Numerical differentiation with annihilators in noisy environment

Mamadou Mboup 1, 2, * Cédric Join 2, 3 Michel Fliess 2, 4
* Corresponding author
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
Abstract : Numerical differentiation in noisy environment is revised through an algebraic approach. For each given order, an explicit formula yielding a pointwise derivative estimation is derived, using elementary differential algebraic operations. These expressions are composed of iterated integrals of the noisy observation signal. We show in particular that the introduction of delayed estimates affords significant improvement. An implementation in terms of a classical finite impulse response (FIR) digital filter is given. Several simulation results are presented.
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Mamadou Mboup, Cédric Join, Michel Fliess. Numerical differentiation with annihilators in noisy environment. Numerical Algorithms, Springer Verlag, 2009, 50 (4), pp.439-467. ⟨10.1007/s11075-008-9236-1⟩. ⟨inria-00319240⟩

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