Assistance system for a road vehicle which can be used on a roadway having one or more lanes, comprising - a position determination system for determining a lateral position of the road vehicle on the roadway, wherein the position determination system has: - an electrical signal line arranged parallel to the roadway, wherein the signal line is arranged above the roadway at defined lateral distances (Y) to a lane centre of the or a lane, - a signal generator for generating and feeding an electrical signal into the signal line, as a result of which a current flow is generated in the signal line, - an on-vehicle sensor assembly for capturing a field strength and/or a field direction of an electromagnetic field forming about the signal line as a result of the current flow generated and - an on-vehicle evaluation unit, which is designed - to determine, from the captured field strength and/or field direction, a lateral relative position of the road vehicle relative to the signal line, and - to determine, from the determined relative position, the defined lateral distances (Y) and a defined lane width of a plurality of lanes of the roadway, a lane currently used by the road vehicle and a current lateral offset (ΔY) of the road vehicle from the lane centre of the used lane. - a position determination system for determining a lateral position of the road vehicle on the roadway, wherein the position determination system has: - an electrical signal line arranged parallel to the roadway, wherein the signal line is arranged above the roadway at defined lateral distances (Y) to a lane centre of the or a lane, - a signal generator for generating and feeding an electrical signal into the signal line, as a result of which a current flow is generated in the signal line, - an on-vehicle sensor assembly for capturing a field strength and/or a field direction of an electromagnetic field forming about the signal line as a result of the current flow generated and - an on-vehicle evaluation unit, which is designed - to determine, from the captured field strength and/or field direction, a lateral relative position of the road vehicle relative to the signal line, and - to determine, from the determined relative position, the defined lateral distances (Y) and a defined lane width of a plurality of lanes of the roadway, a lane currently used by the road vehicle and a current lateral offset (ΔY) of the road vehicle from the lane centre of the used lane. - an electrical signal line arranged parallel to the roadway, wherein the signal line is arranged above the roadway at defined lateral distances (Y) to a lane centre of the or a lane, - a signal generator for generating and feeding an electrical signal into the signal line, as a result of which a current flow is generated in the signal line, - an on-vehicle sensor assembly for capturing a field strength and/or a field direction of an electromagnetic field forming about the signal line as a result of the current flow generated and - an on-vehicle evaluation unit, which is designed - to determine, from the captured field strength and/or field direction, a lateral relative position of the road vehicle relative to the signal line, and - to determine, from the determined relative position, the defined lateral distances (Y) and a defined lane width of a plurality of lanes of the roadway, a lane currently used by the road vehicle and a current lateral offset (ΔY) of the road vehicle from the lane centre of the used lane. - to determine, from the captured field strength and/or field direction, a lateral relative position of the road vehicle relative to the signal line, and - to determine, from the determined relative position, the defined lateral distances (Y) and a defined lane width of a plurality of lanes of the roadway, a lane currently used by the road vehicle and a current lateral offset (ΔY) of the road vehicle from the lane centre of the used lane.