# NR5G-SAM: A SLAM Framework for Field Robot Applications Based on 5G New Radio
## 5 Results and Discussion
LIO-SAM performed with an overall error of 0.12 m compared to the ground truth with a standard deviation of \(\pm\)0.26 m, demonstrating the huge potential of LiDAR SLAM approaches in favorable scenarios. Despite underperforming, NR5G-SAM preserved the localization of the robot bounded, during the post failure case and until the end of the robot's trajectory by scoring a RMSE of 0.52 m with a standard deviation of \(\pm\)0.46 m, compared to LIO-SAM with 52.87 m and a standard deviation of \(\pm\)106.84 m. The results of the 5G positioning were similar for the prior case at 0.91 m on average, with a standard deviation of \(\pm\)0.65 m. The estimated trajectories for this setup can be seen on the top of Figure 7.  
In the FR2 setup and prior to LIO-SAM's failure, 5G positioning presents a RMSE of 0.22 m, with a standard deviation of \(\pm\)0.16 m. NR5G-SAM presents a RMSE of 0.23 m and LIO-SAM yields a RMSE of 0.12 m, with a standard deviation of \(\pm\)0.26 m. This significant increase in the accuracy of NR5G-SAM is due to the numerology features of the the 5G NR mmWave and the minimization in the sub-carrier spacing of the slots, hence transmitted frames of the signal. For the post-failure case, the 5G positioning presents the same RMSE with 0.22 m and a standard deviation of \(\pm\)0.16 m. NR5G-SAM shows an error of 0.19 m, with a standard deviation of \(\pm\)0.19 m. This increase in performance is due to the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **5G Positioning** & **NR5G-SAM** & **LIO-SAM** \\ \hline Prior & \(0.22\pm 0.16\) & \(0.23\pm 0.22\) & \(0.12\pm 0.26\) \\ Post & \(0.22\pm 0.16\) & \(0.19\pm 0.19\) & \(52.87\pm 106.84\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: FR2 results for the estimated trajectories for 5G Positioning, NR5G-SAM, and LIO-SAM, including the average RMSEs and their standard deviations for the cases of prior and post LIO-SAM failure (in meters). Figure 10: Error distributions of the estimated trajectories for the FR2 setup at the point of LIO-SAM failure. mobility of the robot performing linear trajectories, instead of curved ones and having less rotations, as opposed to the area of the environment prior to LIO-SAM's failure (as shown in Figure 5). Again, LIO-SAM was not able to support the localization for the previously mentioned reasons and, hence, provided an error of 53.61 m, with a standard deviation of \(\pm\)107.49 m. The estimated trajectories for the FR2 setup can be seen on the bottom of Figure 8.  
As the result of the radio mapping process, individual maps have been generated and can be seen in Figure 11 and their 2D representation in Figure 12. Each map consists of the RSSI measurements, expanded to the additional cells of the grid using the UMa propagation equations. The measured signal strength is measured along the recorded trajectory. We observe in each individual map that values tend to increase as we approach nearer to a gNB station, which can provide us with proximity information and, hence, can be used to estimate positioning in the global reference frame. We can estimate the position based on the comparison between the measured RSSI and the estimated one using the UMa model. As can be seen in Figures 9b and 10, the cyan trajectory of the BEB poses is in general larger in error than the NRSG-SAM localization, but some measurements are more accurate over time, which we use for corrections. For the mapping pose estimates that have less covariance than the UE pose, we select the BEB pose estimate for position correction. During robot motion, we consider the pose as an additional factor in the graph. Figure 11: Individual Radio Environmental Maps created from the UMa Path Loss model using five gNB stations. The global 5G REM is the result of merging the individual \([rem_{1},rem_{2},\ldots,rem_{n}]\) maps. In the current stage of our work, we provide a representation of a unified grid map representation (as shown in Figure 13) consisting of an \(n=5\) sized vector for each cell.