Algebraic estimation of a biased and noisy continuous signal via orthogonal polynomials

Rosane Ushirobira 1 Alban Quadrat 1
1 NON-A - Non-Asymptotic estimation for online systems
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189, Inria Lille - Nord Europe
Abstract : Many important problems in Signal Processing and Control Engineering concern the reconstitution of a noisy biased signal. For this issue, in this paper we consider the signal written as an orthogonal polynomial series expansion and we provide an algebraic estimation of its coefficients. We specialize in Hermite polynomials. On the other hand, the dynamical system described by the noisy biased signal may be given by a differential equation associated with classical orthogonal polynomials. The signal may be recovered through the coefficients identification. As an example, we illustrate our algebraic method on the parameter estimation in the case of Hermite polynomials differential equations.
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Rosane Ushirobira, Alban Quadrat. Algebraic estimation of a biased and noisy continuous signal via orthogonal polynomials. CDC 2016 - 55th IEEE Conference on Decision and Control, Dec 2016, Las Vegas, United States. ⟨hal-01380320⟩

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