# Moving Vehicle Tracking with a Moving Drone Based on Track Association
## 4 Results
### Multiple Target Tracking
#### 4.3.1 Tracking Results of Video 1  
In Video 1, a total of 13 valid tracks are generated without track association; four redundant tracks are generated for Targets 1, 3, 4, and 7. With track association, 3 of the 4 tracks are successfully merged, resulting in 10 valid tracks. Therefore, tracking efficiency was improved from 69% to 90%. Figure 12a,b show the tracking results without and with track association, respectively, in the expanded frame. Two supplementary multimedia files (MP4 format) for tracking vehicles are available online. One is target tracking without track association (Supplementary Material Video S1) and the other is using the proposed method (Supplementary Material Video S2). The red bounding boxes of the MP4 file are the boundaries of the object windows, the blue dots are position estimates, and the numbers represent the track numbers in the order they were created.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Video 1** & **Video 2** \\ \hline \(V_{max}\) (m/s) for speed gating & & 30 & \\ \(\sigma_{x}=\sigma_{y}\) (m/s\({}^{2}\)) & 30 & 10 \\ \(r_{x}=r_{y}\) (m/s) & 0.5 & 1.5 \\ \(\gamma_{g}\) for measurement association & 8 & 10 \\ \(\gamma_{f}\) for track association & 170 & 70 \\ Valid track criteria & & 9 \\ (Minimum track life) & & \\ Track terminaion criteria & & 15 & \\ (Maximum searching number) & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameter design.  
Figure 11: Video 2: 1016 detections in the expanded frame.  
Figure 10: Video 1: 709 detections in the expanded frame.  
To evaluate the accuracy of the position and velocity estimates, the ground truth of the target position for Video 1 is manually obtained as shown in Figure 17. The ground truth of the velocity is obtained as the difference in position between consecutive frames divided by the sampling time.  
Figures 18 and 19 show each target's position and velocity errors. The position errors of Targets 2 and 4 are reduced drastically at the moment when the track association occurs as shown in Figure 18b,d. The number of track associations for Target 2 and 4 are 25 and 20, respectively, but only two associations occurred for Target 1.  
Figure 16: Tracking results of Target 7.  
Figure 17: Ground truths of Video 1.  
Figure 15: Tracking results of Target 4, (**a**) without track association; (**b**) with the proposed method.  
Figure 19: _Cont._  
Figure 18: Position RMSE of (**a**) Target 1; (**b**) Target 2; (**c**) Target 3; (**d**) Target 4; (**e**) Target 5; (**f**) Target 6; (**g**) Target 7; (**h**) Target 8; (i) Target 9.  
Table 3 show the average position and velocity RMSE with and without track association, respectively. If there is more than one track for the target (Target 1, 2, 4), the longer track is considered to obtain the RMSEs. The average RMSE of position decreased from 2.56 m to 2.42 m, but the average RMSE of velocity increased from 2.20 m/s to 3.19 m/s.  
Table 4 only considers the fused states of Targets 2 and 4. The second and fourth rows of the RMSE is counted for errors when track association occurs. Although the average RMSE of velocity increases from 1.11 m/s to 1.77 m/s, the position RMSE shows the accuracy improvement from 2.61 m to 0.67 m.