Please use this identifier to cite or link to this item: doi:10.22028/D291-37200
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Title: Survey on algebraic numerical differentiation: historical developments, parametrization, examples, and applications
Author(s): Othmane, Amine
Kiltz, Lothar
Rudolph, Joachim
Language: English
Title: International journal of systems science
Volume: 53
Issue: 9
Startpage: 1848
Endpage: 1887
Publisher/Platform: Taylor & Francis
Year of Publication: 2022
Free key words: Numerical differentiation
algebraic differentiators
orthogonal polynomials
linear filtering
confluent hypergeometric function
FIR filters
DDC notations: 620 Engineering and machine engineering
Publikation type: Journal Article
Abstract: The historical developments, parametrization, and numerous applications of algebraic numerical differentiation methods initiated by Fliess, Mboup, Join, and Sira-Ramírez are presented. These numerical non-asymptotic approximation approaches for higher-order derivatives of noisy signals are suited for real-time embedded systems. The different derivation approaches are reviewed according to their historical developments. Links to numerous established numerical differentiation algorithms like the Savitzky-Golay filters are discussed. Recent tuning approaches that are reviewed facilitate a parametrization for a good estimation accuracy without relying on trial-and-error approaches, which is essential for industrial applications. The use of these guidelines is demonstrated using two concrete examples: Identification of system parameters from noisy measurements and numerical inversion of the dynamics of analogue anti-aliasing filters. Moreover, an extensive literature survey with various applications of these methods by the control community in all engineering areas is presented. The problems solved include, but are not limited to, parameter estimation, state reconstruction, feedback control, fault diagnosis, anomaly detection, fault-tolerant control, and model-free control. A MATLAB and Python toolbox implementing all necessary functions for the design, analysis, and discretization of the filters is made available, for which a link is provided. Its use is demonstrated in a short appendix.
DOI of the first publication: 10.1080/00207721.2022.2025948
URL of the first publication: https://www.tandfonline.com/doi/full/10.1080/00207721.2022.2025948
Link to this record: urn:nbn:de:bsz:291--ds-372002
hdl:20.500.11880/33744
http://dx.doi.org/10.22028/D291-37200
ISSN: 1464-5319
0020-7721
Date of registration: 14-Sep-2022
Faculty: NT - Naturwissenschaftlich- Technische Fakultät
Department: NT - Systems Engineering
Professorship: NT - Prof. Dr. Joachim Rudolph
Collections:Die Universitätsbibliographie

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