A Novel Sliding Mode Filter with Implicit-Euler Discretization for Simultaneous Noise Attenuation and Derivative Estimation

Zuoping  Zhao; Dongyang  Li; Zhengjian  Lai

doi:10.6180/jase.202607_30.028

A Novel Sliding Mode Filter with Implicit-Euler Discretization for Simultaneous Noise Attenuation and Derivative Estimation

Zuoping Zhao¹This email address is being protected from spambots. You need JavaScript enabled to view it., Dongyang Li², and Zhengjian Lai³

¹College of Engineering, Yanbian University, Yanji, 133002, China

²Technology Center, Nanyang Beifangxiangdong Industrial Co., Ltd., Nanyang, 474677, China

³College of Automotive Technology, Sichuan Vocational and Technical College, Suining, 629099, China

Received: September 8, 2025
Accepted: December 14, 2025
Publication Date: January 10, 2026

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202607_30.028

In control systems, obtaining reliable filtered signals and their derivatives simultaneously from noise contaminated inputs represents a key challenge. To this end, this paper presents a novel sliding mode filter for f iltering noise and estimating derivatives. The proposed filter enhances conventional parabolic sliding mode design by introducing a fast factor that boosts the response speed without sacrificing filtering performance, and the system stability is further analyzed via the Lyapunov method. In addition, the discrete-time algorithm is derived via the implicit-Euler method; the resulting output signals are far less likely to exhibit chattering than those from the conventional explicit-Euler discretization, and numerical simulations verify its effectiveness.

Keywords: sliding mode; filtering performance; implicit-Euler; chattering phenomenon

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