Abstract: A novel dynamic state space model was established for Global Positioning System (GPS) navigation by adopting the polynomial predictive filtering idea and state dimension expansion. We called the new model expanded state space model which was established without the exact knowledge of the original state dynamics, i.e., we way use the proposed model to describe the state dynamics no matter we know the original state propagation well or not. A correspondent Expanded State Space Kalman filter (ESSKF) was then presented based on the proposed model. The results of the GPS navigation examples demonstrated that the proposed method did work better than the existed Extended Kalman Filter (EKF), especially in the situations that the state dynamics were not known well.