# Hybrid Approach for Indoor Localization Using Received Signal Strength of Dual-Band Wi-Fi
## 6 Performance Evaluation
### Analysis of the Ranging Accuracy  
Several existing ranging methods were used as benchmarks to verify the effectiveness of the proposed method. Most previous RSS based ranging method used a single-band RSS, To analyze the effect of using dual-band RSS, benchmarks 1 and 2 were set as a rule-based raging method using only RSS in the 2.4 and 5.2 GHz bands, respectively. These were based on a two-slope PLM as described in (2) that has been widely used in existing studies. The PLM parameters for each frequency band were optimized with linear regression to best fit the training data. For a single RSS measurement, the distance can be estimated by PLM inversion as presented in (4). The ranging accuracy of these methods can be affected by the accuracy of the PLM models. To consider more complex PLM, benchmarks 4 and 5 used a non-linear regression model using a neural network for single-band RSS data. Similar to the proposed method, deep regression models were learned using the only RSS in the 2.4 and 5.2 GHz bands. The benchmark 3 is the result of an existing rule-based ranging algorithm that uses the dual-band RSS described in [34]. In the ranging method of Benchmark 3, the channel states were divided into LOS, NLOS, and severe NLOS, and the path-loss exponents were different for each state. The parameters of this rule-based methods were also optimized to best fit the training data. In Figure 8, the results of benchmarks 1 and 2, which use the regression methods based on the two-slope PLM, are represented by black lines, and the regression model  
Figure 6: RSS map for an AP in the 2.4 GHz band. Figure 7: RSS map for an AP in the 5.2 GHz band. based on the neural network is expressed in green lines. The results in Figure 8b,c show the limitations of the ranging method using a single-band RSS. As only one distance is mapped to one RSS value, the NLOS conditions cannot be distinguished. The regression results of the two-slope PLM and the results of the neural network are similar when using the single-band RSS. The ranging method using a neural network shows an improvement in ranging accuracy. However, there is an upper limit for the ranging method using the single-band RSS, regardless of how detailed the tuning applied is. Figure 8d shows the ranging results of the existing rule-based ranging method using the dual-band RSS. In this method, two or more distances may correspond to the RSS value of one band. The distance can be estimated by classifying the NLOS conditions, but reflecting all of the various cases shown in (a) is difficult. In addition, because only the path-loss exponent is adjusted to estimate the distance for the NLOS conditions, there is a risk of amplifying the ranging error for misclassified cases. The regression results of the proposed model are shown in Figure 9. The NLOS conditions were divided into several stages by using the dual-band RSS input. This reflects the severe NLOS conditions, especially when there are multiple walls between antennas. The deep regression model was trained using data from various cases. Therefore, it describes the ground truth of the test data better than the other rule-based models. In the performance evaluation, the number of nodes in the hidden block was set to 64, and the number of hidden blocks was set to 10. Figure 10 shows the empirical cumulative distribution function (ECDF) of the ranging errors according to the ranging methods. The key indicators of the results are summarized in Table 1. In terms of the error between the estimated distance and the actual distance, the proposed method showed the best performance with a median error of 1.49 m. This is approximately 36.1% lower than those of the benchmark techniques. The benchmark results using the single-band RSS showed similar performances. This is because there is a limit to the information that can be obtained from the single-band RSS. The results of  
Figure 8: (**a**) Distance–RSS data of the ground truth, and the regression results of the (**b**) 2.4 GHz, (**c**) 5.2 GHz, and (**d**) dual-band frequencies.