Gradient‐based iterative parameter estimation for bilinear‐in‐parameter systems using the model decomposition technique

The parameter estimation issues of a block-oriented non-linear system that is bilinear in the parameters are studied, i.e. the bilinear-in-parameter system. Using the model decomposition technique, the bilinear-in-parameter model is decomposed into two fictitious submodels: one containing the unknown parameters in the non-linear block and the other containing the unknown parameters in the linear dynamic one and the noise model. Then a gradient-based iterative algorithm is proposed to estimate all the unknown parameters by formulating and minimising two criterion functions. The stochastic gradient algorithms are provided for comparison. The simulation results indicate that the proposed iterative algorithm can give higher parameter estimation accuracy than the stochastic gradient algorithms.

[1]  Yinghong Wen,et al.  Performance Evaluation with Improved Receiver Design for Asynchronous Coordinated Multipoint Transmissions , 2016 .

[2]  F. Alsaadi,et al.  Recursive parameter identification of the dynamical models for bilinear state space systems , 2017 .

[3]  Feng Ding,et al.  Iterative Parameter Estimation for Signal Models Based on Measured Data , 2018, Circuits Syst. Signal Process..

[4]  Feng Ding,et al.  Parameter estimation for control systems based on impulse responses , 2017 .

[5]  Feng Ding,et al.  Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation , 2018, Int. J. Syst. Sci..

[6]  Feng Ding,et al.  Recursive least squares algorithm and gradient algorithm for Hammerstein–Wiener systems using the data filtering , 2016 .

[7]  Feng Ding,et al.  A recursive least squares parameter estimation algorithm for output nonlinear autoregressive systems using the input-output data filtering , 2017, J. Frankl. Inst..

[8]  Vojislav Z. Filipovic,et al.  Consistency of the robust recursive Hammerstein model identification algorithm , 2015, J. Frankl. Inst..

[9]  Feng Ding,et al.  A filtering based multi-innovation gradient estimation algorithm and performance analysis for nonlinear dynamical systems , 2017 .

[10]  F. Z. Geng,et al.  An optimal reproducing kernel method for linear nonlocal boundary value problems , 2018, Appl. Math. Lett..

[11]  Meihang Li,et al.  The least squares based iterative algorithms for parameter estimation of a bilinear system with autoregressive noise using the data filtering technique , 2018, Signal Process..

[12]  Jian Pan,et al.  Adaptive Gradient-Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique , 2018, Complex..

[13]  Feng Liu,et al.  Regularity of discrete multisublinear fractional maximal functions , 2017 .

[14]  Fuad E. Alsaadi,et al.  Iterative parameter identification for pseudo-linear systems with ARMA noise using the filtering technique , 2018 .

[15]  Boying Wu,et al.  A new reproducing kernel collocation method for nonlocal fractional boundary value problems with non-smooth solutions , 2018, Appl. Math. Lett..

[16]  Liang Liang,et al.  Optimization of Information Interaction Protocols in Cooperative Vehicle-Infrastructure Systems , 2018 .

[17]  Feng Ding,et al.  Convergence Analysis of the Hierarchical Least Squares Algorithm for Bilinear-in-Parameter Systems , 2016, Circuits Syst. Signal Process..

[18]  Johan A. K. Suykens,et al.  A two-experiment approach to Wiener system identification , 2018, Autom..

[19]  Feng Ding,et al.  Least Squares based Iterative Parameter Estimation Algorithm for Stochastic Dynamical Systems with ARMA Noise Using the Model Equivalence , 2018 .

[20]  Feng Liu,et al.  Singular integrals related to homogeneous mappings in Triebel-Lizorkin spaces , 2017 .

[21]  Erfu Yang,et al.  State filtering‐based least squares parameter estimation for bilinear systems using the hierarchical identification principle , 2018, IET Control Theory & Applications.

[22]  Xia Zhang,et al.  Standard Analysis for Transfer Delay in CTCS-3 , 2017 .

[23]  Weihai Zhang,et al.  ℋ- index for discrete-time stochastic systems with Markovian jump and multiplicative noise , 2018, Autom..

[24]  Er-Wei Bai,et al.  Least squares solutions of bilinear equations , 2006, Syst. Control. Lett..

[25]  Feng Ding,et al.  A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation , 2018, J. Frankl. Inst..

[26]  Weihai Zhang,et al.  Necessary/sufficient conditions for Pareto optimum in cooperative difference game , 2018 .

[27]  Petre Stoica,et al.  Recursive nonlinear-system identification using latent variables , 2016, Autom..

[28]  Jacob Benesty,et al.  Adaptive filtering for the identification of bilinear forms , 2018, Digit. Signal Process..

[29]  Ying Shen,et al.  Exit problems for jump processes with applications to dividend problems , 2013, J. Comput. Appl. Math..

[30]  C. Yin,et al.  The Perturbed Compound Poisson Risk Process with Investment and Debit Interest , 2010 .

[31]  Feng Ding,et al.  A multi-innovation state and parameter estimation algorithm for a state space system with d-step state-delay , 2017, Signal Process..

[32]  T. Hayat,et al.  Hierarchical Parameter Estimation for the Frequency Response Based on the Dynamical Window Data , 2018, International Journal of Control, Automation and Systems.

[33]  Feng Ding,et al.  Iterative identification algorithms for bilinear-in-parameter systems with autoregressive moving average noise , 2017, J. Frankl. Inst..

[34]  Keith J. Burnham,et al.  Parameter estimation of the fractional-order Hammerstein–Wiener model using simplified refined instrumental variable fractional-order continuous time , 2017 .

[35]  Jiling Ding,et al.  Recursive and Iterative Least Squares Parameter Estimation Algorithms for Multiple-Input–Output-Error Systems with Autoregressive Noise , 2018, Circuits Syst. Signal Process..

[36]  C. Yin,et al.  Optimality of the threshold dividend strategy for the compound Poisson model , 2011 .

[37]  Weihai Zhang,et al.  Global stabilization for a class of stochastic nonlinear systems with SISS‐like conditions and time delay , 2018 .

[38]  Feng Ding,et al.  Some new results of designing an IIR filter with colored noise for signal processing , 2018, Digit. Signal Process..

[39]  Wei Xing Zheng,et al.  A Recursive Identification Algorithm for Wiener Nonlinear Systems with Linear State-Space Subsystem , 2018, Circuits Syst. Signal Process..

[40]  Peng Li,et al.  Parallel processing algorithm for railway signal fault diagnosis data based on cloud computing , 2018, Future Gener. Comput. Syst..

[41]  Min Liu,et al.  Research on a handwritten character recognition algorithm based on an extended nonlinear kernel residual network , 2018, KSII Trans. Internet Inf. Syst..

[42]  Ling Xu.  The parameter estimation algorithms based on the dynamical response measurement data , 2017 .

[43]  C. Yin,et al.  Optimal dividends problem with a terminal value for spectrally positive Levy processes , 2013, 1302.6011.

[44]  Xuemei Ren,et al.  Modified multi-innovation stochastic gradient algorithm for Wiener-Hammerstein systems with backlash , 2018, J. Frankl. Inst..

[45]  Feng Ding,et al.  A novel parameter separation based identification algorithm for Hammerstein systems , 2016, Appl. Math. Lett..

[46]  Jiling Ding,et al.  The Hierarchical Iterative Identification Algorithm for Multi-Input-Output-Error Systems with Autoregressive Noise , 2017, Complex..

[47]  Feng Ding,et al.  Combined state and parameter estimation for a bilinear state space system with moving average noise , 2018, J. Frankl. Inst..

[48]  Jacob Benesty,et al.  On the Identification of Bilinear Forms With the Wiener Filter , 2017, IEEE Signal Processing Letters.

[49]  Rui Liu,et al.  Contract design for relay incentive mechanism under dual asymmetric information in cooperative networks , 2018, Wirel. Networks.

[50]  Xiao Li,et al.  Particle Swarm Optimization Iterative Identification Algorithm and Gradient Iterative Identification Algorithm for Wiener Systems with Colored Noise , 2018, Complex..