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Fourth-order cumulants based-least squares methods for fractional Multiple-Input-Single-Output Errors-In-Variables system identification

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Abstract

This paper presents new consistent methods for continuous-time Multiple-Input-Single-Output (MISO) Errors-In-Variables (EIV) systems by fractional models. The proposed idea is to use Higher-Order Statistics (HOS), such as fourth-order cumulants (foc), instead of noisy input and output measurements to obtain unbiased estimates. Firstly, all differentiation orders are assumed to be known a priori and linear coefficients are estimated. The developed estimator is based on minimizing the equation error and it is called fractional fourth-order based-least squares estimator (\(frac-foc-ls\)). Secondly, the global commensurability of the fractional MISO system is considered. The \(frac-foc-ls\) is combined with a non linear technique to estimate the global commensurate order along with linear coefficients. The developed algorithm is based on minimizing the output error and called fractional fourth-order cumulants based-least squares combined with global commensurate order optimization (\(frac-foc-gcools\)). The consistency of the developed estimators, in presence of high levels of noise corrupting both the input and output measurements, is assessed through a numerical example with the help of Monte Carlo simulations.

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Notes

  1. The time space contains the lines of cumulants obtained for \(N_t\) samples of data.

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  1. Research Laboratory Modeling, Analysis and Control of Systems (MACS) LR16ES22, National Engineering School of Gabes, University of Gabes, Gabès, Tunisia

    Manel Chetoui & Mohamed Aoun

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  1. Manel Chetoui
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  2. Mohamed Aoun
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Correspondence to Manel Chetoui.

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Chetoui, M., Aoun, M. Fourth-order cumulants based-least squares methods for fractional Multiple-Input-Single-Output Errors-In-Variables system identification. Fract Calc Appl Anal 26, 1868–1893 (2023). https://doi.org/10.1007/s13540-023-00174-z

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