In this paper we present a user-centric position sensing system that is based on asynchronous, independent ultrasonic beacons. These stationary transmitter units are small, cheap to manufacture, and have power requirements low enough to run each from a small solar cell and a nearby light source. Each beacon is programmed to emit a short, 40 kHz ultrasonic signal with a unique transmission period. The mobile receiver unit first associates a received signal with a beacon based on the observed periodicity, then measures the Doppler shift in the periodicity that results from movements of the receiver. Using Doppler shifts from a number of different beacons, the receiver is able to estimate both its position and velocity by employing a particle filter. In this paper, we describe our positioning algorithm, the hardware, and proof-of-concept results.