Maximum likelihood based recursive parameter estimation for controlled autoregressive ARMA systems using the data filtering technique

Abstract Using the maximum likelihood principle, a filtering based maximum likelihood recursive least squares parameter estimation algorithm is derived for controlled autoregressive ARMA systems. The basic idea is to use the noise transfer function to filter the input–output data and to replace the unmeasurable noise terms in the information vectors with their estimates. The simulation results indicate that the proposed estimation algorithm can effectively estimate the parameters of such systems and can generate more precise parameter estimates than the recursive maximum likelihood and the recursive generalized extended least squares algorithms.

[1]  Feng Ding,et al.  Input-output data filtering based recursive least squares identification for CARARMA systems , 2010, Digit. Signal Process..

[2]  Levy Boccato,et al.  Application of natural computing algorithms to maximum likelihood estimation of direction of arrival , 2012, Signal Process..

[3]  Feng Ding,et al.  Recursive Least Squares Parameter Estimation for a Class of Output Nonlinear Systems Based on the Model Decomposition , 2016, Circuits Syst. Signal Process..

[4]  Asier Ibeas,et al.  Identification and control of delayed SISO systems through pattern search methods , 2013, J. Frankl. Inst..

[5]  Feng Ding,et al.  Highly Efficient Identification Methods for Dual-Rate Hammerstein Systems , 2015, IEEE Transactions on Control Systems Technology.

[6]  Masoud Hajarian,et al.  Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations , 2013, J. Frankl. Inst..

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

[8]  Bernt Øksendal,et al.  Maximum principles for jump diffusion processes with infinite horizon , 2012, Autom..

[9]  Junhong Li,et al.  Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration , 2013, Appl. Math. Lett..

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

[11]  Feng Ding,et al.  Auxiliary model based least squares parameter estimation algorithm for feedback nonlinear systems using the hierarchical identification principle , 2013, J. Frankl. Inst..

[12]  Rik Pintelon,et al.  Blind Maximum-Likelihood Identification of Wiener Systems , 2009, IEEE Transactions on Signal Processing.

[13]  Fei Liu,et al.  H∞ Control for Discrete-Time Markov Jump Systems With Uncertain Transition Probabilities , 2013, IEEE Transactions on Automatic Control.

[14]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[15]  David Burshtein,et al.  The Approximate Maximum-Likelihood Certificate , 2013, IEEE Trans. Inf. Theory.

[16]  Qing Hui.  Convergence and stability analysis for iterative dynamics with application to compartmental networks: A trajectory distance based Lyapunov approach , 2013, J. Frankl. Inst..

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

[18]  Huizhong Yang,et al.  Interactive parameter estimation for output error moving average systems , 2013 .

[19]  Wei Zhang,et al.  Improved least squares identification algorithm for multivariable Hammerstein systems , 2015, J. Frankl. Inst..

[20]  Feng Ding,et al.  Recursive least squares parameter identification algorithms for systems with colored noise using the filtering technique and the auxilary model , 2015, Digit. Signal Process..

[21]  Fei Liu,et al.  H∞ Filtering for Discrete-Time Systems With Stochastic Incomplete Measurement and Mixed Delays , 2012, IEEE Trans. Ind. Electron..

[22]  Simon X. Yang,et al.  A Bioinspired Filtered Backstepping Tracking Control of 7000-m Manned Submarine Vehicle , 2014, IEEE Transactions on Industrial Electronics.

[23]  Jie Ding,et al.  Auxiliary model based parameter estimation for dual-rate output error systems with colored noise ☆ , 2013 .

[24]  Huiping Li,et al.  Robust H∞ filtering for nonlinear stochastic systems with uncertainties and Markov delays , 2012, Autom..

[25]  Simon X. Yang,et al.  Dynamic Task Assignment and Path Planning of Multi-AUV System Based on an Improved Self-Organizing Map and Velocity Synthesis Method in Three-Dimensional Underwater Workspace , 2013, IEEE Transactions on Cybernetics.

[26]  Yang Shi,et al.  Output Feedback Stabilization of Networked Control Systems With Random Delays Modeled by Markov Chains , 2009, IEEE Transactions on Automatic Control.

[27]  Wei Xing Zheng,et al.  A bias-correction method for indirect identification of closed-loop systems , 1995, Autom..

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

[29]  Joseph Shmuel Picard,et al.  Error bounds for convex parameter estimation , 2012, Signal Process..

[30]  Torsten Söderström,et al.  Accuracy analysis of time domain maximum likelihood method and sample maximum likelihood method for errors-in-variables and output error identification , 2010, Autom..

[31]  Tao Tang,et al.  Several gradient-based iterative estimation algorithms for a class of nonlinear systems using the filtering technique , 2014 .

[32]  Zhen Wu,et al.  A general maximum principle for optimal control of forward-backward stochastic systems , 2013, Autom..

[33]  W. Zheng.  Least-squares identification of a class of multivariable systems with correlated disturbances , 1999 .

[34]  Yuanbiao Hu,et al.  Iterative and recursive least squares estimation algorithms for moving average systems , 2013, Simul. Model. Pract. Theory.

[35]  Aurora Hermoso-Carazo,et al.  Unscented filtering algorithm using two-step randomly delayed observations in nonlinear systems , 2009 .

[36]  Badong Chen,et al.  Quantized Kernel Recursive Least Squares Algorithm , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[37]  F. Ding,et al.  Maximum likelihood gradient-based iterative estimation algorithm for a class of input nonlinear controlled autoregressive ARMA systems , 2015 .

[38]  Ulisses Braga-Neto,et al.  Maximum-Likelihood Estimation of the Discrete Coefficient of Determination in Stochastic Boolean Systems , 2013, IEEE Transactions on Signal Processing.

[39]  F. Ding,et al.  Convergence of the recursive identification algorithms for multivariate pseudo‐linear regressive systems , 2016 .