系直接得到MA参数, 最后利用辨识出的MA参数计算出噪声方差. 与扩展最小二乘法的数值仿真比较验证了这种两阶段辨识方法的有效性.
- 自回归移动平均模型 /
- 参数辨识 /
- Durbin方法 /
- 偏差消除最小二乘法
Abstract: This paper proposes a two-stage identification approach for the parameter identification of autoregressive moving average with exogenous variable (ARMAX) model. First, a bias-eliminated least squares method is employed to identify the autoregressive part with exogenous variable (ARX). Then, the Durbin's method is employed to transform the parameter identification of the moving average (MA) part into that of a long autoregressive (AR) model. The MA parameters are derived directly from the parameter relationship between the MA part and its equivalent long AR model. Finally, the noise variance can be computed by using the identified MA parameters. The performance comparison against the extended least-squares method in numerical simulations validates the effectiveness of the two-stage identification approach.
- Autoregressive moving average with exogenous variable (ARMAX) model /
- parameter identification /
- Durbin0s method /
- bias-eliminated least squares method

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参考文献(1)

[1]

Ljung L. System Identification: Theory for the User (Second Edition). New Jersey: Prentice Hall, 1999[2] Hannan E J, Deistler M. The Statistical Theory for Linear Systems. New York: John Wiley and Sons, 1988[3] Ljung L. Perspectives on system identification. In: Proceedings of the 17th IFAC World Congress. Seoul, Korea: IFAC, 2008. 7172-7184[4] Gevers M. A personal view of the development of system identification: a 30-year journey through an exciting field. IEEE Control Systems Magazine, 2006, 26(6): 93-105[5] Yang H T, Huang C M, Huang C L. Identification of ARMAX model for short term load forecasting: an evolutionary programming approach. IEEE Transactions on Power Systems, 1996, 11(1): 403-408[6] Huang C M, Huang C J, Wang M L. A particle swarm optimization to identifying the ARMAX model for short-term load forecasting. IEEE Transactions on Power Systems, 2005, 20(2): 1126-1133[7] Hu J L, Hirasawa K, Kumamaru K. A homotopy approach to improving PEM identification of ARMAX models. Automatica, 2001, 37(9): 1323-1334[8] Davidson J E H. Problems with the estimation of moving average processes. Journal of Econometrics, 1981, 16(3): 295- 310[9] Bauer D. Estimating ARMAX systems for multivariate time series using the state approach to subspace algorithms. Journal of Multivariate Analysis, 2009, 100(3): 397-421[10] Yang Hua, Li Shao-Yuan. Closed-loop subspace identification based on augmented input with consistency analysis. Acta Automatica Sinica, 2007, 33(7): 703-708(杨华, 李少远. 基于输入扩张的闭环系统自空间辨识及其强一致性分析. 自动化学报, 2007, 33(7): 703-708)[11] Chen Xi, Fang Hai-Tao. Recursive identification for Hammerstein systems with state-space model. Acta Automatica Sinica, 2010, 36(10): 1460-1467[12] Ding F, Chen T W. Identification of Hammerstein nonlinear ARMAX systems. Automatica, 2005, 41(9): 1479-1489[13] Ding F, Shi Y, Chen T W. Performance analysis of estimation algorithms of nonstationary ARMA processes. IEEE Transactions on Signal Processing, 2006, 54(3): 1041-1053[14] Ding F, Chen T. Hierarchical least squares identification methods for multivariable systems. IEEE Transactions on Automatic Control, 2005, 50(3): 397-402[15] Ding F, Liu P X, Liu G J. Multiinnovation least-squares identification for system modeling. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2010, 40(3): 767-778[16] Ding F. Several multi-innovation identification methods. Digital Signal Processing, 2010, 20(4): 1027-1039[17] Wang D Q, Ding F. Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Processing, 2011, 91(5): 1182-1189[18] Wang Dong-Qing. Recursive extended least squares identification method based on auxiliary models. Control Theory and Applications, 2009, 26(1): 51-56(王冬青. 基于辅助模型的递归增广最小二乘辨识方法. 控制理论与应用, 2009, 26(1): 51-56)[19] Ding F, Ding J. Least-squares parameter estimation for systems with irregularly missing data. International Journal of Adaptive Control and Signal Processing, 2010, 24(7): 540- 553[20] Wang D Q, Ding F. Input-output data filtering based recursive least squares identification for CARARMA systems. Digital Signal Processing, 2010, 20(4): 991-999[21] Wang D Q, Chu Y Y, Ding F. Auxiliary model-based RELS and MI-ELS algorithm for Hammerstein OEMA systems. Computers and Mathematics with Applications, 2010, 59(9): 3092-3098[22] Ding F, Chen T W, Qiu L. Bias compensation based recursive least-squares identification algorithm for MISO systems. IEEE Transactions on Circuits and Systems II: Express Briefs, 2006, 53(5): 349-353[23] Zhang Yong, Yang Hui-Zhong. Bias compensation recursive least squares identification for output error systems with colored noises. Acta Automatica Sinica, 2007, 33(10): 1053- 1060(张勇, 杨慧中. 有色噪声干扰输出误差系统的偏差补偿递推最小二乘辨识方法. 自动化学报, 2007, 33(10): 1053-1060)[24] Li Yan, Mao Zhi-Zhong, Wang Yan, Yuan Ping, Jia Ming-Xing. Identification of Hammerstein-Wiener models based on bias compensation recursive least squares. Acta Automatica Sinica, 2010, 36(1): 163-168(李妍, 毛志忠, 王琰, 袁平, 贾明兴. 基于偏差补偿递推最小二乘的Hammerstein-Wiener模型辨识. 自动化学报, 2010, 36(1): 163 -168)[25] Ding Feng, Chen Tong-Wen. Modeling and identification of multirate systems. Acta Automatica Sinica, 2005, 31(1): 105 -122[26] Han H Q, Xie L, Ding F, Liu X G. Hierarchical least-squares based iterative identification for multivariable systems with moving average noises. Mathematical and Computer Modelling, 2010, 51(9-10): 1213-1220[27] Bao B, Xu Y Q, Sheng J, Ding R F. Least squares based iterative parameter estimation algorithm for multivariable controlled ARMA system modelling with finite measurement data. Mathematical and Computer Modelling, 2011, 53(9-10): 1664-1669[28] Zhang Y, Cui G M. Bias compensation method for stochastic systems with colored noise. Applied Mathematical Modelling, 2011, 35(4): 1709-1716[29] Ding F, Chen T. Performance analysis of multi-innovation gradient type identification methods. Automatica, 2007, 43(1): 1-14[30] Ding F, Liu P X, Liu G J. Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises. Signal Processing, 2009, 89(10): 1883-1890[31] Han L L, Ding F. Multi-innovation stochastic gradient algorithms for multi-input multi-output systems. Digital Signal Processing, 2009, 19(4): 545-554[32] Wang D Q, Ding F. Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems. Computers and Mathematics with Applications, 2008, 56(12): 3157-3164[33] Wang D Q, Yang G W, Ding R F. Gradient-based iterative parameter estimation for Box-Jenkins systems. Computers and Mathematics with Applications, 2010, 60(5): 1200- 1208[34] Zhang Z N, Ding F, Liu X G. Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems. Computers and Mathematics with Applications, 2011, 61(3): 672-682[35] Ding F, Liu X P. Auxiliary model-based stochastic gradient algorithm for multivariable output error systems. Acta Automatica Sinica, 2010, 36(7): 993-998[36] Fkirin M A. Choice of least-squares algorithms for the identification of ARMAX dynamic systems. International Journal of Systems Science, 1989, 20(7): 1221-1226[37] Guo L, Huang D W. Least-squares identification for ARMAX models without the positive real condition. IEEE Transactions on Automatic Control, 1989, 34(10): 1094- 1098[38] Chen H F. Recursive identification for EIV ARMAX systems. Science in China Series F: Information Sciences, 2009, 52(11): 1964-1972[39] Chen H F. New approach to recursive identification for ARMAX systems. IEEE Transactions on Automatic Control, 2010, 55(4): 868-879[40] Stoica P, McKelvey T, Mari J. MA estimation in polynomial time. IEEE Transactions on Signal Processing, 1999, 48(7): 1999-2012[41] Giannakis G B, Inouye Y, Mendel J M. Cumulant based identification of multichannel moving-average models. IEEE Transactions on Automatic Control, 1989, 34(7): 783-787[42] Tong L, Inouye Y, Liu R W. A finite-step global convergence algorithm for the parameter estimation of multichannel MA processes. IEEE Transactions on Signal Processing, 1992, 40(10): 2547-2558[43] Boss D, Jelonnek B, Kammeyer K D. Eigenvector algorithm for blind MA system identification. Signal Processing, 1998, 66(1): 1-26[44] Durbin J. Efficient estimation of parameters in moving-average models. Biometrika, 1959, 46(3-4): 306-316[45] Broersen P M T, Waele S. Automatic identification of time-series models from long autoregressive models. IEEE Transactions on Instrumentation and Measurement, 2005, 54(5): 1862-1868[46] Broersen P M T. Modified Durbin method for accurate estimation of moving-average models. IEEE Transactions on Instrumentation and Measurement, 2009, 58(5): 1361-1369[47] Zheng W X. A revisit to least-squares parameter estimation of ARMAX systems. In: Proceedings of the 43rd IEEE Conference on Decision and Control. Nassau, Bahamas, USA: IEEE, 2004. 3587-3592

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