## 4 Performance Evaluation
### Constant Faults
This result seems to be due to the high value of the second threshold \(\sigma^{v}\) which may cause an increase in FN. Regardless of velocities, as the duration and intensity are shorter (\(\delta=5\) and 10) and smaller (\(\eta_{0}=1.5\) and 2) respectively, the RT has better performance. From these results, we find out that RT is sensitive to small changes. However, if the intensity is higher, both the TPs and FPs increase at the same time while the TNs decreases. This fact is again evident from plotting the precision. Figure 5 shows the recall presenting the relationship between TPs and FNs. As mentioned above, because our adaptive thresholds are designed for the safety-critical application, achieving the low false  
Figure 4: Accuracy according to each intensity as a function of constant fault duration: (**a**) Cumulative sum of the accuracy at 0.7 m/s of Jackal unmanned ground vehicle (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. negatives is very important. Since the magnitude of the constant faults injected is not large, FNs tends to increase in all thresholds as the duration decreases. In other words, such data are actually the faults although they are identified in the normal state. Especially, RT has a significantly higher FNs and fewer TPs when the duration and the intensity are shorter and smaller, respectively, resulting in no recall or very low recall. In the case of KT, since FNs is much higher in short fault duration (\(\delta=5\) and 10) than in large duration even though the velocity increases, its recall performance is poor. This is because the shorter duration never helps determine the anomalous region by the first threshold of KT. In AT, as the duration increases, the data to be faults within the particular anomalous region increases in the number and the detection is performed well by the second low threshold, which is more sophisticated than that of KT. As the velocity increases, the AT performance becomes more distinct because the proposed optimal thresholds are adapted well to the high uncertainty in the driving environment where the data variation is high. Only at the recall at 0.7 m/s and \(\delta=5\), the recall appears low since the FNs of AT is a little larger than those of KT. This seems to be due to the wide normal region because the first threshold of AT is slightly larger than that of KT when its velocity is the slowest. The precision with regard to false positives is shown in Figure 6. Both AT and KT which show 0% of the FP rate for all velocities conduct the elaborate detection of faults from the anomalous region. As mentioned earlier, in the case of RT, both FPs and TPs are increased at the same time as the intensity is larger and the duration is longer. On the contrary to this, RT does not respond to the small changes to which the intensity and duration are applied with the low values. Figure 5: Recall according to each intensity as a function of constant fault duration: (**a**) Cumulative sum of the recall at 0.7 m/s of Jackal UGV; (**b**) Cumulative sum of the recall at 1.0 m/s; (**c**) Cumulative sum of the recall at 1.3 m/s; (**d**) Cumulative sum of the recall at 1.6 m/s.