A method, a device and a computer-readable storage medium with instructions for determining the lateral position of a transportation vehicle relative to the lanes of a carriageway. An image processing unit acquires geometry information and property information relating to carriageway markings. A position-determining unit determines an approximate position of the transportation vehicle. An evaluation unit determines the lateral position of the transportation vehicle by comparing the determined geometry information and property information of the carriageway markings with carriageway marking geometries at the approximate position determined for the transportation vehicle, from a lane geometry map. The lane geometry map contains lane center geometries and lane edge geometries with a high level of accuracy with respect to one another.