Fourth-order cumulants based method for continuous-time EIV fractional model identification

The errors-in-variables (EIV) system identification problem concerns the dynamic systems whose discrete input and output are corrupted by additive noises, that can be white, colored and/or mutually correlated. In this paper, a new estimator based on Higher-Order Statistics (fourth-order cumulants) is proposed for continuous-time system identification with fractional models. Under some assumptions on the distributional properties of the noise and noisefree signals, the fractional fourth-order cumulants based least squares (ffocls) estimator gives consistent results. A numerical example illustrates the performance of the proposed method.

[1]  Thierry Poinot,et al.  Fractional modelling and identification of thermal systems , 2011, Signal Process..

[2]  Jitendra K. Tugnait,et al.  Stochastic system identification with noisy input using cumulant statistics , 1990, 29th IEEE Conference on Decision and Control.

[3]  Alain Oustaloup,et al.  Instrumental variable method with optimal fractional differentiation order for continuous-time system identification , 2009 .

[4]  Magalie Thomassin,et al.  DETC 2009-86975 MULTIVARIABLE IDENTIFICATION OF CONTINUOUS-TIME FRACTIONAL SYSTEM , 2009 .

[5]  Peter C. Young,et al.  Parameter Estimation for Continuous Time Models - A Survey , 1979 .

[6]  Hugues Garnier,et al.  Third-order cumulants based methods for continuous-time errors-in-variables model identification , 2008, Autom..

[7]  Mohamed Naceur Abdelkrim,et al.  EIV methods for system identification with fractional models , 2012 .

[8]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[9]  M. N. Abdelkrim,et al.  Third-order cumulants based method for continuous-time Errors-In-Variables system identification by fractional models , 2011, Eighth International Multi-Conference on Systems, Signals & Devices.

[10]  Kaushik Mahata,et al.  An improved bias-compensation approach for errors-in-variables model identification , 2007, Autom..

[11]  Umberto Soverini,et al.  Maximum likelihood identification of noisy input-output models , 2007, Autom..

[12]  Hugues Garnier,et al.  Continuous-time model identification from noisy input/output measurements using fourth-order cumulants , 2007, 2007 46th IEEE Conference on Decision and Control.

[13]  Hugues Garnier,et al.  Parameter and differentiation order estimation in fractional models , 2013, Autom..

[14]  Hugues Garnier,et al.  Identification of continuous-time errors-in-variables models , 2006, Autom..

[15]  T. Raïssi,et al.  Set membership parameter estimation of fractional models based on bounded frequency domain data , 2010 .

[16]  Mohamed Naceur Abdelkrim,et al.  Guaranteed frequency-domain identification of fractional order systems: application to a real system , 2012, Int. J. Model. Identif. Control..

[17]  R. Malti,et al.  Subspace method for continuous-time fractional system identification , 2009 .

[18]  Jerry M. Mendel,et al.  Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications , 1991, Proc. IEEE.

[19]  Torsten Söderström,et al.  A generalized instrumental variable estimation method for errors-in-variables identification problems , 2011, Autom..

[20]  T. Poinot,et al.  Identification of Fractional Systems Using an Output-Error Technique , 2004 .

[21]  Marion Gilson,et al.  Survey of Analytical IV Estimates for Errors-In-Variables Model Identification , 2011 .

[22]  Alain Oustaloup,et al.  Fractional system identification for lead acid battery state of charge estimation , 2006, Signal Process..

[23]  Magalie Thomassin,et al.  Higher-Order Statistics-based methods for order and parameter estimation of continuous-time errors-in-variables fractional models , 2012 .

[24]  Peter Young,et al.  Parameter estimation for continuous-time models - A survey , 1979, Autom..

[25]  D. Brillinger.  Time series - data analysis and theory , 1981, Classics in applied mathematics.

[26]  A. Oustaloup,et al.  Numerical Simulations of Fractional Systems: An Overview of Existing Methods and Improvements , 2004 .