# Amplitude Modeling of Specular Multipath Components for Robust Indoor Localization
## 7 Conclusions  
In this paper, radio environment maps (REMs) have been formulated, taking into account amplitude information of specular multipath components (SMCs) that are learned  
Figure 11: LLHF values obtained using (**a**) SALMA-light, (**b**) LHF+GPR with exact sigma. LLHF values at evaluation points are plotted with color code. The red circle denotes the estimation result, while the filled black circle denotes the true position.  
Figure 12: 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. Visibility test is carried out, followed by overlap checking, before implementing the algorithms.  
by means of Gaussian process regression (GPR). The regression method allows predicting the mean and variance of the SMC amplitudes. From these parameters, the position-error-bound (PEB) has been computed as a performance metric for positioning algorithms that exploit range information contained in the SMCs, so-called multipath-based localization schemes.  
The amplitude information can also be used to formulate REMs of communication performance metrics, e.g., the channel capacity or the bit-error rate, in order to realize more efficient and robust, location-aware protocols for medium access control. Using a set of training measurements from the environment, the REMs can be computed for any point within the environment. The paper evaluates to what extent the REM represents the multipath components in the analyzed data. It has been found that 50% to 90% of the received power can be attributed to the resolvable SMCs contained in our model, which corresponds to the fraction of power that can be predicted by the REM.  
The REM is applied in this paper to improve the robustness of a single-anchor multipath-based localization method which sometimes suffers from outliers resulting in large errors. Using the REM as a channel prior knowledge helps to avoid these outliers.  
Conceptualization, H.A.N. and K.W.; methodology, H.A.N. and K.W.; software, H.A.N.; validation, H.A.N.; formal analysis, H.A.N.; investigation, H.A.N.; resources, K.W.; writing--original draft preparation, H.A.N.; writing--review and editing, H.A.N. and K.W.; visualization, H.A.N.; supervision, V.K.N. and K.W. All authors have read and agreed to the published version of the manuscript.  
The research of K.W. was partly funded by TU Graz under the Lead Project \"Dependable Things\".  
Not applicable.  
The measurement data are available on request from the authors, c.f. [[https://www.spsc.tugraz.at/databases-and-tools/uwb-indoor-channel-experimental-data.html](https://www.spsc.tugraz.at/databases-and-tools/uwb-indoor-channel-experimental-data.html)]([https://www.spsc.tugraz.at/databases-and-tools/uwb-indoor-channel-experimental-data.html](https://www.spsc.tugraz.at/databases-and-tools/uwb-indoor-channel-experimental-data.html)).  
The authors declare no conflict of interest.