A Discrete-Time Matching Filtering Differentiator

TL;DR

This paper introduces a discrete-time version of a robust filtering differentiator that accurately estimates derivatives of noisy signals, leveraging homogeneity properties for improved implementation and convergence analysis.

Contribution

It proposes a novel discrete-time formulation of the filtering differentiator, enabling implementation with or without knowledge of higher-order derivative bounds.

Findings

Trajectories converge to a neighborhood of the origin with noise-free inputs.

The method can be implemented with or without knowing the bound of higher-order derivatives.

Comparative analysis shows the effect of different design parameters.

Abstract

This paper presents a time discretization of the robust exact filtering differentiator, a sliding mode differentiator coupled to filter, which provides a suitable approximation to the derivatives of some noisy signals. This proposal takes advantage of the homogeneity of the differentiator, allowing the use of similar techniques to those of the linear systems. As in the original case, the convergence robust exact filtering differentiator depends on the bound of a higher-order derivative; nevertheless, this new realization can be implemented with or without the knowledge of such constant. It is demonstrated that the system's trajectories converge to a neighborhood of the origin with a free-noise input. Finally, comparisons between the behavior of the differentiator with different design parameters are presented.