# Precise Positioning of Autonomous Vehicles Combining UWB Ranging Estimations with On-Board Sensors
## 5 Experiments and Results
### Tests Results
#### 5.3.2 Positioning  
The proposed positioning approach is based on using a complementary system based on UWB to correct the long term drifts of the IMU-Odometry solution. Meaning that, the UWB complementary system is required to achieve an accurate solution to position the vehicle during more than 30 s.  
Figures 13 and 14 show a graphical comparison between the RTK-SN trajectory (green line) used as ground truth, the IMU-Odometry trajectory (black line) and the UWB-IMU-Odometry (processed) trajectory (blue line). As stated before, Figure 13 reflects how both the IMU-Odometry and the UWB-IMU-Odometry (processed) trajectories are able to track the RTK-SN trajectory with a similar positioning performance during the initial steps. However, Figure 14 shows that the positioning performance of both trajectories is significantly different at the end of the trajectory. Hence, the UWB-IMU-Odometry (processed) trajectory continues tracking the RTK-SN trajectory in an accurate way while the RC car on-board data trajectory does not track the ground truth. It can be seen how the final point of the IMU-Odometry trajectory is situated far behind the final one of the other two trajectories. This is due to the fact that the IMU and Odometry data have a tendency to drift with time, increasing their error. In consequence, as time passes, the position computed from these data has a higher uncertainty and it is not able to track the real trajectory followed by the vehicle. Figure 12: UWB ranging estimates after post-processing. Figure 13: Comparison of the different trajectories at the beginning of the experiment. Next, we will compare the positioning distance error of the three solutions: only using the RC car on-board data (IMU-Odometry), by merging these data with UWB ranging estimates, both with (UWB-IMU-Odometry (processed)) and without (UWB-IMU-Odometry (raw)) post-processing. Figure 15 shows the positioning distance error, \(\epsilon_{p}\), of the three solutions throughout the trajectory. The obtained results show that the position computed by only taking into account the RC car on-board data (IMU-Odometry) remains accurate enough when the elapsed time is lower than 30 s. However, as can be seen, the positioning distance error is higher than 4 m at the end of the trajectory. Figure 15 shows how by using an UWB system the positioning performance is significantly enhanced. Combining raw UWB ranging estimates together with the vehicle's on-board data (UWB-IMU-Odometry (raw)) has a major impact on the positioning performance. As a result of this combination, the positioning distance error is bounded over time and the maximum positioning distance error is reduced up to approximately 175 cm. On the other hand, these data also show that the positioning performance is degraded in the areas close to the RSUs (see Figure 12) with a positioning distance error much higher than in the rest of the trajectory. However, using the post-processing UWB ranging estimates (UWB-IMU-Odometry (processed)) instead of the the raw data, reduces significantly the positioning distance error in those areas. Meaning that, the discard of the NLOS UWB ranging estimates allows to bound the positioning distance error throughout the whole trajectory. Thus, the UWB-IMU-Odometry (processed) solution is able to track in an accurate way the RC car RTK-SN position with its maximum positioning distance error lower than 46 cm over the whole trajectory. Figure 14: Comparison of the different trajectories at the end of the experiment. Figure 15: Comparison of the positioning distance error, \(\epsilon_{p}\), of the different positioning systems. Table 3 shows the statistical data of the positioning distance error, \(\epsilon_{p}\), of the evaluated positioning solutions. When only the IMU-Odometry data are used, the RMSE of the positioning distance error is 249.8 cm. Moreover, the 95% of the computed positions have a positioning distance error of 407.3 cm or less.