# Hand Trajectory Recognition by Radar with a Finite-State Machine and a Bi-LSTM
## 2 Related Works
### Gesture Design  
In daily life, gestures play a ubiquitous role exemplified by the directive motions employed by traffic officers. Thus, the gesture protocols ought to align with the everyday customs, facilitating an intuitive comprehension and application for users.  
The three-dimensional spatial model utilized for millimeter-wave radar to detect human gesture motion is illustrated in Figure 2(a), and the real scene to collect human gesture data is shown in Figure 2(b). The radar is located at the coordinate origin, and the antenna array plane is parallel to the XOZ plane, enabling the detection of gesture motion across the three-dimensional coordinates of X, Y, and Z. The radar can obtain target parameters such as range, azimuth, elevation angle, radial velocity, and scattering cross-section. However, due to the dispersion of electromagnetic power after being scattered by the hands, there is no obvious characteristic in the target scattering cross-section of gestures in actual measurements, rendering it ineffective for recognition. Therefore, the scattering cross-section parameter is not considered a feature for gesture motion.  
According to the complexity of commonly used gesture motion trajectories, gestures can be divided into two categories: simple trajectory gestures and complex trajectory gestures. Simple trajectory gestures refer to gestures that move in a single direction along a straight line, which are easily recognizable. Complex trajectory gestures, on the other hand, involve not only linear motion but also reciprocating and circular arc movements, making their motion trajectories relatively complex and not directly recognizable. Therefore, for these two different categories of gestures, simple trajectory gestures can be recognized directly based on the solution of trajectory parameters, while deep learning algorithms are employed to recognize complex trajectory gestures.  
According to Figure 3, the positive direction of the \(Z\)-axis is defined as upward and the negative direction is defined as downward. The positive direction of the \(X\)-axis is defined as leftward and the negative direction as rightward. The positive direction of the \(Y\)-axis is defined as backward and the negative direction as forward. Therefore, simple trajectory gestures are designed as six types of gestures: upward, downward, leftward, rightward, forward, and backward. All these gestures are the most frequently used ones in human daily life. The schematic diagram of these six gesture motions is shown in Figure 4.  
Considering the practical and easily distinguishable features, complex trajectory gestures are designed as four types of gestures: waving to the left and right, drawing circles counterclockwise, drawing a check mark, and drawing a cross mark. For example, in applications, the users can switch file views by waving left or right, adjust the progress bar or volume by drawing circles, and operate the confirmation and cancellation in certain scenarios by drawing check or cross marks. The schematic diagram of these four gesture motions is shown in Figure 5.  
Figure 3: The spatial position model and real scene for gesture motion. (**a**) The spatial position model. (**b**) The real scene for collecting gesture data.