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On Algebraic Approach for MSD Parametric Estimation

Marouene Oueslati 1, 2 Stéphane Thiery 1, 2 Olivier Gibaru 1, 2 Richard Béarée 2 George Moraru 2 
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : This article address the identification problem of the natural frequency and the damping ratio of a second order continuous system where the input is a sinusoidal signal. An algebra based approach for identifying parameters of a Mass Spring Damper (MSD) system is proposed and compared to the Kalman-Bucy filter. The proposed estimator uses the algebraic parametric method in the frequency domain yielding exact formula, when placed in the time domain to identify the unknown parameters. We focus on finding the optimal sinusoidal exciting trajectory which allow to minimize the variance of the identification algorithms. We show that the variance of the estimators issued from the algebraic identification method introduced by Fliess and Sira-Ramirez is less sensitive to the input frequency than the ones obtained by the classical recursive Kalman-Bucy filter. Unlike conventional estimation approach, where the knowledge of the statistical properties of the noise is required, algebraic method is deterministic and non-asymptotic. We show that we don't need to know the variance of the noise so as to perform these algebraic estimators. Moreover, as they are non-asymptotic, we give numerical results where we show that they can be used directly for online estimations without any special setting.
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Submitted on : Thursday, December 1, 2011 - 4:49:36 PM
Last modification on : Tuesday, November 22, 2022 - 2:26:15 PM
Long-term archiving on: : Monday, December 5, 2016 - 10:28:59 AM


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  • HAL Id : hal-00647231, version 1


Marouene Oueslati, Stéphane Thiery, Olivier Gibaru, Richard Béarée, George Moraru. On Algebraic Approach for MSD Parametric Estimation. IMAACA 2011 - 5th International Conference on Integrated Modeling and Analysis in Applied Control and Automation conference, Sep 2011, Rome, Italy. pp.Pages 83-91. ⟨hal-00647231⟩



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