Harmonic Components Isolation in Vehicle Vibrations: Enhancing Quarter-Car Model Analysis with an Extended Kalman Filter Approach

<div>This article addresses the essential task of understanding vibrations produced by vehicles to enhance the design of authentic laboratory tests. The article focuses on two primary sources of vibrations: those arising from vehicle–road surface interaction, which is largely random, and those emanating from the drivetrain, characterized as a summation of harmonics with a time-varying fundamental frequency. The method involves the application of the extended Kalman filter (EKF) paired with robust nonlinear least-squares (NLS) initialization to isolate the harmonic components effectively. Through a comprehensive analysis involving mean-square-error (MSE) evaluation via Monte Carlo simulation, considering additive white Gaussian noise (AWGN) and a two-degrees-of-freedom quarter-car model’s simulation response to the road, the research demonstrates the EKF’s proficiency. The results indicate the EKF’s capability to accommodate AWGN with a signal-to-noise ratio (SNR) up to 0 dB and road-induced random background vibrations up to an SNR of −3 dB, maintaining an MSE order of approximately 10⁻³.</div>