# Hand Trajectory Recognition by Radar with a Finite-State Machine and a Bi-LSTM
## 4 Results  
### Simple Trajectory Gesture Recognition Results  
To verify the effectiveness of the proposed simple trajectory gesture recognition method, a millimeter-wave radar was built to collect multiple sets of gesture data. During the experiment, the radar was installed on a tripod, with the radar antenna line of sight facing being straight ahead. The azimuth antenna array was arranged in a horizontal direction, and the elevation antenna array in a vertical direction, as shown in Figure 3.  
This experiment aims to verify six simple straight-line trajectories: forward, backward, leftward, rightward, upward, and downward. Experimental subjects continuously perform dynamic gestures from the perspective of the radar antenna. During the gesture movement, they can assess the current status of the gesture in real-time and generate the corresponding gesture. Then, the type of gesture action can be determined without the need to wait for the completion of the entire gesture. The measured data of six gesture actions are shown in Figure 17, where the blue part of the trajectory represents the starting position, the yellow part represents the ending position, and the image title is the corresponding gesture action automatically recognized based on the gesture trajectory. According to Figure 17, the proposed method can effectively recognize six simple trajectory gesture actions. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Layer** & **Layer Size** & **Output Size** \\ \hline Input layer & 32 \(\times\) 32 \(\times\) 1 & 32 \(\times\) 32 \(\times\) 1 \\ \hline  & CNN & \\ \hline Conv1 + ReLU & 5 \(\times\) 5 & 28 \(\times\) 28 \(\times\) 6 \\ Maxpooing1 & 2 \(\times\) 2 & 14 \(\times\) 14 \(\times\) 6 \\ Conv2 + ReLU & 5 \(\times\) 5 & 10 \(\times\) 10 \(\times\) 6 \\ Maxpooling2 & 2 \(\times\) 2 & 5 \(\times\) 5 \(\times\) 16 \\ FC1 & 84 & 84 \\ \hline  & Fusion classification module & \\ \hline Self-attention layer & 3 \(\times\) 84 & 3 \(\times\) 84 \\ FC2 & 84 & 84 \\ FC3 & 4 & 4 \\ Softmax & \(\backslash\) & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Three-channel CNN parameters. To further verify the recognition accuracy and robustness of the proposed method, 80 sets of data were collected for each gesture, totaling 480 sets for testing. By employing the proposed method to analyze the collected data, the recognition results and accuracy for the six gestures can be obtained. The recognition accuracy is presented in Table 5.  
The experimental results show that under actual conditions, the proposed method has an average recognition accuracy of 99.58% for six gestures, achieving good recognition results. Reference [29] employs 2 DCNN and LSTM neural networks to classify and recognize a total of ten gestures, which include the six simple gestures listed above. This is achieved by fusing radar images and optical images as inputs to the neural network. And the average accuracy of recognition is 95.36%. Compared to the referenced method, the proposed simple trajectory gesture recognition method demonstrates superior recognition performance. By directly extracting the trajectory parameters of gesture, we achieve gesture recognition through discriminating gesture motion status, thus reducing the complexity of feature extraction, simplifying the process of gesture recognition, and enhancing recognition accuracy. Moreover, by employing finite-state machine to recognize gestures, this method can continuously recognize gesture actions without any interruptions, aligning more closely with practical operating habits. Figure 17: Measurement data and recognition results of 6 gesture actions. (**a**) Gesture Forward recognition. (**b**) Gesture Backward recognition. (**c**) Gesture Leftward recognition. (**d**) Gesture Rightward recognition. (**e**) Gesture Upward recognition. (**f**) Gesture Downward recognition. The gesture trajectories begin with the dark blue points and end with the light yellow points.