## 1 Introduction  
Nowadays, ultrasound is broadly applied in several fields, and the major areas include medical and structural diagnoses and range-finding-related applications. For example, Doppler radar can be used in aviation, meteorology, speed gun, motion detection, intruder warning, and light control. In particular, Doppler radar has been used for posture and gesture recognition in motion sensing [1, 2, 3, 4, 5]. Posture or gesture recognition commonly uses mechanical or light stimulation sensors, such as cameras, infrared sensors, and wearable devices. Although their installation may not be difficult and the obtained results could be intuitively analyzed, these devices have inherent limitations [6]. Cameras can infringe on users' privacy; infrared sensors are susceptible to misjudgment; securing wearable sensors is necessary for functional operation [7]. In contrast, acoustic stimulus sensing, such as sonar, possesses several unique advantages, particularly for the monitoring of the home environment and can be fully operated in the dark [8]. In addition, visuals need not be recorded so that the privacy of users will not be affected [9]. These characteristics make sonar a superior sensing system for gesture recognition applications. The hand gesture detection system possesses several advantages. The contactless interaction mode allows the users not to touch the control panel. This avoids the potential cross-contamination of multiple users via the touch panel/screen and the likely damage/fatigue of the physical control device due to inappropriate/intensified operation. In addition, the proposed hand gestures in the study are aimed at robot manipulation. The hand gestures intuitively correspond to the motion of the robot. This facilitates the users not only to operate the robot but to collaborate with the robot to execute a task. [PERSON] et al. used a single speaker and microphone in a smartphone with the Doppler effect to study gesture recognition via ultrasound. The vectors containing \(+1\) and \(-1\) can be used to indicate the direction of gesture movement in each time period [10]. The Sound-Wave team also used a microphone and speaker in a mobile device. The gestures investigated by them consisted of scrolling, single or double tapping, forward and backward hand gestures, and continuous motion. These gestures can be judged from the amplitude of the reflected signal [11]. [PERSON] et al. developed a three-dimensional range-finding function chip. Its searchable range is up to 1 m in a 45\({}^{\circ}\) field of view. Low power consumption is the main feature of the chip [12]. [PERSON] et al. reported the ultrasonic hand gesture recognition system which is capable of recognizing 3D micro-hand gestures with a high cross-user recognition rate. This system possesses the potential to develop a practical low-power human machine interaction system [13]. On the other hand, researchers working in the field of computer vision have broadly employed image processing methods such as feature detection, description, and matching for object recognition, image classification, and retrieval. Features, such as points, edges, or corners, can be considered as the information of interest within the investigated image [14]. A good feature detector can find features possessing strong information changes that are repeatedly recognized among several images taken with different viewing angles and lighting conditions [15]. A feature descriptor is an algorithm used to process the image feature points into meaningful feature vectors. Feature descriptors encode interesting image features into a series of numbers and act as a type of numerical identifier that can be employed to differentiate one feature from another.