In this paper, we address a driver behavior reconstruction problem which is important to enhance traffic safety. More specifically, the task in this study is to estimate the longitude tire force which can be transferred to the corresponding throttle/brake positions under the assumption that the steering angles are known. Although the sensors mounted on the throttle/brake pedals can directly measure the pedal positions and multimodal sensors can also be used to measure vehicle states to estimate the longitude tire force, the sensors are costly and cannot be readily mounted in the vehicle. In order to avoid such shortcomings, we consider using a low cost 1Hz GPS receiver as the vehicle data acquisition equipment. In our work, a longitude force estimation scenario is developed for the nonlinear extended 2-wheel vehicle dynamic model only according to the GPS information. Firstly, two states, i.e. the sideslip angle and the yaw rate are estimated since they are not available from GPS measurements. Secondly, an optimization scheme is proposed to estimate the longitude tire force. Finally, the estimation results can validate our methods by comparing to the reference longitude tire force command.