Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique

This paper considers the identification problems of Hammerstein finite impulse response moving average (FIR-MA) systems using the maximum likelihood principle and stochastic gradient method based on the key term separation technique. In order to improve the convergence rate, a maximum likelihood multi-innovation stochastic gradient algorithm is presented. The simulation results show that the proposed algorithms can effectively estimate the parameters of the Hammerstein FIR-MA systems.

[1]  Feng Ding,et al.  Recursive least squares identification for multirate multi-input single-output systems , 2009, 2009 American Control Conference.

[2]  Jie Ding,et al.  Bias compensation‐based parameter estimation for output error moving average systems , 2011 .

[3]  Feng Ding,et al.  Auxiliary model identification method for multirate multi-input systems based on least squares , 2009, Math. Comput. Model..

[4]  Wei Wang,et al.  Maximum likelihood parameter estimation algorithm for controlled autoregressive autoregressive models , 2011, Int. J. Comput. Math..

[5]  Yan Zhang,et al.  Auxiliary model based multi-innovation algorithms for multivariable nonlinear systems , 2010, Math. Comput. Model..

[6]  Feng Ding,et al.  Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems , 2010, Digit. Signal Process..

[7]  Daqi Zhu,et al.  Fault-tolerant Control of Unmanned Underwater Vehicles with Continuous Faults: Simulations and Experiments , 2009 .

[8]  F. Ding,et al.  Least‐squares parameter estimation for systems with irregularly missing data , 2009 .

[9]  Feng Ding,et al.  Adaptive Digital Control of Hammerstein Nonlinear Systems with Limited Output Sampling , 2007, SIAM J. Control. Optim..

[10]  Feng Ding,et al.  Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems , 2008, Comput. Math. Appl..

[11]  Feng Ding,et al.  Gradient based and least-squares based iterative identification methods for OE and OEMA systems , 2010, Digit. Signal Process..

[12]  Y. Liu,et al.  Gradient-based and least-squares-based iterative estimation algorithms for multi-input multi-output systems , 2012, J. Syst. Control. Eng..

[13]  Feng Ding,et al.  Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems , 2012, Math. Comput. Model..

[14]  J. Schoukens,et al.  Blind Maximum Likelihood Identification of Hammerstein Systems , 2008 .

[15]  Yong Zhang,et al.  Computers and Mathematics with Applications , 2022 .

[16]  Feng Ding,et al.  Self-tuning control based on multi-innovation stochastic gradient parameter estimation , 2009, Syst. Control. Lett..

[17]  Huazhen Fang,et al.  Identification of Hammerstein Output-Error Systems with Two-Segment Nonlinearities: Algorithm and Applications 1 , 2010, Control. Intell. Syst..

[18]  Feng Ding,et al.  Auxiliary model based recursive generalized least squares parameter estimation for Hammerstein OEAR systems , 2010, Math. Comput. Model..

[19]  Lijun Bo,et al.  Maximum likelihood estimation for reflected Ornstein–Uhlenbeck processes , 2011 .

[20]  Ferenc Izsák,et al.  Maximum likelihood estimation for constrained parameters of multinomial distributions - Application to Zipf-Mandelbrot models , 2006, Comput. Stat. Data Anal..

[21]  Jing Lu,et al.  Least squares based iterative identification for a class of multirate systems , 2010, Autom..

[22]  D. Wang.  Brief paper: Lleast squares-based recursive and iterative estimation for output error moving average systems using data filtering , 2011 .

[23]  Huazhen Fang,et al.  Genetic adaptive state estimation with missing input/output data , 2010 .

[24]  Feng Ding,et al.  Parameter Identification and Intersample Output Estimation for Dual-Rate Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[25]  Huazhen Fang,et al.  Kalman filter-based identification for systems with randomly missing measurements in a network environment , 2010, Int. J. Control.

[26]  Feng Ding,et al.  Computers and Mathematics with Applications Identification for Multirate Multi-input Systems Using the Multi-innovation Identification Theory , 2022 .

[27]  Feng Ding,et al.  Multi-innovation stochastic gradient algorithms for multi-input multi-output systems , 2009, Digit. Signal Process..

[28]  Guanrong Chen,et al.  Identifying chaotic systems using Wiener and Hammerstein cascade models , 2001 .

[29]  Feng Ding,et al.  Identification methods for Hammerstein nonlinear systems , 2011, Digit. Signal Process..

[30]  Qian Liu,et al.  AN INTEGRATED FAULT-TOLERANT CONTROL FOR NONLINEAR SYSTEMS WITH MULTI-FAULT , 2009 .

[31]  Feng Ding,et al.  Identification of Hammerstein nonlinear ARMAX systems , 2005, Autom..

[32]  Tongwen Chen,et al.  A GRADIENT BASED ADAPTIVE CONTROL ALGORITHM FOR DUAL‐RATE SYSTEMS , 2006 .

[33]  Feng Ding,et al.  Auxiliary model-based RELS and MI-ELS algorithm for Hammerstein OEMA systems , 2010, Comput. Math. Appl..

[34]  P. X. Liu,et al.  Multiinnovation Least-Squares Identification for System Modeling , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[35]  J. Schoukens,et al.  Blind maximum likelihood identification of Wiener systems , 2007 .

[36]  Guowei Yang,et al.  Gradient-based iterative parameter estimation for Box-Jenkins systems , 2010, Comput. Math. Appl..

[37]  Feng Ding,et al.  Parameter estimation with scarce measurements , 2011, Autom..

[38]  Yanjun Liu,et al.  Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model , 2009, Appl. Math. Comput..

[39]  F. Ding,et al.  An auxiliary model based on a recursive least-squares parameter estimation algorithm for non-uniformly sampled multirate systems , 2009 .

[40]  Feng Ding,et al.  Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises , 2009, Signal Process..

[41]  Feng Ding,et al.  Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems , 2009, Autom..

[42]  Feng Ding,et al.  Auxiliary model-based least-squares identification methods for Hammerstein output-error systems , 2007, Syst. Control. Lett..

[43]  Wei Wang,et al.  Maximum likelihood least squares identification for systems with autoregressive moving average noise , 2012 .

[44]  Feng Ding,et al.  Least squares based and gradient based iterative identification for Wiener nonlinear systems , 2011, Signal Process..

[45]  Feng Ding,et al.  Performance analysis of multi-innovation gradient type identification methods , 2007, Autom..

[46]  Simon X. Yang,et al.  A Multi-Fault Diagnosis Method for Sensor Systems Based on Principle Component Analysis , 2009, Sensors.

[47]  Hamed Mojallali,et al.  Identification of multiple-input single-output Hammerstein models using Bezier curves and Bernstein polynomials , 2011 .

[48]  Jozef Vörös,et al.  Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones , 2003, IEEE Trans. Autom. Control..

[49]  Jie Sheng,et al.  Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems , 2010, Comput. Math. Appl..

[50]  Feng Ding,et al.  Gradient-Based Identification Methods for Hammerstein Nonlinear ARMAX Models , 2006 .

[51]  Feng Ding,et al.  Several multi-innovation identification methods , 2010, Digit. Signal Process..

[52]  Feng Ding,et al.  Partially Coupled Stochastic Gradient Identification Methods for Non-Uniformly Sampled Systems , 2010, IEEE Transactions on Automatic Control.