Global Positioning System (GPS) signal outage and noise in the sensor reading impact the accuracy of vehicle position. Thus, noise covariance must be regularly adjusted. A priori knowledge about noise statistics in vehicle positioning applications is difficult to obtain. This study proposes the adaptive Kalman filter (KF) and the fuzzy intersection method for free GPS localization. The KF's parameters were adapted using the fuzzy intersection method and fuzzy model. First, a dataset based on map information was developed to capture road coordinates and predict noise covariance. Second, fuzzy intersection method obtained a good initial state vector. Third, a fuzzy clustering algorithm based on a weighted fuzzy expected value was used to conclude the problem space into the cluster prototypes. Fourth, the fuzzy parameter model was learned from the clustering algorithm in the previous step without expert systems. This study used two road network configurations characterized as single and multiple road entry points. The position accuracy was estimated using the root mean square error. In the first network, the proposed method achieved 1 m accuracy compared to 4, 7, and 9 m accuracies in other related papers, while in the second network; it achieved 2 m accuracy compared to 5, 7, and 10 m accuracies in other related works.