The maximum likelihood least squares based iterative estimation algorithm for bilinear systems with autoregressive moving average noise

Abstract Maximum likelihood methods are significant for parameter estimation and system modeling. This paper gives the input-output representation of a bilinear system through eliminating the state variables in it, and derives a maximum likelihood least squares based iterative for identifying the parameters of bilinear systems with colored noises by using the maximum likelihood principle. A least squares based iterative (LSI) algorithm is presented for comparison. It is proved that the maximum of the likelihood function is equivalent to minimize the least squares cost function. The simulation results indicate that the proposed algorithm is effective for identifying bilinear systems and the maximum likelihood LSI algorithm is more accurate than the LSI algorithm.

[1]  Roland Hostettler,et al.  Maximum Likelihood Estimation of the Non-Parametric FRF for Pulse-Like Excitations , 2016, IEEE Transactions on Automatic Control.

[2]  F. Ding,et al.  The filtering based maximum likelihood recursive least squares estimation for multiple-input single-output systems ☆ , 2016 .

[3]  Patrick T. Brewick,et al.  An evaluation of data-driven identification strategies for complex nonlinear dynamic systems , 2016 .

[4]  Jian Pan,et al.  Image noise smoothing using a modified Kalman filter , 2016, Neurocomputing.

[5]  Feng Ding,et al.  Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model , 2016, Autom..

[6]  Dongqing Wang,et al.  Recursive maximum likelihood identification method for a multivariable controlled autoregressive moving average system , 2016, IMA J. Math. Control. Inf..

[7]  Huijun Gao,et al.  A direct maximum likelihood optimization approach to identification of LPV time-delay systems , 2016, J. Frankl. Inst..

[8]  Emanuele Garone,et al.  Explicit Reference Governor for Constrained Nonlinear Systems , 2016, IEEE Transactions on Automatic Control.

[9]  Feng Ding,et al.  Recursive Least Squares and Multi-innovation Stochastic Gradient Parameter Estimation Methods for Signal Modeling , 2017, Circuits Syst. Signal Process..

[10]  Dandan Meng.  Recursive Least Squares and Multi-innovation Gradient Estimation Algorithms for Bilinear Stochastic Systems , 2017, Circuits Syst. Signal Process..

[11]  Yide Wang,et al.  Fault diagnosis method based on FFT-RPCA-SVM for Cascaded-Multilevel Inverter. , 2016, ISA transactions.

[12]  Ling Xu,et al.  The damping iterative parameter identification method for dynamical systems based on the sine signal measurement , 2016, Signal Process..

[13]  Wei Xing Zheng,et al.  Parameter estimation algorithms for Hammerstein output error systems using Levenberg-Marquardt optimization method with varying interval measurements , 2017, J. Frankl. Inst..

[14]  Feng Ding,et al.  Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering , 2017, J. Frankl. Inst..

[15]  Ai-Guo Wu,et al.  New Iterative Algorithms for Solving Coupled Markovian Jump Lyapunov Equations , 2015, IEEE Transactions on Automatic Control.

[16]  Xudong Zhao,et al.  Stabilization for a Class of Switched Nonlinear Systems With Novel Average Dwell Time Switching by T–S Fuzzy Modeling , 2016, IEEE Transactions on Cybernetics.

[17]  Ling Xu,et al.  Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration , 2015 .

[18]  N. Sinha,et al.  Robust recursive least-squares method with modified weights for bilinear system identification , 1989 .

[19]  Fredrik Lindsten,et al.  Recursive Maximum Likelihood Identification of Jump Markov Nonlinear Systems , 2013, IEEE Transactions on Signal Processing.

[20]  F. Ding,et al.  Filtering-based iterative identification for multivariable systems , 2016 .

[21]  Huiping Li,et al.  Continuous-time model predictive control of under-actuated spacecraft with bounded control torques , 2017, Autom..

[22]  Feng Ding,et al.  Parameter estimation algorithms for multivariable Hammerstein CARMA systems , 2016, Inf. Sci..

[23]  Guoqi Li,et al.  Fixed point iteration in identifying bilinear models , 2015, Syst. Control. Lett..

[24]  Feng Ding,et al.  The Gradient-Based Iterative Estimation Algorithms for Bilinear Systems with Autoregressive Noise , 2017, Circuits, Systems, and Signal Processing.

[25]  F. Ding,et al.  Least-squares-based iterative and gradient-based iterative estimation algorithms for bilinear systems , 2017 .

[26]  T. Hayat,et al.  Parameter estimation for pseudo-linear systems using the auxiliary model and the decomposition technique , 2017 .

[27]  Ali Dziri,et al.  Maximum Likelihood Parameter Estimation of Nakagami-Gamma Shadowed Fading Channels , 2015, IEEE Communications Letters.

[28]  F. Ding,et al.  Recasted models-based hierarchical extended stochastic gradient method for MIMO nonlinear systems , 2017 .

[29]  Hajime Ase,et al.  Linear approximation and identification of MIMO Wiener-Hammerstein systems , 2016, Autom..

[30]  Ling Xu,et al.  A proportional differential control method for a time-delay system using the Taylor expansion approximation , 2014, Appl. Math. Comput..

[31]  Qingxia Li,et al.  Array Factor Forming for Image Reconstruction of One-Dimensional Nonuniform Aperture Synthesis Radiometers , 2016, IEEE Geoscience and Remote Sensing Letters.

[32]  Cheng Wang,et al.  Parameter identification of a class of nonlinear systems based on the multi-innovation identification theory , 2015, J. Frankl. Inst..

[33]  Feng Ding,et al.  Data filtering based multi-innovation extended gradient method for controlled autoregressive autoregressive moving average systems using the maximum likelihood principle , 2017, Math. Comput. Simul..

[34]  Hao Wu,et al.  An adaptive confidence limit for periodic non-steady conditions fault detection , 2016 .

[35]  Wan Xiangkui,et al.  A T-wave alternans assessment method based on least squares curve fitting technique , 2016 .

[36]  Roland Siegwart,et al.  Maximum Likelihood Identification of Inertial Sensor Noise Model Parameters , 2016, IEEE Sensors Journal.

[37]  Huiping Li,et al.  On Neighbor Information Utilization in Distributed Receding Horizon Control for Consensus-Seeking , 2016, IEEE Transactions on Cybernetics.

[38]  Feng Ding,et al.  The auxiliary model based hierarchical gradient algorithms and convergence analysis using the filtering technique , 2016, Signal Process..

[39]  Muhammad Saeed Aslam.  Maximum likelihood least squares identification method for active noise control systems with autoregressive moving average noise , 2016, Autom..

[40]  F. Ding,et al.  Performance analysis of the generalised projection identification for time-varying systems , 2016 .

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

[42]  Ling Xu,et al.  Application of the Newton iteration algorithm to the parameter estimation for dynamical systems , 2015, J. Comput. Appl. Math..

[43]  Dongqing Wang,et al.  Hierarchical parameter estimation for a class of MIMO Hammerstein systems based on the reframed models , 2016, Appl. Math. Lett..

[44]  Yan Ji,et al.  Unified Synchronization Criteria for Hybrid Switching-Impulsive Dynamical Networks , 2015, Circuits Syst. Signal Process..

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

[46]  Jing Wang,et al.  Least squares based iterative identification for multivariable integrating and unstable processes in closed loop , 2014, Appl. Math. Comput..

[47]  Huiping Li,et al.  Distributed receding horizon control of constrained nonlinear vehicle formations with guaranteed γ-gain stability , 2016, Autom..