This study addresses the divergence issues in GPS navigation systems caused by inaccuracies in dynamic modeling and explores solutions using the extended Kalman filter (EKF). Since algorithms such as the Kalman filter (KF) and EKF rely on assumed process models that often deviate from real-world conditions, their performance in real-time applications can degrade. This paper introduces fictitious process noise as an effective remedy to mitigate divergence, demonstrating its benefits through covariance estimation and tuning factors to enhance observability and controllability, particularly for continuous differential GPS (DGPS) access. The study evaluates several motion scenarios, including stationary receivers, straight-line trajectories with constant and varying speeds, and turning trajectories. The inclusion of process noise allows the EKF to adapt to changes in direction and speed without explicitly modeling turning or acceleration dynamics. To ensure robustness, the simulations incorporate a variety of scenarios to assess the statistical reliability and real-world performance of the EKF, ensuring the findings are statistically robust and widely applicable. Simulated receivers were used to evaluate the position (P), position-velocity (PV), and position-velocity-acceleration (PVA) models. The results from both the Ordinary Least-Squares (OLS) and EKF simulations show improved vehicle trajectory tracking and demonstrate the EKF's potential for broader navigation system applications. This paper's novel contribution lies in its thorough analysis of the divergence issues in GPS navigation filter designs due to dynamic modeling inaccuracies, providing a systematic approach to addressing these challenges and offering new insights to improve estimation accuracy.