Convergence Rate of the Causal Jacobi Derivative Estimator

Liu, Da-Yan; Gibaru, Olivier; Perruquetti, Wilfrid

Document type :

Partie d'ouvrage: Chapitre

DOI :

10.1007/978-3-642-27413-8_28

Title :

Convergence Rate of the Causal Jacobi Derivative Estimator

Author(s) :

Liu, Da-Yan [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Laboratoire d'Automatique, Génie Informatique et Signal [LAGIS]
Non-Asymptotic estimation for online systems [NON-A]
Gibaru, Olivier [Auteur]
Laboratoire de Métrologie et de Mathématiques Appliquées [L2MA]
Non-Asymptotic estimation for online systems [NON-A]
Perruquetti, Wilfrid [Auteur]

Centrale Lille
Systèmes Non Linéaires et à Retards [SyNeR]
Non-Asymptotic estimation for online systems [NON-A]

Book title :

Curves and Surfaces 2011

Publication date :

2011

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

Numerical causal derivative estimators from noisy data are essential for real time applications especially for control applications or fluid simulation so as to address the new paradigms in solid modeling and video ...
Show more >Numerical causal derivative estimators from noisy data are essential for real time applications especially for control applications or fluid simulation so as to address the new paradigms in solid modeling and video compression. By using an analytical point of view due to Lanczos \cite{C. Lanczos} to this causal case, we revisit $n^{th}$\ order derivative estimators originally introduced within an algebraic framework by Mboup, Fliess and Join in \cite{num,num0}. Thanks to a given noise level $\delta$ and a well-suitable integration length window, we show that the derivative estimator error can be $\mathcal{O}(\delta ^{\frac{q+1}{n+1+q}})$ where $q$\ is the order of truncation of the Jacobi polynomial series expansion used. This so obtained bound helps us to choose the values of our parameter estimators. We show the efficiency of our method on some examples.Show less >

Language :

Anglais

Audience :

Internationale

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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