In this paper we present a novel positioning technique that is based on transmissions from independent ultrasound beacons. These unsynchronised beacons emit narrow-band ultrasonic pulses and do not use any other medium, such as radio frequency or infra-red. A passive mobile positioning unit locates itself using the signatures of the received ultrasound signals. This unit measures shifts in the periodicities of the signals, a form of the Doppler effect, in order to estimate its location and velocity. We have initially tested the system using a simulator; the results suggest that the device is able to position itself with a 95\% accuracy of 20~cm, and a 50\% accuracy of 6~cm. Our previous experience is that these figures will degrade with the use of real hardware, but we aim for a 95\% accuracy of better than 40~cm. The advantages of our system are three-fold: the infrastructure contains no wiring and, as such, can be easily retro-fitted with minimal aesthetic impact; it scales to any number of mobile positioning units; and the beacons are low-power, cheap and simple to construct.