# Multi-Lidar System Localization and Mapping with Online Calibration
## 4 Real-World Experiment Validation and Result Analysis
### Online Calibration Experiment Results and Analysis
#### 4.1.1 Comparison and Analysis of Online Calibration Results for Different Lidar Layouts  
This section employs six multi-radar layouts, deriving actual inter-radar external parameters through manual measurements. Multiple individuals participated in the measurements, and the mean of all measurements was taken as the ultimate value, aiming to minimize manual measurement errors. The online calibration results and corresponding radar layouts are shown in Table 1.  
Upon reviewing Table 1, it is evident that the online calibration outcomes closely align with actual measurements, affirming the efficacy of the calibration algorithm. Further analysis will be conducted to statistically assess deviations between the online calibration results and actual measurements, as shown in Table 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **X (m)** & **Y (m)** & **Z (m)** & **Roll (°)** & **Pitch (°)** & **Yaw (°)** \\ \hline \hline \multicolumn{8}{c}{The 32-line lidar is placed at the center of the roof, while the 16-line lidar is placed at the center of the front of the vehicle.} \\ \hline Actual measurement values & 0.82 & 0 & \(-\)0.05 & 0 & 15 & 5 \\ Algorithm calibration values & 0.848785 & \(-\)0.069597 & \(-\)0.110832 & \(-\)1.01514 & 15.052825 & 4.54818 \\ \hline \multicolumn{8}{c}{The 32-line lidar is centered on the roof, and the 16-line lidar is centered on the front of the vehicle.} \\ \hline Actual measurement values & 0.82 & 0.45 & \(-\)0.05 & \(-\)2 & 15 & 5 \\ Algorithm calibration values & 0.788523 & 0.450865 & \(-\)0.0857012 & \(-\)2.90022 & 15.0670923 & 4.27292 \\ \hline \multicolumn{8}{c}{The 32-line lidar is placed at the center of the roof, and the 16-line lidar is placed at the left side of the rear end.} \\ \hline Actual measurement values & \(-\)0.63 & 0.45 & \(-\)0.03 & 1 & \(-\)1 & \(-\)1 \\ Algorithm calibration values & \(-\)0.69039 & 0.440672 & \(-\)0.010485 & 0.38109943 & \(-\)0.78497562 & \(-\)1.66093791 \\ \hline \multicolumn{8}{c}{The 32-line lidar is mounted on the center of the roof, and the 16-line lidar is mounted on the front right of the vehicle.} \\ \hline Actual measurement values & 0.82 & \(-\)0.45 & \(-\)0.05 & 8 & 15 & \(-\)10 \\ Algorithm calibration values & 0.812278 & \(-\)0.428665 & \(-\)0.0959522 & 7.30276 & 16.0154646 & \(-\)9.31442 \\ \hline \multicolumn{8}{c}{The 32-line lidar is placed on the roof in the center, while the 16-line Lidar is placed on the rear of the car and to the right.} \\ \hline Actual measurement values & \(-\)0.63 & \(-\)0.45 & \(-\)0.03 & 10 & \(-\)3 & \(-\)10 \\ Algorithm calibration values & \(-\)0.644347 & \(-\)0.37646 & \(-\)0.078509 & 10.6063 & \(-\)3.16483 & \(-\)11.497818 \\ \hline \multicolumn{8}{c}{The 32-line lidar is mounted on the right side of the roof, and the 16-line lidar is mounted on the left side of the roof.} \\ \hline Actual measurement values & 0 & 0.67 & \(-\)0.02 & 0 & 0 \\ Algorithm calibration values & 0.0617705 & 0.732039 & \(-\)0.0673341 & 0.39993226 & \(-\)0.10664561 & 1.47808788 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Online calibration results for different lidar layouts. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **X (m)** & **Y (m)** & **Z (m)** & **Roll (°)** & **Pitch (°)** & **Yaw (°)** \\ \hline maximum deviation & 0.0617705 & 0.07364 & 0.060832 & 1.01514 & 1.0154646 & 1.497818 \\ \hline minimum deviation & 0.007722 & 0.000865 & 0.019515 & 0.3993226 & 0.052825 & 0.45182 \\ \hline mean deviation & 0.0340818 & 0.0390111 & 0.0429739 & 0.7062888 & 0.270 Upon analyzing Table 2, it is deduced that the maximum translation error of the online calibration algorithm is 0.0617705 m, and the maximum rotation error is 1.497818\({}^{\circ}\), both falling within acceptable limits. The smaller deviation in translation calibration results can be attributed to the precision of actual translation measurements as well as minimal translation deviation between the two lidars, rendering this paper's algorithm more capable of achieving accurate calibration results.