## 4 Results and Discussion
### Outlier Classification Analysis  
Figure 12 shows a required time for stabilized time synchronization when \(l\) was set as 100. It was estimated that about 20 s was required to achieve stabilized synchronization. One thing to note when using the method proposed in this study is that there is a certain amount of waiting time for synchronization. The communication delay was confirmed to have a round-trip delay of 52 ms when conducted with a general ping test, which is about twice the size of the average communication delay of 29.3 ms measured in this experiment (Figure 12). Figure 13 shows an estimated instant coverage interval when \(l\) was set as 100. Since the method proposed in this study uses time synchronization using GPS, a certain amount of time is required to achieve time synchronization, and, in the experiment, stable communication time comparison was possible after about 20 s (Figure 13). Meanwhile, among the systems used in the experiment, the NTP-based time synchronization method using Chrony can set various offsets and synchronization cycles, so faster synchronization times can be expected by adjusting the settings based on the measurement environment. Figure 14 shows the comparison of instant coverage interval and estimated mean values of each Gaussian component. Communication delay occurs as a complex condition and cannot escape the fundamental limitations of wireless communication. Regardless of the quality of wireless communication itself, the quality may deteriorate due to the momentary influence of the branch communication network. This is not only difficult  
Figure 12: Required time analysis for stabilized time synchronization when \(l\) is set as 100. Figure 13: Estimated instant coverage interval when \(l\) is set as 100, showing that the overall mean value of the estimated first Gaussian is 29.36 ms.  
to predict, but there is little basis for modeling it. Therefore, in this study, a dynamic judgment criterion using a probability-based coverage interval was used to adaptively design an instantaneous communication delay outlier (23). The area with a coverage interval of 5.16 \(\sigma\) from the estimated average value of the first Gaussian was assumed to be an acceptable communication delay zone, and samples outside that area were defined as outliers (Figure 14). Figure 15 shows the result of the detected outlier based on the estimated communication delay outlier. Note that the detected red circles denote the detected erroneous mean value of the second Gaussian component, which is the latent moment of the communication delay outlier, which is dominant at that instant. As a result, it was possible to capture moments that may include communication delay outliers, and the resolution was determined depending on the sample interval \(l\) set in advance (Figure 15). One thing to note is that the moments captured here are sections where outliers exist based on the sample interval, and the entire sample is not treated as a communication outlier. Therefore, it is necessary to design the sample interval to suit the needs, and, if the sample interval is overestimated or less discrete than necessary, a decrease in performance is expected. Figure 16 shows the total communication delay analysis based on the estimated coverage interval where the red markers represent the detected outlier delay samples among the total measured \(T_{\text{c}}\). Among the total measured communication delay samples \(T_{\text{c}}\), the communication delay outlier was distinguished (Figure 16). The communication delay  
Figure 14: Comparison of instant coverage interval when \(l\) is set as 100 and estimated mean values of each Gaussian component. Figure 15: Result of detected outlier based on the estimated communication delay outlier. outlier detected in this way is greatly affected by the coverage interval, and the sensitivity can be adjusted by adjusting the \(\alpha\) value (23).