System for determining the position of a transmitting unit, having: an arrangement of at least four transmitting units (1, 2, 3, 4); wherein a first transmitting unit of the at least four transmitting units (1, 2, 3, 4) is designed to emit a first transmission signal to each of the three remaining transmitting units (2, 3, 4); wherein each of the three remaining transmitting units (2, 3, 4) is designed to receive the first transmission signal and, after receiving the first transmission signal, to return a first response signal to the first transmitting unit; wherein the first transmitting unit is designed to determine relative position data relating to the first transmitting unit with respect to the three remaining transmitting units (2, 3, 4) on the basis of the returned first response signals; characterised in that: the three remaining transmitting units (2, 3, 4) each have stored position data relating to desired positions (1a, 2a, 3a, 4a) of each transmitting unit (1, 2, 3, 4) of the arrangement of transmitting units (1, 2, 3, 4); wherein the first transmitting unit is designed to obtain the stored position data relating to the desired positions (1a, 2a, 3a, 4a) from the three remaining transmitting units (2, 3, 4); wherein the first transmitting unit is designed to allocate to the first transmitting unit the obtained position data relating to a single desired position in order to determine the position and an identity of the first transmitting unit within the arrangement of transmitting units (1, 2, 3, 4); wherein the allocation is based on a discrepancy (d) between all obtained desired positions (1a, 2a, 3a, 4a) and the relative position data determined by the first transmitting unit. an arrangement of at least four transmitting units (1, 2, 3, 4); wherein a first transmitting unit of the at least four transmitting units (1, 2, 3, 4) is designed to emit a first transmission signal to each of the three remaining transmitting units (2, 3, 4); wherein each of the three remaining transmitting units (2, 3, 4) is designed to receive the first transmission signal and, after receiving the first transmission signal, to return a first response signal to the first transmitting unit; wherein the first transmitting unit is designed to determine relative position data relating to the first transmitting unit with respect to the three remaining transmitting units (2, 3, 4) on the basis of the returned first response signals; characterised in that: the three remaining transmitting units (2, 3, 4) each have stored position data relating to desired positions (1a, 2a, 3a, 4a) of each transmitting unit (1, 2, 3, 4) of the arrangement of transmitting units (1, 2, 3, 4); wherein the first transmitting unit is designed to obtain the stored position data relating to the desired positions (1a, 2a, 3a, 4a) from the three remaining transmitting units (2, 3, 4); wherein the first transmitting unit is designed to allocate to the first transmitting unit the obtained position data relating to a single desired position in order to determine the position and an identity of the first transmitting unit within the arrangement of transmitting units (1, 2, 3, 4); wherein the allocation is based on a discrepancy (d) between all obtained desired positions (1a, 2a, 3a, 4a) and the relative position data determined by the first transmitting unit. the three remaining transmitting units (2, 3, 4) each have stored position data relating to desired positions (1a, 2a, 3a, 4a) of each transmitting unit (1, 2, 3, 4) of the arrangement of transmitting units (1, 2, 3, 4); wherein the first transmitting unit is designed to obtain the stored position data relating to the desired positions (1a, 2a, 3a, 4a) from the three remaining transmitting units (2, 3, 4); wherein the first transmitting unit is designed to allocate to the first transmitting unit the obtained position data relating to a single desired position in order to determine the position and an identity of the first transmitting unit within the arrangement of transmitting units (1, 2, 3, 4); wherein the allocation is based on a discrepancy (d) between all obtained desired positions (1a, 2a, 3a, 4a) and the relative position data determined by the first transmitting unit.