## 5 Simulation Results and Discussion  
The performance of the outlier detection methods presented in Section 3 is determined and compared using an online RSS dataset available in [40]. The dataset is made up of LTE RSS power measurements taken with an LTE-enabled mobile device at a fixed reference location. Measurements were taken between the hours of 7:30 a.m. and 11:00 p.m. at 30 min intervals for 30 days, resulting in approximately 32 RSS observations per day and 960 RSS observations for the entire months. Only eight RSS datasets from eight different days have 100% RSS observations, i.e., no missing measurements, and these eight RSS datasets will be used for the analysis. Figure 1 shows the time-series RSS distribution for each dataset. Looking at the distribution of each RSS observation in Figure 1, we can see that the time-series RSS observations lack a Gaussian distribution and are thus asymmetrical. This means that detecting outliers in these datasets using the Z-score method with MAD as a scale estimator will be inefficient. The \(\gamma\), as mentioned earlier, is the Z-score threshold value above which an RSS observation is considered to be an outlier. The total number of RSS observations in each dataset considered an outlier is determined and presented in Figure 2 using each of the techniques presented in Section 3 and by varying \(\gamma\) from 0.5 to 5 at a step of 0.5. Figure 2 shows that for all eight RSS datasets, the Z-score method based on the \(S_{n}\) scale estimator detects fewer outliers than the Z-score method based on the MAD scale estimator. Detecting more or fewer outliers is insufficient to determine an outlier detection method's performance. A comparison of the gross error sensitivity of the \(S_{n}\) and MAD scale estimators, on the other hand, reveals that the MAD scale estimator has a higher gross error sensitivity, making it more likely to detect an outlier falsely. This could be the reason why the Z-score method based on the MAD scale estimator detected a higher number of outliers. Further analysis of the outlier detection performance is performed with \(\gamma=1.28\), which is considered the optimum Z-score threshold value to detect an outlier as presented in [28]. Figures 3-10 compare the outlier detection performance of the two scale estimators at \(\gamma=1.28\). Figure 1: RSS Dataset distribution: (**a**) RSS observation 1, (**b**) RSS observation 2, (**c**) RSS observation 3, (**d**) RSS observation 4, (**e**) RSS observation 5, (**f**) RSS observation 6, (**g**) RSS observation 7, and (**h**) RSS observation 8. Figure 3: RSS outlier detection comparison for RSS Dataset 1. (**a**) \(S_{n}\) scale estimator, and (**b**) MAD scale estimator. Figure 2: Number of detected RSS outliers for different \(\gamma\) values: (**a**) RSS observation 1, (**b**) RSS observation 2, (**c**) RSS observation 3, (**d**) RSS observation 4, (**e**) RSS observation 5, (**f**) RSS observation 6, (**g**) RSS observation 7, and (**h**) RSS observation 8. Figure 4: RSS outlier detection comparison for RSS Dataset 2. (a) \(S_{n}\) scale estimator, and (b) MAD scale estimator. Figure 5: RSS outlier detection comparison for RSS Dataset 3. (a) \(S_{n}\) scale estimator, and (b) MAD scale estimator. Figure 6: RSS outlier detection comparison for RSS Dataset 4. (a) \(S_{n}\) scale estimator, and (b) MAD scale estimator. Figure 8: RSS outlier detection comparison for RSS Dataset 6. (**a**) \(S_{n}\) scale estimator, and (**b**) MAD scale estimator. Figure 7: RSS outlier detection comparison for RSS Dataset 5. (**a**) \(S_{n}\) scale estimator, and (**b**) MAD scale estimator. Figure 9: RSS outlier detection comparison for RSS Dataset 7. (**a**) \(S_{n}\) scale estimator, and (**b**) MAD scale estimator. Looking at the distribution of RSS observations for each dataset, it is possible that very few, if any, of the RSS observations could be considered outliers. Both methods identified some RSS observations as outliers.