Method for determining the position of a track-based mobile component, a trajectory portion covered by the mobile component being detected odometrically, the curve over time of the signals of angle sensors being evaluated for the purpose of the odometric detection, a first of the angle sensors being provided for detecting the angular position of a first wheel of the mobile component, and a second of the angle sensors being provided for detecting the angular position of a second wheel of the mobile component, the first wheel and the second wheel being axially spaced apart from one another, characterised in that an image of the trajectory portion is then determined by rotating and/or shifting the detected trajectory portion in such a way that - as small an amount of deviation as possible from a trajectory stored in the mobile component is achieved, the current position of the track-based mobile component corresponding to the end point of the image, the current position of the track-based mobile component corresponding to the image of the most recently detected point of the trajectory portion, the current direction, i.e. direction of travel, of the track-based mobile component corresponding to the image of the most recently detected direction of the trajectory portion, an alternating current being applied to the track conductor that is installed on the floor of a facility for the purpose of track guidance, in such a way that energy can be transmitted inductively from the track conductor to a secondary winding of the mobile component to power a traction drive of the mobile component. a trajectory portion covered by the mobile component being detected odometrically, the curve over time of the signals of angle sensors being evaluated for the purpose of the odometric detection, a first of the angle sensors being provided for detecting the angular position of a first wheel of the mobile component, and a second of the angle sensors being provided for detecting the angular position of a second wheel of the mobile component, the first wheel and the second wheel being axially spaced apart from one another, characterised in that an image of the trajectory portion is then determined by rotating and/or shifting the detected trajectory portion in such a way that - as small an amount of deviation as possible from a trajectory stored in the mobile component is achieved, - as small an amount of deviation as possible from a trajectory stored in the mobile component is achieved, the current position of the track-based mobile component corresponding to the end point of the image, the current position of the track-based mobile component corresponding to the image of the most recently detected point of the trajectory portion, the current direction, i.e. direction of travel, of the track-based mobile component corresponding to the image of the most recently detected direction of the trajectory portion, an alternating current being applied to the track conductor that is installed on the floor of a facility for the purpose of track guidance, in such a way that energy can be transmitted inductively from the track conductor to a secondary winding of the mobile component to power a traction drive of the mobile component.