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

In control systems, obtaining reliable filtered signals and their derivatives simultaneously from noisecontaminated inputs represents a key challenge. To this end, this paper presents a novel sliding mode filter for filtering 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.