## 4 Results and Discussion
### Teleoperation Command Signal Analysis  
Figure 17 presents a comprehensive depiction of the teleoperation signal concerning the steering angle. Notably, given the prescribed course of the test site, which entails a consistent right rotation direction, a discernible bias towards positive values is evident in the overall distribution of steering angles. Additionally, the application of the predictor-based approach (denoted as 'Pred') is noteworthy, as it appears to effectively alleviate the impact of signal delay on the received steering angle. It should be noted that the parameter \(\lambda\) was tuned using \(0.3\lambda_{\text{max}}\), where \(\lambda_{\text{max}}(T_{\text{c}}(t))=3/(2\tilde{T}_{\text{c}}(t))\)[6].  
The probability density histogram of the estimated error between the non-delayed signal and the predictor-based approach with a delayed signal is illustrated in Figure 18. It  
Figure 16: Total communication delay analysis based on the estimated coverage interval.  
Figure 17: Overall teleoperation signal of sent steering angle comparing non-delayed signal, delayed signal, and predicted signal.  
is imperative to note that, due to disparate timestamps between the non-delayed signal and the delayed signals, a linear interpolation was employed for both delayed signals to facilitate the estimation of errors vis-a-vis the non-delayed signal. From the analysis, it may look like the error deviation of the delayed signal surpasses that of the predictor-based approach; however, the result of the computed standard deviations rather shows that the predictor-based approach (std.Predictor: 3.544) was higher than the delayed signal (std.Delayed: 0.077).  
As previously indicated, Figure 19 demonstrates that the predictor-based approach exhibits a higher count of erroneous samples in comparison to delayed signal samples. This observation implies that the predictor-based approach may be vulnerable to extreme scenarios where communication delay outliers coexist. Therefore, by using (26), the effect of communication outliers was suppressed, as shown in Figure 20. In Figure 20, the occurrence of a communication outlier is marked with an asterisk (*), illustrating the behavior of the original predictor-based approach under such circumstances. Specifically, when encountering communication delay outliers, it was observed that the sudden increase in communication delay resulted in an over/underestimation of the derivative of the predicted states. On the other hand, employing the proposed method within the outlier compensation predictor-based framework led to a notable decrease in the effect of the outlier because the derivative of the predicted state was not updated.  
Figure 19: Probability density histogram showing that the predictor-based approach contains more erroneous samples.  
Figure 18: Comparison of error between the non-delayed signal and predictor-based approach with the delayed signal, where rdiff is a comparison of the delayed signal, and pdiff is a comparison of the predictor-based approach.  
Figure 21 shows a comparison of the estimated error between each method and non-delayed signal samples. As a result of implementing the proposed method to reduce the effect of the communication delay outlier, the mean error and the deviations decreased, as shown in Table 1.