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Chetoui, Manel; Thomassin, Magalie; Malti, Rachid; Aoun, Mohamed; Najar, Slaheddine; Abdelkrim, Mohamed Naceur; Oustaloup, Alain

New consistent methods for order and coefficient estimation of continuous-time errors-in-variables fractional models. (English) Zbl 1345.37087

Comput. Math. Appl. 66, No. 5, 860-872 (2013).
Summary: The errors-in-variables identification problem concerns dynamic systems in which input and output signals are contaminated by an additive noise. Several estimation methods have been proposed for identifying dynamic errors-in-variables rational models. This paper presents new consistent methods for order and coefficient estimation of continuous-time systems by errors-in-variables fractional models. First, differentiation orders are assumed to be known and only differential equation coefficients are estimated. Two estimators based on Higher-Order Statistics (third-order cumulants) are developed: the fractional third-order based least squares algorithm (ftocls) and the fractional third-order based iterative least squares algorithm (ftocils). Then, they are extended, using a nonlinear optimization algorithm, to estimate both the differential equation coefficients and the commensurate order. The performances of the proposed algorithms are illustrated with a numerical example.

Cited in 5 Documents

MSC:

37M10 Time series analysis of dynamical systems
34A08 Fractional ordinary differential equations

Keywords:

system identification; fractional differentiation; errors-in-variables; higher-order statistics; third-order cumulant; commensurate order

Software:

CRONE
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Full Text: DOI

References:

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