Abstract: The invention relates to a system (1) for positioning at least one mobile receiver (2), comprising at least two stationary transmitter bases (4, 4A, 4B). Each transmitter base (4, 4A, 4B) is configured to transmit radio frequency signals (S1A, S1B, sdA, sdB, srA, srB) and to transmit a sum (S1A, S1B) of at least two unmodulated pure carrier signals of different frequencies; and the mobile receiver (2) further comprises: means for measuring phases of the signals; and computing means configured to: apply a Fourier transform to a signal consisting of the various measured phases of the radio frequency signals; determine a time-of-flight between the mobile receiver (2) and each base (4A, 4B); calculate at least one time-of-flight difference between the mobile (2) and two transmitter bases (4A, 4B); determine the position of the mobile receiver (2) from the calculated time-of-flight difference(s).