## 5 Obtained Results and Evaluation
### Simulation-Based Positioning Accuracy  
First, noiseless elevation and azimuth AoA with respect to the mmWave AP together with the RSSI (at the robot) without shadow fading are plotted in Figure 6 for the comparison with the acquired experimental results, as will be shown in the next subsection. Specifically, the robot trajectory is divided into three segments, which are marked with different colors: first, the robot remains static in the light green region performing operational system initialization. Thereafter, it moves toward the office entrance (the light red region), where the robot makes a turn (black dashed line), and drives inside the office (toward the NLoS region w.r.t. the mmWave AP, i.e., the light blue region). On its way into the office, the robot passes the LoS-NLoS border, where the RSSI value significantly drops. The positioning accuracy via a numerical simulation shown in Figure 7 is characterized by the 2D root mean square error (RMSE) and the corresponding cdf of the 2D positioning error along the considered robot track within the LoS region (see the red curve in Figure 3b). Further, the applied parameters of the simulation are summarized in Table 3, where the utilized pathloss model refers to the 3 gpp indoor hotspot (InH)-office LoS scenario. In our simulation campaign, the Cramer-Rao lower bound (CRLB)-based LRMs ([33] Ch. 3), i.e., the elevation and azimuth AoA measurements based on the RSSI (see Figure 6a) are generated according to the methods in [35], which are then utilized as the input LRMs (\(\hat{\varphi},\hat{\theta}\)) of Algorithm 1 to obtain the corresponding theoretical accuracy in Figure 7. It is worth pointing out that, in Figure 7a, the positioning performance gradually becomes better in the light red region before the turning point, this is due to the fact that  
Figure 5: Procedures of the proposed LHO scheme. the robot is moving towards the mmWave AP, the RSSI level becomes higher (as shown in Figure 6a) which leads to more accurate AoA measurements that yields lower positioning errors. The array orientation measurement \(\hat{\alpha}\) is assumed to be corrupted by an un-biased Gaussian error with the standard deviation of \(\sigma_{\alpha}\) that is set to two different values in the simulation campaign. Specifically, the curves in Figure 7 manifest the difference in terms of the obtained positioning accuracy at two different orientation error statistics (\(\sigma_{\alpha}=0.1^{\circ}\)or \(5^{\circ}\)[51]), which reflects the impact to the LRMs that stems from the stable or coarse orientation measurements obtained from a six-axis sensor on the robot. As it is observed in Figure 7, the positioning accuracy by GBP is generally higher for a smaller orientation error statistics \(\sigma_{\alpha}\), as well as when the robot approaches the mmWave AP owing to the fact that for a given AoA measurement error, the robot suffers a smaller positioning error when it is closer to the mmWave AP. In other words, the AoA measurement error is translated into a larger/smaller positioning error at a larger/smaller UE-AP distance. It is also worth noting that the RMSE curve stops when the robot enters the NLoS region, thus indicating the fact that the communication with the mmWave AP is discontinued when the LoS is blocked. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Carrier frequency & 60.5 GHz \\ Signal bandwidth & 2.16 GHz \\ Transmit power @ AP * & 21.64 dBm \\ Max. array gain @ AP * & 13.48 dBi \\ Max. array gain @ robot & 13.48 dBi \\ Robot update interval & 0.5 s \\ Pathloss model & InH-office [52] \\ Fast fading model & Rician distribution \\ \hline \hline \end{tabular}  
* The “AP”s mentioned in the table refer to the mmWave AP rather than WiFi since the simulation is carried out to model the communication between the mmWave AP and the robot.  
\end{table} 
Table 3: Utilized simulation parameters. Figure 6: Simulation-based numerical characterization as a function of time along the simulated robot trajectory (see Figure 3b).