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 -