Air-writing systems have recently been proposed as tools for human-machine interaction where instructions can be represented using letters or digits written in the air. Different technologies have been used to realize air-writing systems. In this paper, we propose an air-writing system using acoustic waves. The proposed system consists of two components: a motion tracking component, and a text recognition component. For motion tracking, we utilize direction-of-arrival (DOA) information. An

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... sonic receiver array tracks the motion of a wearable ultrasonic transmitter by observing the change in the DOA of the signals. We propose a novel 2-D DOA estimation algorithm that can track the change in the direction of the transmitter using measured phase-differences between the receiver array elements. The proposed phase-difference projection (PDP) algorithm can provide accurate tracking with a 3-sensor receiver array. The motion tracking information is passed next for text recognition. To this end, and in order to strike the desired balance between flexibility, processing speed, and accuracy, a training-free orderrestricted matching (ORM) classifier is designed. The proposed air-writing system, which combines the proposed DOA estimation and text recognition algorithms, achieves a letter classification accuracy of 96.31%. The utility, processing time, and classification accuracy are compared with four training-free classifiers and two machine learning classifiers to demonstrate the efficiency of the proposed system.