# NR5G-SAM: A SLAM Framework for Field Robot Applications Based on 5G New Radio
## 3 Methodology
### Back-End Block (Beb)  
The BEB utilizes the generated real-time NR5G-SAM localization data from the FEB as an initial estimate for a GA optimization step. The GA then seeks to minimize the difference between the RSSI measured by the mobile robot and the estimated grid-based REM, generated using the UMa model. The RSSI vector consists of the individual power level measurements of each gNB and is formulated as Equation (14). It is then used as a reference for the GA to find the most suitable position within the global search space and within the bounds of radius \(R_{s}\) around the FEB estimation. This approach generates RSSI positioning similar to other interpolation methods, such as inverse distance weighting (IDW). It is important to note that larger values of \(R_{s}\) result in longer convergence times for the GA, which may lead to less frequent position estimates from the BEB. Conversely, a smaller \(R_{s}\) increases the dependence on the NR5G-SAM localization data from the FEB, which operates at the IMU frequency. Figure 4 exemplifies how RSSI measurements from a single gNoneB station vary while a robot traverses an environment, following the UMa path loss model. From both the RSSI measurements and the UMa model, we find the optimal position that minimizes error of the GA's fitness function. Specifically, we adopt the following path loss model, as per Equation (13) :  
\[PL=28.0+22*log10(d_{r})+20*log10(fc), \tag{13}\]  
for the LoS use case from [13], where \(d_{r}\) is the estimated range generated based on the RSSI acquired by the robot for each gNB and \(f_{c}\) is the carrier frequency in GHz set accordingly for the sub-6 GHz FR1 and the mmWave FR2 cases (see Section 4). Moreover, the RSSI positioning is coupled with IMU and the wheel velocity measurements within an EKF, using the same configuration as the UEB. This is a necessary step due to the nature of the RSSI measurements varying and being sensitive to the environmental conditions. This process reduces noisy estimations of the RSSI positioning and fuses the information to obtain a complete mapping pose estimate. In addition to providing a position estimation based on the RSSI values, the BEB is also responsible for performing a cellular 5G radio mapping, which is foreseen as a crucial component for the future implementation of a loop closure condition. This process involves mapping out the signal strength and coverage of a given area as the robot navigates. This is performed by storing the radio signal data of all available gNBs from different locations. These maps are commonly known as REMs and provide a representation of the signal power drop over the robot's environment, represented as a bi-dimensional grid map of RSSI values for each gNB. The **rem** grid map is formulated as Equation (15). The generated REMs are based on the 5G UMa model and represent the slopes of the received signal power indication levels paired along with a grid of positions in the surrounding area. The grid size can be set to a specific size, which in our case includes the wider application area including the gNB locations. A resolution threshold can be set according to a fixed distance ratio. A color coding scheme has been introduced for the grid map cells, which represents the degradation of the signal power due to propagation distance. The peaks observed represent the points where the base stations have maximum RSSI levels (i.e., where the gNBs are located). The following equations are the representation of the REMs based on the **rss** vector and the merged global map,which is indexed by position and has the world frame \(W\) as a common reference. \[\textbf{rss}=[\textit{rss}_{1},\textit{rss}_{2},\dots,\textit{rss}_{n}] \tag{14}\]  
\[\textbf{rem}_{i}^{W}=\sum_{i}^{k}[x_{i},y_{i},\textit{rss}_{i}] \tag{15}\]  
Figure 2 also presents a global 5G radio environmental map, which was created by overlaying the individual maps for each station. This global map can be computed as each local map is represented in the global frame of reference \(W\).