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We present a system that can identify positions of objects in three-dimensional space using ultrasonic communications. The proposed system uses the time of flight of ultrasonic waves to calculate the distance between a transmitter and a microphone. An innovative method called the Phase Accordance Method is used for accurate detection of the arrival time of the ultrasonic signal for distance measurements. The main benefit of the proposed system is that it can locate positions of static and moving objects in a three-dimensional space by using only one compact receiver unit mounting three ultrasonic microphones; this will reduce the users' deployment tasks. Experimental results prove that the system possesses sufficient accuracy levels and stable performance of position measurements in static and dynamic situations, even though the beacon geometry of the system is poor.