Methods for detecting the passing of a virtual tolling point by a vehicle travelling on a road network are performed by systems and apparatuses. In the methods, a sequence of distances between position fixes and the virtual tolling point are calculated, where the position fixes are sequentially obtained from a GNSS receiver carried by the vehicle. The sequence of distances are searched for a global minimum followed by an increase and, if such is found, then the passing of the virtual tolling point is detected. Otherwise, a new distance calculated between a newly obtained position fix and the virtual tolling point is appended to the sequence while discarding the oldest distance from the sequence. The method is then repeated from the sequence of distances being searched until the passing of the virtual tolling point is detected.