In the development of physical tire models, the complexity of the composite structure and the multiphysical variables require strongly nonlinear mathematical formulations to guarantee a desired degree of accuracy. The aim of the current work is to extend the applicability of the multiphysical magic formula-based tire model, already developed and presented by the authors, within a wider frequency range, interposing a rigid ring body between the contact patch and the wheel hub. The contact patch, varying in terms of size, shape, and relative position, is evaluated using instantaneous cams to define the effective plane. Here the advanced slip model, taking into account thermodynamic and wear effects, is then integrated. The adopted formulations have been mathematically and physically justified. They have been analytically compared to formulations related to the rigid-ring implementation available in the literature. Specific experimental activities concerning both the tire’s vertical kinematics and dynamics have been conducted to demonstrate the model’s improved physical consistency on small wavelength unevennesses.

Accurate real-time estimation of the instantaneous vehicle state plays a crucial role in modern automotive research, both in the state diagnostics and anomaly detection and in the design and development of advanced control systems and onboard monitoring strategies. In particular, accurate knowledge of chassis motion and wheel dynamics in response to road disturbances is essential for advanced control strategies aimed at simultaneously enhancing ride quality and handling. However, the road profile represents an unmeasured and highly variable input, often requiring complex and costly sensors such as LiDAR for direct observation: this motivates the development of virtual sensing approaches capable of inferring road irregularities from standard onboard sensors. This work presents a novel state observer based on an Extended Kalman Filter (EKF) architecture for the online estimation of road-induced excitations and key vehicle dynamic quantities, including chassis out-of-plane motions, suspension displacements, and tyre-loaded radii. The observer relies on a computationally efficient 7-degree-of-freedom vehicle model, analytically derived through a streamlined multibody formulation, and validated against a high-fidelity multibody reference model under two sensor configurations, both limited to signals typically available in mass-produced vehicles. The results achieved, even when using high-noise measurements, are encouraging for further applications in real-world virtual sensing scenarios.

Nowadays, control is pervasive in vehicles, and a full and accurate knowledge of vehicle states is crucial to guarantee safety levels and support the development of Advanced Driver-Assistance Systems (ADASs). In this scenario, real-time monitoring of the vehicle sideslip angle becomes fundamental, and various virtual sensing techniques based on both vehicle dynamics models and data-driven methods are widely presented in the literature. Given the need for on-board embedded device solutions in autonomous vehicles, it is mandatory to find the correct balance between estimation accuracy and the computational burden required. This work mainly presents different physical KF-based methodologies and proposes both mathematical and graphical analysis to explore the effectiveness of these solutions, all employing equal tire and vehicle simplified models. For this purpose, results are compared with accurate sensor acquisition provided by the on-track campaign on passenger vehicles; moreover, to truthfully represent the possibility of using such virtual sensing techniques in real-world scenarios, the vehicle is also equipped with low-end sensors that provide information to all the employed observers.