In indoor context awareness applications the location of people, devices or objects is often required. Ultrasound technology enables high resolution indoor position measurements. A disadvantage of state-of-the-art ultrasonic systems is that several base stations are required to estimate 3D position. Since fewer base stations leads to lower cost and easier setup, a novel method is presented that requires just one base station. The method uses information from acoustic reflections in a room, and estimates 3D positions using an acoustic room-model. The method has been implemented, and verified within an empty room. It can be concluded that ultrasonic reflection data provides useful clues about the 3D position of a device.