Vehicle motion and tire forces have been estimated using extended Kalman filters for many years. The use of extended Kalman filters is primarily motivated by the simultaneous presence of nonlinear dynamics and sensor noise. Two versions of extended Kalman filters are employed in this thesis: one using a deterministic tire-force model and the other using a stochastic tire-force model. Previous literature has focused on linear stochastic tire-force models and on linear deterministic tire-force models. However, it is well known that there exists a nonlinear relationship between slip variables and tire-force variables. For this reason, it is suitable to use a nonlinear deterministic tire-force model for the extended Kalman filter, and this is the novel aspect at this work. The objective of this research is to show the improvement of the extended Kalman filter using a nonlinear deterministic tire-force model in comparison to linear stochastic tire-force model. The simulation model is a seven degree-of-freedom bicycle model that includes vertical suspension dynamics but neglects the roll motion. A comparison between the linear stochastic tire-force model and the nonlinear deterministic tire-force model confirms the expected results. Simulation studies are performed on some illustrative examples obtaining good tracking performance.