Fitting the exponential autoregressive model through recursive search

Abstract This paper focuses on the recursive parameter estimation methods for the exponential autoregressive (ExpAR) model. Applying the negative gradient search and introducing a forgetting factor, a stochastic gradient and a forgetting factor stochastic gradient algorithms are presented. In order to improve the parameter estimation accuracy and the convergence rate, the multi-innovation identification theory is employed to derive a forgetting factor multi-innovation stochastic gradient algorithm. A simulation example is provided to test the effectiveness of the proposed algorithms.

[1]  Jing Na,et al.  Improving transient performance of adaptive control via a modified reference model and novel adaptation , 2017 .

[2]  Meihang Li,et al.  Auxiliary Model Based Least Squares Iterative Algorithms for Parameter Estimation of Bilinear Systems Using Interval-Varying Measurements , 2018, IEEE Access.

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

[4]  Wei Li,et al.  Control Algorithms of Magnetic Suspension Systems Based on the Improved Double Exponential Reaching Law of Sliding Mode Control , 2018, International Journal of Control, Automation and Systems.

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

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

[7]  Feng Ding,et al.  Iterative estimation for a non-linear IIR filter with moving average noise by means of the data filtering technique , 2017, IMA J. Math. Control. Inf..

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

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

[10]  Hong Wang,et al.  Fault Diagnosis and Tolerant Control for Discrete Stochastic Distribution Collaborative Control Systems , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

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

[12]  T. Teräsvirta.  Specification, Estimation, and Evaluation of Smooth Transition Autoregressive Models , 1994 .

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

[14]  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..

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

[16]  Feng Ding,et al.  Auxiliary Model-Based Recursive Generalized Least Squares Algorithm for Multivariate Output-Error Autoregressive Systems Using the Data Filtering , 2018, Circuits Syst. Signal Process..

[17]  C. L. Philip Chen,et al.  Exploiting the interpretability and forecasting ability of the RBF-AR model for nonlinear time series , 2016, Int. J. Syst. Sci..

[18]  Zupeng Zhou,et al.  State and fault estimation of sandwich systems with hysteresis , 2018 .

[19]  H. Dridi,et al.  Test for periodicity in restrictive EXPAR models , 2016 .

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

[21]  Erfu Yang,et al.  Modeling a nonlinear process using the exponential autoregressive time series model , 2019 .

[22]  C. L. Philip Chen,et al.  A Two-Stage Estimation Algorithm Based on Variable Projection Method for GPS Positioning , 2018, IEEE Transactions on Instrumentation and Measurement.

[23]  T. Ozaki,et al.  Non-linear time series models for non-linear random vibrations , 1980, Journal of Applied Probability.

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

[25]  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.

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

[27]  Feng Ding,et al.  Filtering-Based Maximum Likelihood Gradient Iterative Estimation Algorithm for Bilinear Systems with Autoregressive Moving Average Noise , 2018, Circuits Syst. Signal Process..

[28]  Jelloul Allal,et al.  Optimal Detection of Exponential Component in Autoregressive Models , 2006 .

[29]  T. Ozaki.  THE STATISTICAL ANALYSIS OF PERTURBED LIMIT CYCLE PROCESSES USING NONLINEAR TIME SERIES MODELS , 1982 .

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

[31]  Min Gan,et al.  An Efficient Variable Projection Formulation for Separable Nonlinear Least Squares Problems , 2014, IEEE Transactions on Cybernetics.

[32]  Guido Herrmann,et al.  Robust adaptive finite‐time parameter estimation and control for robotic systems , 2015 .

[33]  Zhaoyun Shi,et al.  Monitoring the stability of BWR oscillation by nonlinear time series modeling , 2001 .

[34]  Jianqiang Pan,et al.  A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems , 2017 .

[35]  Esmail Amiri,et al.  Forecasting daily river flows using nonlinear time series models , 2015 .

[36]  Min Gan,et al.  A Variable Projection Approach for Efficient Estimation of RBF-ARX Model , 2015, IEEE Transactions on Cybernetics.

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

[38]  C. L. Philip Chen,et al.  A Regularized Variable Projection Algorithm for Separable Nonlinear Least-Squares Problems , 2019, IEEE Transactions on Automatic Control.

[39]  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..

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

[41]  Yanjun Liu,et al.  Model recovery for Hammerstein systems using the hierarchical orthogonal matching pursuit method , 2019, J. Comput. Appl. Math..

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

[43]  Anton Schick,et al.  Efficient estimation in nonlinear autoregressive time-series models , 1997 .

[44]  Michel Verhaegen,et al.  Blind multivariable ARMA subspace identification , 2016, Autom..

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

[46]  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..

[47]  Xiangli Li,et al.  State space model identification of multirate processes with time-delay using the expectation maximization , 2019, J. Frankl. Inst..

[48]  Min Gan,et al.  Generalized exponential autoregressive models for nonlinear time series: Stationarity, estimation and applications , 2018, Inf. Sci..

[49]  C. L. Philip Chen,et al.  Gradient Radial Basis Function Based Varying-Coefficient Autoregressive Model for Nonlinear and Nonstationary Time Series , 2015, IEEE Signal Processing Letters.

[50]  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..

[51]  Feng Ding,et al.  Multi-innovation gradient identification for input nonlinear state space systems , 2015 .

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

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

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

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

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

[57]  Feng Ding,et al.  Gradient-based iterative identification method for multivariate equation-error autoregressive moving average systems using the decomposition technique , 2019, J. Frankl. Inst..

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

[59]  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..

[60]  Long Chen,et al.  On Some Separated Algorithms for Separable Nonlinear Least Squares Problems , 2018, IEEE Transactions on Cybernetics.

[61]  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..

[62]  T. Ozaki,et al.  Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model , 1981 .

[63]  Feng Ding,et al.  Hierarchical gradient parameter estimation algorithm for Hammerstein nonlinear systems using the key term separation principle , 2014, Appl. Math. Comput..

[64]  Bo Fu,et al.  An Improved Mixed Integer Linear Programming Approach Based on Symmetry Diminishing for Unit Commitment of Hybrid Power System , 2019, Energies.

[65]  Yuehong Su,et al.  A Capacity Configuration Control Strategy to Alleviate Power Fluctuation of Hybrid Energy Storage System Based on Improved Particle Swarm Optimization , 2019, Energies.

[66]  Mouna Merzougui,et al.  Estimation in periodic restricted EXPAR(1) models , 2018, Commun. Stat. Simul. Comput..

[67]  Feng Ding,et al.  Decomposition- and Gradient-Based Iterative Identification Algorithms for Multivariable Systems Using the Multi-innovation Theory , 2019, Circuits Syst. Signal Process..