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An algebraic method for multi-dimensional derivative estimation

Samer Riachy 1, 2 Yara Bachalany 1 Mamadou Mboup 2, 3, 4 Jean-Pierre Richard 2, 5
2 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
5 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : This communication revisits the algebra-based results for derivative estimation presented by Fliess and coauthors in 2005. It is proposed, here, to consider multidimensional functions, namely scalar or vector fields of several variables. Such fields are locally represented by a vector Taylor series expansion, and a computation technique is presented so to put successive partial derivatives (for instance, the gradient, the Hessian matrix...) as functions of iterated integrals of the measured quantities.
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Submitted on : Wednesday, April 23, 2008 - 11:18:14 PM
Last modification on : Friday, December 11, 2020 - 6:44:07 PM
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  • HAL Id : inria-00275461, version 1


Samer Riachy, Yara Bachalany, Mamadou Mboup, Jean-Pierre Richard. An algebraic method for multi-dimensional derivative estimation. MED'08, 16th IEEE Mediterranean Conference on Control and Automation, IEEE, Jun 2008, Ajaccio, Corsica, France. ⟨inria-00275461⟩



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