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An Adaptive Derivative Estimator for Fault-Detection Using a Dynamic System with a Suboptimal Parameter

1
Institute of Product- and Processinnovation, Leuphana University of Lueneburg, Volgershall 1, D-21339 Lueneburg, Germany
2
Institute for Electrical Engineering and Information Technology, Kiel University, Kaiserstraße 2, D-24143 Kiel, Germany
*
Author to whom correspondence should be addressed.
Algorithms 2019, 12(5), 101; https://doi.org/10.3390/a12050101
Received: 20 December 2018 / Revised: 11 April 2019 / Accepted: 22 April 2019 / Published: 10 May 2019
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Abstract

This paper deals with an approximation of a first derivative of a signal using a dynamic system of the first order. After formulating the problem, a proposition and a theorem are proven for a possible approximation structure, which consists of a dynamic system. In particular, a proposition based on a Lyapunov approach is proven to show the convergence of the approximation. The proven theorem is a constructive one and shows directly the suboptimality condition in the presence of noise. Based on these two results, an adaptive algorithm is conceived to calculate the derivative of a signal with convergence in infinite time. Results are compared with an approximation of the derivative using an adaptive Kalman filter (KF). View Full-Text
Keywords: derivative approximation; estimator; Lyapunov approach; least squares method derivative approximation; estimator; Lyapunov approach; least squares method
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Schimmack, M.; Mercorelli, P. An Adaptive Derivative Estimator for Fault-Detection Using a Dynamic System with a Suboptimal Parameter. Algorithms 2019, 12, 101.

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