A positioning system uses a multiplicity of commercial broadcast stereo FM radio signal transmitters, at known fixed locations, each of which transmits a beacon signal having a phase that is un-synchronized with the phases of the beacon signals of the other transmitters. All the beacon signals have a frequency approximately equal to a 19 KHz. A fixed position observer unit, positioned at a known location, receives the beacon signals from all the transmitters in the vicinity, determines their relative phases, and broadcasts data representing these relative phases. Mobile units, at unknown locations, receive these broadcast values, as well as beacon signals from at least three radio transmitters. Each mobile unit includes phase detection circuitry that detects the phases of the beacon signals at the mobile receivers current position. This is accomplished using a single radio signal receiver. A digital phase-locked loop, coupled to the radio signal receiver, generates a phase error signal for each beacon signal. The phase error signals are then used to compute a distinct phase value for each beacon signal. In the preferred embodiment, each mobile receiver includes a computer for computing its location based on the broadcast relative phase values and the detected phases. In yet another embodiment a common timing signal is provided to the fixed observer unit and to the mobile units in order to establish a common time basis throughout the positioning system, thereby facilitating determination of an initial position for each mobile unit.