Iterative Parameter Estimation for a Class of Multivariable Systems Based on the Hierarchical Identification Principle and the Gradient Search

For a multivariable controlled autoregressive system with autoregressive noises, its corresponding identification model contains a parameter matrix and a parameter vector. This paper presents the hierarchical gradient-based iterative (HGI) algorithm to interactively estimate the parameter matrix and the parameter vector by using the hierarchical identification principle and the gradient search. The simulation results show that the HGI algorithm is effective.

[1]  Feng Ding,et al.  Iterative least-squares solutions of coupled Sylvester matrix equations , 2005, Syst. Control. Lett..

[2]  Feng Ding,et al.  Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique , 2011, Comput. Math. Appl..

[3]  Jie Ding,et al.  Time series AR modeling with missing observations based on the polynomial transformation , 2010, Math. Comput. Model..

[4]  Feng Ding,et al.  Multi-innovation Extended Stochastic Gradient Algorithm and Its Performance Analysis , 2010, Circuits Syst. Signal Process..

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

[6]  Feng Ding,et al.  Iterative solutions to matrix equations of the form AiXBi=Fi , 2010, Comput. Math. Appl..

[7]  Feng Ding,et al.  Hierarchical identification of lifted state-space models for general dual-rate systems , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  Ying Liu,et al.  Complex Adaptive LMS Algorithm Employing the Conjugate Gradient Principle for Channel Estimation and Equalization , 2012, Circuits Syst. Signal Process..

[9]  Ali A. Nasir,et al.  Timing and Carrier Synchronization With Channel Estimation in Multi-Relay Cooperative Networks , 2012, IEEE Transactions on Signal Processing.

[10]  Yanjun Liu,et al.  Gradient based and least squares based iterative algorithms for matrix equations AXB + CXTD = F , 2010, Appl. Math. Comput..

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

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

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

[14]  Feng Ding,et al.  Hierarchical gradient-based identification of multivariable discrete-time systems , 2005, Autom..

[15]  Feng Ding,et al.  Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems , 2011, Comput. Math. Appl..

[16]  Feng Ding,et al.  Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle , 2008, Appl. Math. Comput..

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

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

[19]  Feng Ding,et al.  Hierarchical least squares identification methods for multivariable systems , 2005, IEEE Trans. Autom. Control..

[20]  Simona Halunga,et al.  Performance evaluation for conventional and MMSE multiuser detection algorithms in imperfect reception conditions , 2010, Digit. Signal Process..

[21]  Huizhong Yang,et al.  Modelling and identification for non-uniformly periodically sampled-data systems , 2010 .

[22]  Sen Li,et al.  Steady-state and Tracking Analysis of Fractional Lower-order Constant Modulus Algorithm , 2011, Circuits Syst. Signal Process..

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

[24]  Feng Ding,et al.  Least squares based iterative algorithms for identifying Box-Jenkins models with finite measurement data , 2010, Digit. Signal Process..

[25]  Mao Ze-hui,et al.  Sliding mode observer-based fault estimation for nonlinear networked control systems , 2008, 2008 27th Chinese Control Conference.

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

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

[28]  Feng Ding,et al.  Hierarchical least-squares based iterative identification for multivariable systems with moving average noises , 2010, Math. Comput. Model..

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

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

[31]  Angelia Nedic,et al.  Distributed and Recursive Parameter Estimation in Parametrized Linear State-Space Models , 2008, IEEE Transactions on Automatic Control.

[32]  Li Xie,et al.  The residual based interactive stochastic gradient algorithms for controlled moving average models , 2009, Appl. Math. Comput..

[33]  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.

[34]  Feng Ding,et al.  On Iterative Solutions of General Coupled Matrix Equations , 2006, SIAM J. Control. Optim..

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

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

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

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

[39]  Octavian Fratu,et al.  Imperfect cross-correlation and amplitude balance effects on conventional multiuser decoder with turbo encoding , 2010, Digit. Signal Process..

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

[41]  Feng Ding,et al.  Gradient based iterative solutions for general linear matrix equations , 2009, Comput. Math. Appl..

[42]  Jingang Yi,et al.  On stable simultaneous input and state estimation for discrete‐time linear systems , 2011 .

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

[44]  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..

[45]  Feng Ding,et al.  Transformations between some special matrices , 2010, Comput. Math. Appl..

[46]  Feng Ding,et al.  Multirate crosstalk identification in xDSL systems , 2006, IEEE Transactions on Communications.

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

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

[49]  Hichem Snoussi,et al.  Channel estimation and multiple target tracking in wireless sensor networks based on quantised proximity sensors , 2011, IET Wirel. Sens. Syst..

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

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

[52]  G. Goodwin,et al.  Identification of continuous-time state-space models from non-uniform fast-sampled data , 2011 .

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

[54]  Feng Ding,et al.  Gradient Based Iterative Algorithms for Solving a Class of Matrix Equations , 2005, IEEE Trans. Autom. Control..

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

[56]  Guang Meng,et al.  MIMO Instantaneous Blind Identification Based on Second-Order Temporal Structure and Steepest-Descent Method , 2011, Circuits Syst. Signal Process..