Vehicle localization is an important technical factor in autonomous driving vehicles. Particularly, accurate and precise information about the vehicle position should be obtained, with robustness towards various weather and road conditions. A method using magnetic road markers as coordinate reference points for vehicle localization has proven to achieve the above requirements. However, such method has various limitations. For example, it is unable to localize the vehicle when the vehicle veers off the course of magnetic marker system. This is problematic especially in places where vehicles can take various paths, such as intersections. In this paper, we propose a concept to localize the vehicle using only one set of magnetic sensors, and a novel marker placement method, where markers are placed in a grid-like patterns to enable localization for various paths. To achieve this, extended Kalman filter was used to integrate information from inertial measurement unit with the information from magnetic markers. Maximum likelihood estimation was used to associate the coordinates of detected markers from a known marker coordinate map. Simulation using MATLAB showed that the proposed method is plausible. The proposed localization algorithm was able to correctly associate the marker coordinates and accurately estimate the vehicle position and heading in some conditions. It also suggested that the marker placement pattern could affect the precision of the marker association algorithm.