This study proposes an innovative methodology for accurate vehicle maneuver analysis using time-differenced GNSS carrier-phase (TDCP) measurements from smartphones, combined with a vehicle motion estimation approach based on factor-graph optimization (FGO). By leveraging the centimeterlevel precision of TDCP, the method achieves accurate vehicle displacement measurements, while the FGO framework enhances the estimation of vehicle speed, acceleration, pitch and heading angles, as well as angular velocity. Extensive experiments involving multiple vehicles and drivers validate the method's effectiveness in vehicle motion estimation, maneuver identification, and risk classification. The results demonstrate a reduction in speed and angular velocity estimation errors by up to 47.28% and 66.95%, respectively, compared to traditional GNSS solutions. Furthermore, classification accuracy for highrisk driving behaviors improves by 27.37%, making the method suitable for applications such as usage-based insurance (UBI), fleet management, and autonomous driving.