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Algorithmic study of the algebraic parameter estimation problem for a class of perturbations

Abstract : We consider the algebraic parameter estimation problem for a class of standard perturbations. We assume that the measurement z(t) of a solution x(t) of a linear ordinary differential equation -- whose coefficients depend on a set \theta := {\theta_1, ..., \theta_r} of unknown constant parameters -- is affected by a perturbation \gamma(t) whose structure is supposed to be known (e.g., an unknown bias, an unknown ramp), i.e., z(t)=x(t, \theta)+\gamma(t). We investigate the problem of obtaining closed-form expressions for the parameters \theta_i's in terms of iterative indefinite integrals or convolutions of z. The different results are illustrated by explicit examples computed using the NonA package -- developed in Maple -- in which we have implemented our main contributions.
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https://hal.inria.fr/hal-03502443
Contributor : Alban Quadrat Connect in order to contact the contributor
Submitted on : Saturday, December 25, 2021 - 11:27:22 AM
Last modification on : Friday, February 4, 2022 - 3:12:53 AM
Long-term archiving on: : Saturday, March 26, 2022 - 6:08:03 PM

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  • HAL Id : hal-03502443, version 1

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Maya Chartouny, Thomas Cluzeau, Alban Quadrat. Algorithmic study of the algebraic parameter estimation problem for a class of perturbations. [Research Report] RR-9441, Inria Paris, Sobonne Université; XLIM. 2021, pp.26. ⟨hal-03502443⟩

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