Fast parameter estimation is a non-trivial task, and it is critical when the system parameters evolve with time, as demanded in real-time control applications. In this study, a new computational approach for parameter identification is proposed based on the application of polynomial chaos theory. The polynomial chaos approach has been shown to be considerably more efficient than Monte Carlo in the simulation of systems with a small number of uncertain parameters. In the framework of this new approach, a (suboptimal) Extended Kalman Filter (EKF) is used to recalculate the polynomial chaos expansions for the uncertain states and the uncertain parameters. As a case study, the proposed parameter estimation method is applied to a four degree-of-freedom roll plane model of a vehicle for which the vertical stiffnesses of the tires are estimated from periodic observations of the displacements and velocities across the suspensions. The results obtained with this approach are close to the actual values of the parameters. In addition, the EKF approach gives more information about the parameters of interest than a simple estimated value: the estimation comes in the form of a probability density function. The approach presented in this paper has shown great promise for an improvement in the computational efficiency of current parameter estimation methods. Possible applications of this theory to the field of off-road vehicle simulations include the estimation of various vehicle parameters of interest, as well as the estimation of parameters related to the tire-terrain contact.