This paper describes a driver distraction detection scenario which is important to enhance driving safety. We employ data obtained by a GPS to reproduce the driver behavior. Gaussian Mixture model (GMM) is used to capture the sequence of driving characteristics according to the reconstructed vehicle's information and it is also used as a classifier to assign the driving behavior to normal or distraction category. In our work, we consider using a low cost 1Hz GPS receiver as the vehicle data acquisition equipment instead of the costly sensors (steering angle sensor, throttle/brake position sensor, etc). The nonlinear extended 2-wheel vehicle dynamic model is adopted in this study. Firstly, two states, i.e. the sideslip angle and the yaw rate are calculated since they are not available from GPS measurements. Secondly, a piecewise optimization scheme is proposed to reconstruct the driving behaviors which include the steering angle and the longitude force. Finally, a GMM classifier is applied to identify whether the driver is under distraction.