## 6 RSS Difference-Aware Graph-Based Semi-Supervised Learning RSS Smoothing Method
### Experimental Results  
In order to verify our method, we collected RSS data from the 4 th floor of the Bahen Building at the University of Toronto. The radio map was constructed using a step-counter-assisted RSS measurement method. Sensor information from the accelerometer is used to estimate the distance between the RPs. Using this system, a radio map consisting of 251 RPs throughout the entire 4 th floor of the Bahen building has been created in less than 30 minutes. However, the resulting radio map has only 5 RSS measurements at each RP. Consequently, it is more error-prone compared to the traditionally generated radio maps in which for each RP hundreds of measurements are collected. The Proposed localization procedure is tested on a sequence of 35 test points collected on a path from Room 4000 (top of Figure 9) to Room 4148 (bottom of Figure 9). The RSS values from a single AP in the original radio map and the test points are shown in Figures 10a and 11a respectively. As can be seen, although the RSS values are generally consistent with the signal propagation model, there are some large fluctuations at some RPs. To eliminate the negative effects caused by this fluctuation, the proposed RG-SSL method is applied to smooth the RSS values. In order to obtain more accurate results, 125 unlabelled data throughout the whole 4 th floor of the Bahen Building are considered. Following steps are repeated until all the labelled points are smoothed:  
As comparisons, the G-SSL method, SCTW method and SPORT method are also simulated in this paper. The simulation results are shown in Figures 10 and 11. From Figures 10b and 11b we can see that the RG-SSL method successfully smooths out the radio map and the effect of signal fluctuation is mitigated. Because most of the information in the radio map is abandoned in the SCTW algorithm, it cannot achieve the optimal result. In the SPORT algorithm, due to the variability of the parameters in the signal propagation model, we can obtain suboptimal solution of the RSS values rather than the best results. In the G-SSL algorithm, all the collected RSS values are used to correct the outliers, which leads to a better result. Furthermore, the RSS difference between different locations is used to improve the G-SSL method and the estimated RSS values are more accurate. As a result, although the radio map and the online RSS values are also smoothed by the other algorithms, the errors are larger than that in Figures 10b and 11b, especially in the upper part of the corridor. The increasing errors in RSS values in the radio map and the online data will inevitably result in the increased localization errors. The localization result from directly using the original radio map and test point data are shown in Figure 12a. Compared with the actual locations in Figure 9, there are some significant errors in the localization results as certain distinct test points have been localized erroneously to a single location. The localization result using the modified radio map can be seen in Figure 12b-e. We see that the localization results are improved compared to the results in Figure 12a. Most of the test points were erroneously localized to one location in Figure 12a are now localized to correct distinct locations. These incorrect estimates were causing a large amount of localization error in the original method however are greatly reduced using both the RG-SSL method and the other methods. Clearly, the localization results of the proposed RG-SSL method are closer to actual locations than the results calculated by the other methods. Furthermore, the trajectory obtained in Figure 12b is clearly smoother than those in Figure 12c-e.  
Figure 11: Comparison of signal distribution of test data. (**a**) Original radio map (**b**) RG-SSL method (**c**) G-SSL method (**d**) SCTW method (**e**) SPORT method.