An adaptive derivative estimator for fault-detection Using a dynamic system with a suboptimal parameter
Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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in: Algorithms, Jahrgang 12, Nr. 5, 101, 10.05.2019.
Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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TY - JOUR
T1 - An adaptive derivative estimator for fault-detection Using a dynamic system with a suboptimal parameter
AU - Schimmack, Manuel
AU - Mercorelli, Paolo
PY - 2019/5/10
Y1 - 2019/5/10
N2 - 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).
AB - 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).
KW - Derivative approximation
KW - Estimator
KW - Least squares method
KW - Lyapunov approach
KW - Engineering
UR - http://www.scopus.com/inward/record.url?scp=85066603842&partnerID=8YFLogxK
U2 - 10.3390/a12050101
DO - 10.3390/a12050101
M3 - Journal articles
AN - SCOPUS:85066603842
VL - 12
JO - Algorithms
JF - Algorithms
SN - 1999-4893
IS - 5
M1 - 101
ER -