# Motion Target Localization Method for Step Vibration Signals Based on Deep Learning
## 4 Experimental Results and Analysis
### Analysis of Test Results  
To illustrate the positioning effect, the experimental results of a group of data from the test set were randomly selected for detailed analysis. The recorded trajectory length of this data is 26.206 m, taking 34.068 s, and the complete trajectory comparison is shown in Figure 4. The starting point coordinates of the trajectory in Figure 5 are uniform (1.508 m, 1.927 m), with the estimated trajectory endpoint coordinates and the true trajectory endpoint coordinates being (1.865 m, \(-\)2.494 m) and (1.637 m, \(-\)2.326 m), respectively, with an error between them of only 0.28 m. Furthermore, the total estimated trajectory length of this experiment is 24.052 m, compared to the actual value of 26.209 m, with a difference of only 2.15 m.  
In further analysis, special attention was given to the prediction of the speed vector by the network model and compared with the actual speed, as shown in Figure 6. Figure 6a and Figure 6b show the comparisons between \(\widetilde{v}_{x}\) and \(v_{x}\) and between \(\widetilde{v}_{y}\) and \(v_{y}\), respectively. It is clearly observable from the figures that the predicted results maintain consistency with the dynamic trend of the actual speed.  
To more accurately evaluate the model's average performance, the 6 best and 6 worst experiments in the test set were excluded during the experiment, and 16 experiments were randomly selected from the remaining test set for metric evaluation. These experiments covered various types of paths, including straight paths (Figure 7), figure-eight paths (Figure 8), circular paths (Figure 9), and L-shaped paths (Figure 10). The total length of the 16 experiment trajectories reached 285 m, with average RMSE and RTE values of 0.374 and 1.7%, respectively, as shown in Figure 11. Among them, the design of straight paths was simple, and the walking pattern was easy to learn, thus yielding the best experimental  
Figure 5: Comparison of the predicted trajectory and the real trajectory.  
Figure 6: Velocity vector comparison. (**a**) Comparison of real velocity and prediction in the X-axis direction. (**b**) Comparison of real velocity and prediction in the Y-axis direction.  
results, with an average RMSE value of only 0.175 m. Although partial results from the circular and L-shaped paths, such as those depicted in Figures 9c and 10c, failed to accurately track the trajectory, the average RMSE (root mean square error) across multiple experiments is only 0.357 m, which still outperforms the comparative algorithms and demonstrates high positioning accuracy. In comparison, the experimental results for the figure-eight path demonstrate less-than-ideal performance, as illustrated in Figure 8. Despite achieving an average RMSE of 0.529 m, which still constitutes a reasonable positioning outcome, the reason for this is attributed to the design intent of the figure-eight path, which is to test the positioning capabilities of the model under extreme conditions. The continuous and sharply curved turns executed by the pedestrian result in rapid velocity changes, prone to inducing significant trajectory deviations.  
Figure 8: Part of the test result graph around the figure-eight path. (**a**) The test set results of experimenter A. (**b**) The test set results of experimenter B. (**c**) The test set results of experimenter C.  
Figure 7: Part of the linear path test results. (**a**) The test set results of experimenter A. (**b**) The test set results of experimenter B. (**c**) The test set results of experimenter C.  
Figure 9: Part of the loop path test results. (**a**) The test set results of experimenter A. (**b**) The test set results of experimenter B. (**c**) The test set results of experimenter C.  
From the above analysis, it can be concluded that this positioning model exhibits good performance across various types of paths, with trajectory length estimation and speed vector prediction closely matching the actual values, demonstrating high accuracy and reliability.