论文信息 - A new method for estimating derivatives based on a distribution approach

A new method for estimating derivatives based on a distribution approach

In many applications, the estimation of derivatives has to be done from noisy measured signal. In this paper, an original method based on a distribution approach is presented. Its interest is to report the derivatives on infinitely differentiable functions. Thus, the estimation of the derivatives is done only from the signal. Besides, this method gives some explicit formulae leading to fast calculus. For all these reasons, it is an efficient method in the case of noisy signals as it will be confirmed in several examples.

Ghislaine Joly-Blanchard | Lilianne Denis-Vidal | Nathalie Verdière

[1] Peter Craven,et al. Smoothing noisy data with spline functions , 1978 .

[2] S. Diop,et al. A numerical procedure for filtering and efficient high-order signal differentiation , 2004 .

[3] J. Gauthier,et al. A simple observer for nonlinear systems applications to bioreactors , 1992 .

[4] M. Fliess,et al. Questioning some paradigms of signal processing via concrete examples , 2003 .

[5] M. Hutchinson,et al. Smoothing noisy data with spline functions , 1985 .

[6] R. Scattolini,et al. LQG optimal control of multirate sampled-data systems , 1992 .

[7] Carl de Boor,et al. A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[8] Cédric Join,et al. Numerical differentiation with annihilators in noisy environment , 2009, Numerical Algorithms.

[9] Jessy W. Grizzle,et al. Interpolation and numerical differentiation for observer design , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[10] Ghislaine Joly-Blanchard,et al. Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor , 2005 .

[11] Olivier Gibaru,et al. Error analysis of Jacobi derivative estimators for noisy signals , 2011, Numerical Algorithms.

[12] Abhinav Bhandari,et al. Computing Derivatives of Noisy Signals Using Orthogonal Functions Expansions , 2008, J. Sci. Comput..

[13] G. Wahba. Smoothing noisy data with spline functions , 1975 .