Road Roughness Identification in Vehicle Dynamics: The Role of Measurements in Ensuring System Observability

Dynamical systems, as, specifically, vehicles' models, often rely on unknown inputs and on states that may not be directly measured. This represents a challenging research topic, for which various methods and solutions have been proposed. The present study focuses on the recovery of road roughness and the estimation of vertical dynamics states using a quarter-car model and two Kalman filtering-based approaches, even comparing their performance in terms of accuracy, robustness, and computational efficiency. The application of these algorithms may face issues due to certain measurements that are not readily available, impacting system observability. This aspect is thoroughly investigated by collecting different methods scattered in the scientific literature and introducing a new parameter derived from the entries of the observability matrix. Through numerical simulations and a carefully designed experiment, in this effort, we identify critical measurements and determine the most effective method for estimating quantities that are not directly measurable.