Convergence rate of the causal jacobi derivative estimator

  • Authors:

  • Da-yan Liu;Olivier Gibaru;Wilfrid Perruquetti

  • Affiliations:

  • Équipe Projet Non-A, Parc Scientifique de la Haute, INRIA Lille-Nord Europe, Villeneuve d'Ascq, France and Laboratoire de Paul Painlevé, Université de Lille 1, Villeneuve d'Ascq, Fr ...;Équipe Projet Non-A, Parc Scientifique de la Haute, INRIA Lille-Nord Europe, Villeneuve d'Ascq, France and Laboratory of Applied Mathematics and Metrology (L2MA), Arts et Metiers ParisTech ce ...;Équipe Projet Non-A, Parc Scientifique de la Haute, INRIA Lille-Nord Europe, Villeneuve d'Ascq, France and Laboratoire de LAGIS, École Centrale de Lille, Villeneuve d'Ascq, France

  • Venue:
  • Proceedings of the 7th international conference on Curves and Surfaces
  • Year:
  • 2010

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Abstract

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 [9] to this causal case, we revisit nth order derivative estimators originally introduced within an algebraic framework by Mboup, Fliess and Join in [14,15]. Thanks to a given noise level δ 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.