Advanced Driver-Assistance Systems (ADAS) have become an essential part of modern cars. Among the solutions proposed, haptic shared control of the steering wheel is increasingly being studied. A fundamental question is how drivers adapt their behavior to these systems. This article proposes to use the Unscented Kalman Filter (UKF) to identify the variation over time in the psychological and neuromuscular parameters of a driver structured model. The goal here is to understand how the driver adapts to changes, whether regarding the behavior of the steering system, the visibility or the road conditions. The LPV system considered for identification is known as the cybernetic driver model. Two experiments carried out respectively with Simulink© and on a driving simulator provide the data. The methodology proposed for tuning the UKF is studied from the results obtained with those data. A multi-UKF strategy is also considered. The methodology reveals useful when a compromise between rapidity and precision has to be achieved for parameters estimation. It opens the way to a detailed analysis of the driver's parameter variations within the multi-UKF framework.