# Amplitude Modeling of Specular Multipath Components for Robust Indoor Localization
## 6 Result  
To implement the GPR-based positioning algorithm, the data described in Section 3 is divided into two groups. The first group is used for GP training, in which both the agent positions and the corresponding CIRs are known. The GPM hyper-parameters are estimated. The second group contains the remaining data, where only the CIRs are used. The corresponding agent positions are unknown and will be estimated by exploiting the REM, i.e., the SMC amplitudes and SINRs predicted using the GPM hyper-parameters. Errors are computed and their CDFs are plotted in Figure 10. SALMA-light [54; 55], the reference single-anchor localization method described in Section 5, is used for comparison.  
It is shown that, with situational awareness through the REM information, the proposed algorithm outperforms SALMA-light in terms of the outlier robustness, while the accuracy remains comparable.  
To explain this performance improvement, Figure 11 compares the LLHF for the two algorithms. The LLHF has been evaluated at candidate positions lying on a radius that corresponds to the estimated line-of-sight distance [55]. It is shown that the REM-assisted algorithm reduces the number of local maxima in the LLHF and emphasizes the correct maximum, yielding the performance improvement over SALMA-light.  
Figure 12 shows the error CDF for a modified experiment, where a visibility test and overlap checking are conducted to reduce the number of SMCs that are used for position estimation to the most useful ones. This is done for both, SALMA-light and the proposed algorithm. It is shown that again the proposed algorithm outperforms SALMA-light in reducing outliers. The difference in results between Figures 10 and 12 is because, after visibility test and overlap checking, the number of VAs used is reduced, leading to reduced  
Figure 10: CDF of the localization error using (**a**) training segments 1, 2, 3, 7, (**b**) training segments 4, 5, 6. The blue solid line plots the error CDF obtained when SALMA-light is used. The orange solid line plots the error CDF obtained when optimizing the LLHF with prior knowledge from GPR. The phase \(\zeta_{k}\) is approximated by using the phase from CIR. Overlap checking is performed first before implementing the algorithms.  
robustness for SALMA light while the use of the REM avoids such loss of robustness. Note that also the accuracy is improved in this variant.  
These results suggest that the proposed algorithm might perform better in obstructed-LOS or in the presence of humans or obstacles, even though the algorithm has not been tailored to specifically address this problem. The recent publications [57; 58] describe algorithms that are designed to be robust to blocked LOS (in the former) and blocked SMCs (in the latter), in particular when the blocking is due to the influence of the human body on the visibility of SMCs. The belief propagation SLAM algorithm from [38] provides visibility information of SMCs in addition to the amplitude and delay information. This visibility information can be used to pre-select the data points for the construction of the GPR-based REM such that path blocking does not influence the quality of the REM. It is expected that the \"environment part\" of the propagation channel, which is expressed by the GPR-based REM, and the \"device part\" can be separated very well, once a consistent REM has been learned from a large number of independent measurements obtained from different user equipment. The rigorous formulation of such methods is left for future work, however.