The satellite blockage problem, which adversely affects Global Positioning System (GPS) accuracy in urban environments, is addressed in this work. To provide a position solution, there must be at least four satellites within line of sight (LOS) of the receiver (vehicle). However, when satellite blockage occurs, this requirement is not met because most of the sky is obscured by tall buildings, and only a narrow sky sector is exposed to the receiver. Given the short duration of satellite blockages, an efficient solution to this problem can be accomplished through reliable modeling of vehicle motion. In this manner, information regarding vehicle motion can be more precisely obtained in the absence of a sufficient number of measurements. In this paper, a model that uses intrinsic quantities as part of the description of the vehicle path, such as curvature, tangent angle, and tangential speed, is proposed to achieve a more accurate modeling of both the trajectory and kinematics of a land vehicle. The model, which was implemented via an extended Kalman filter, was examined against currently known models during satellite blockage scenarios and demonstrated superior performance.