## 4 Performance Evaluation
### Noise Faults  
In our experiment, injecting noise faults aims to assess the detectability under Additive Gaussian white noise (AGWN) that is most common in communication systems and can occur in nature. This fault is generated by adding the one value drawn from in a zero-mean normal distribution with a given variance to the magnitude of the original data at each velocity. The performance can be bound to vary on the given variance, but for the purpose of noise faults involved in these experiments,  
Figure 9: Precision according to each duration as a function of random fault intensity: (**a**) Cumulative sum of the precision at 0.7 m/s of Jackal UGV; (**b**) Cumulative sum of the precision at 1.0 m/s; (**c**) Cumulative sum of the precision at 1.3 m/s; (**d**) Cumulative sum of the precision at 1.6 m/s. the variance is fixed at one. The duration variation is the same as that of the constant and random faults. The magnitude of noise faults is determined by:  
\[\mu=\mu_{r}+(\gamma\times\eta_{0}), \tag{12}\]  
where \(\gamma\) is a random number drawn from the standard normal distribution, and \(\eta_{0}\) is one of the intensity of \(\eta=\{0.5,1.5,3\}\). This intensity used is quite different from those of the random faults and was already used in the research of [PERSON] et al. [25]. From Equation (12), when \(\eta_{0}=0.5\) is applied, the noise faults with one value in the range of \([\mu_{r},\mu_{r}+m\times 2]\) are generated by about 0% of the total noise faults where \(m\) is the mean value of the training data at the certain velocity, and them in the range of \([\mu_{r}+m\times 3,\mu_{r}+m\times 4]\) account for about 100%. Note that the magnitude of noise faults is much larger than that of random faults. Figure 10 shows the detection accuracy of the three thresholds for noise faults. For all velocities, AT has the precision of 100% and is not affected by the duration and intensity. KT shows that its performance is mainly low at the shortest duration and the lowest intensity for all velocity when it is compared to other conditions. From these results, we discovery that KT is less sensitive to the trivial noise. Although KT has the worst performance at 1.3 m/s for the noise faults, the performance of the noise faults is increased slightly more than that of random faults. In the case of RT, the accuracy is better when the intensity is smaller and the duration is shorter. However, it can be predicted that many FPs can occur since it responds sensitively to small changes. This remark can be seen in the graph of precision. In Figure 11, we present the results of recall at each velocity. We can see that in AT, no FN has occurred for all velocities. In the case of KT of 0.7 m/s, the FNs occur unconditionally when the duration is 5 for all of the intensities. Even as the velocity increases, the sensitivity to small changes is still low when the duration is short. It indicates that KT is not capable of responding to the very short occurrence of noise. In KT, the levels of intensity have little effect on the noise fault detection since the magnitude of the noise faults is already too large as mention above. As with other faults, the recall of KT is the worst at 1.3 m/s, and FNs increases at both \(\delta=5\) and 10 regardless of the intensity, since the lower first and the high second thresholds influ  
Figure 10: Accuracy according to each duration as a function of noise fault intensity: **(a)** Cumulative sum of the accuracy at 0.7 m/s of Jackal UGV; **(b)** Cumulative sum of the accuracy at 1.0 m/s; **(c)** Cumulative sum of the accuracy at 1.3 m/s; **(d)** Cumulative sum of the accuracy at 1.6 m/s. In case of RT, the recall is better than that of KT at 0.7 m/s and is comparable to that of KT except for 0.7 m/s when the intensity is high (\(\eta_{0}=1.5\)and3). From this graph, we can find that RT has the ability to detect faults better than KT in the case of noise with a magnitude of a certain level (\(\eta_{0}\geq 1.5\)). Figure 12 depicts the results of precision.