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An algebraic approach to on-line signal denoising and derivatives estimation.

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Bibliographic Details
Title: An algebraic approach to on-line signal denoising and derivatives estimation.
Authors: Kasac, Josip1, Majetic, Dubravko1, Brezak, Danko1
Source: Journal of the Franklin Institute. Oct2018, Vol. 355 Issue 15, p7799-7825. 27p.
Subjects: Signal denoising, Derivatives (Mathematics), Electric currents, Engineering, Signal processing
Abstract: Abstract In this paper, a new algebraic approach to the on-line signal derivatives estimation is proposed. The proposed approach is based on the conversion of the truncated Taylor series expansion to the set of linearly independent equations regarding the signal derivatives. The nonhomogeneous parts of the obtained set of equations are convolution integrals, which can be transformed to the stable linear state-space filter realization. The proposed algebraic estimator provides stable convergence without the need for periodic re-initialization, as in the case of the conventional algebraic estimators. In contrast to the Taylor series-based tracking differentiators, the proposed estimator also provides an estimation of the arbitrary number of the higher-order signal derivatives. In addition, the tuning of the estimator parameters does not depends on the filter dimension. The efficiency of the proposed estimator is illustrated by the simulation examples and experimental results related to the monitoring of the surgical drilling process. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Abstract In this paper, a new algebraic approach to the on-line signal derivatives estimation is proposed. The proposed approach is based on the conversion of the truncated Taylor series expansion to the set of linearly independent equations regarding the signal derivatives. The nonhomogeneous parts of the obtained set of equations are convolution integrals, which can be transformed to the stable linear state-space filter realization. The proposed algebraic estimator provides stable convergence without the need for periodic re-initialization, as in the case of the conventional algebraic estimators. In contrast to the Taylor series-based tracking differentiators, the proposed estimator also provides an estimation of the arbitrary number of the higher-order signal derivatives. In addition, the tuning of the estimator parameters does not depends on the filter dimension. The efficiency of the proposed estimator is illustrated by the simulation examples and experimental results related to the monitoring of the surgical drilling process. [ABSTRACT FROM AUTHOR]
ISSN:00160032
DOI:10.1016/j.jfranklin.2018.08.016