All wearable centric location sensing technologies must address the issue of clock synchronisation between signal transmitting systems and signal receiving systems. GPS receivers, for example, compensate for synchronisation errors by incorporating a model of the receiver clock offset in the navigation solution. Drift between satellite clocks is also monitored to keep signal data in synch with GPS time. Most ultrasonic positioning systems solve the synchronisation problem by using a second medium for communication between transmitter and receiver devices. The transmitters in these systems emit RF signals (pings) to indicate the transmission of subsequent ultrasound signals (chirps). By subtracting the arrival time of the ping from that of the chirps, the receiver is able to compute the distance to each transmitter. In this paper, we describe an ultrasonic positioning system that does not use RF signals to achieve synchronisation. Instead, it exploits a periodic chirp transmission pattern to model the receiver's position using chirp reception times exclusively. Not only does the system improve on the accuracy of previous technologies but it also eliminates bulky RF circuitry - a definite advantage for wearable applications where component size and weight are critical for usability.