The invention relates to a system for determining positions of labels. Each label includes a processor and a transmitting and receiving device, and each label is configured for transmitting an electromagnetic first type beacon signal. The labels are also configured for receiving first type beacon signals from other labels, and for determining first type positioning data. The labels are also configured to transmit information about the positioning data. The system includes a receiver for receiving transmitted information about the positioning data, and a computer configured to calculate, on the basis of the received information about the positioning data, the relative positions of the labels relative to each other. The information about the relative positions of the labels can be exported, for example by means of an electrical information signal.