Parameter Estimation Based a Conjugate Gradient Iteration Algorithm for Controlled Autoregressive Models

doi:10.3969/j.cnki.jdxb.2016.06.007

Abstract

Abstract:

The auxiliary model is derived for the single-input single-output (SISO) system to reduce computational burden and improve the convergence rate of the new iteration algorithm based on the conjugate gradient.Compared with the interactive stochastic gradient algorithm for controlled moving average models，the proposed new iteration algorithm can give parameter estimates in less steps.In addition，the new algorithm can avoid the inverse of a matrix.The new algorithm is also compared with the biconjugate gradient algorithm.The simulation example shows that the proposed algorithm works quite well.

Key words: parameter estimation, auxiliary model, conjugate gradient iterative algorithm, controlled autoregressive model

HU Zhizeng，LIANG Kaifu. Parameter Estimation Based a Conjugate Gradient Iteration Algorithm for Controlled Autoregressive Models[J]. Journal of Jishou University（Natural Sciences Edition), DOI: 10.3969/j.cnki.jdxb.2016.06.007.

References

[1] MALIK MOHAMMAD BILAL，SALMAN MUHAMMAD.State-Space Least Mean Square[J].Digital Signal Processing，2008，18(3):334-345.
[2] ZHAO Sanxing，WANG Fengcai，XU Hua，et al.Multi-Frequency Identification Method in Signal Processing[J].Digital Signal Processing，2009，19(4):555-566.
[3] HAN Lili，DING Feng.Multi-Innovation Stochastic Gradient Algorithms for Multi-Input Multi-Output Systems[J].Digital Signal Processing，2009，19(4):545-554.
[4] WANG Dongqing,DING Feng.Extended Stochastic Gradient Identification Algorithms for Hammerstein-Wiener ARMAX Systems[J].Computers and Mathematics with Applications，2008，56(12):3 157-3 164.
[5] WANG Lingyun，XIE Li，WANG Xianfang.The Residual Based Interactive Stochastic Gradient Algorithms for Controlled Moving Average Models[J].Applied Mathematics and Computation，2009，211(2):442-449.
[6] LIU Yanjun，XIAO Yongsong，ZHAO Xueliang.Multi-Innovation Stochastic Gradient Algorithm for Multiple-Input Single-Output Systems Using the Auxiliary Model[J].Applied Mathematics and Computation，2009，215(4):1 477-1 483.
[7] DING Feng，LIU PETER X，LIU Guangjun.Gradient Based and Least-Squares Based Iterative Identification Methods for OE and OEMA Systems[J].Digital Signal Processing，2010，20(3):664-677.
[8] 张贤达.矩阵分析与应用[M].2版.北京：清华大学出版社，2013：227-232.
[9] FLETCHER R.Conjugate Gradient Methods for Indefinite Systems[M]∥Numerical Analysis.Berlin Heidelberg：Springer，1976:73-89.
[10] 于佰建，刘君，陈磊.基于MATLAB的ARX模型辨识[C]∥华北电力大学第五届研究生学术交流年会论文集.北京：华北电力大学，2007.
[11] 薛定宇.控制系统计算机辅助设计——MATLAB语言与应用[M].2版.北京：清华大学出版社，2006：105-115.
[12] HESTENES MAGNUS R，STIEFEL EDUARD.Methods of Conjugate Gradients for Solving Linear Systems[J].Journal of Research of the National Bureau of Standards，1952，49(6):99-147.
[13] YOUNG DAVID M，JEA KANG C.Generalized Conjugate-Gradient Acceleration of Nonsymmetrizable Iterative Methods[J].Linear Algebra and Its Applications，1980，34:159-194.
[14] AXELSSON O.Conjugate Gradient Type Methods for Unsymmetric and Inconsistent Systems of Linear Equations[J].Linear Algebra and Its Applications，1980，29：1-16.
[15] DING Feng，CHEN Tongwen.Identification of Dual-Rate Systems Based on Finite Impulse Response Models[J].International Journal of Adaptive Control and Signal Processing，2004，18(7):589-598.
[16] DING Feng，QIU Li，CHEN Tongwen.Reconstruction of Continuous-Time Systems from Their Non-Uniformly Sampled Discrete-Time Systems[J].Automatica，2009，45(2):324-332.
[17] DING Feng，YANG Huizhong，LIU Fei.Performance Analysis of Stochastic Gradient Algorithms Under Weak Conditions[J].Science in China，2008，51(9):1 269-1 280.
[18] DING Feng，CHEN Tongwen.Hierarchical Gradient-Based Identification of Multivariable Discrete-Time Systems[J].Automatica，2005，41(2):315-325.
[19] ZHANG Yong，CUI Guimei.Bias Compensation Methods for Stochastic Systems with Colored Noise[J].Applied Mathematical Modelling，2011，35(4):1 709-1 716.
[20] BAO Bo，XU Yingqin，SHENG Jie，et al.Least Squares Based Iterative Parameter Estimation Algorithm for Multivariable Controlled ARMA System Modelling with Finite Measurement Data[J].Mathematical Computer Modelling，2011，53(910):1 664-1 669.
[21] YAO Guoyu，DING Ruifeng.Two-Stage Least Squares Based Iterative Identification Algorithm for Controlled Autoregressive Moving Average (CARMA) Systems[J].Computers & Mathematics with Applications，2012，63(5):975-984.
[22] DING Feng.Two-Stage Least Squares Based Iterative Estimation Algorithm for CARARMA System Modeling[J].Applied Mathematical Modelling，2013，37(7):4 798-4 808.
[23] LI Junhong.Parameter Estimation for Hammerstein CARARMA Systems Based on the Newton Iteration[J].Applied Mathematics Letters，2013，26(1):91-96.
[24] LIANG Kaifu，LIU Jianzhou.Iterative Algorithms for the Minimum-Norm Solution and the Least-Squares Solution of the Linear Matrix Equations A₁XB₁+C₁X^TD₁=M₁，A₂XB₂+C₂X^TD₂=M₂[J].Applied Mathematics and Computation，2011，218(7):3 166-3 175.