## 2 Challenges and Methodology
### Problems by Data Analysis  
In the model-based fault detection, a common approach to carrying out the residual generation is to use a state-observer as mentioned above. In particular, a well-known Kalman filter is commonly used in a linear system and is capable of estimating states by inferring information about states through dynamics and modeling of a physical system [5; 24; 25; 26]. This model-based method assumes that if the physical system is in a normal state, the values of the residuals are zero. If not, they have non-zero values. In practice, due to model uncertainty and environment uncertainty including disturbances and noise, the residual does not get perfectly zero even in a normal state. In this regard, the residual is often considered as a quantitative measure of uncertainty. Although this residual generation filter is well-suited to a stochastic environment where noise should be considered, it accumulates the filtering and modeling errors over time because the generated residual is fed back into this filter. This is why the threshold is required for responding to uncertainty. Many studies mainly focus on developing an adaptive threshold generator to reduce the modeling uncertainties or to enhance sensitivity by minimizing the residual [10; 14; 17]. In fact, they do not deal with the modeling uncertainties directly since the distribution of modeling errors is unknown. Furthermore, the effect of the modeling uncertainties on the system response is not well captured by model parameters describing a physical system. Although they just employ a classic way that predicts the quantity of uncertainties with a probability distribution, the common assumption of the distribution for uncertainties is far from the real world due to both nonlinearity and complexity of the physical system in the autonomous CPS. In this paper, the operation-varying threshold to be developed can be referred to as an adaptive threshold (AT) in order to distinguish it from the time-varying dynamic threshold. The adaptive threshold is critical in terms of both the adaptability to provide the robustness for automotive CPS and the sensitivity to accurately detect critical faults in the presence of anomalies. We identify a problem with respect to sensitivity and adaptability through the following simple experiment in detail. We exploit an unmanned ground vehicle (UGV) called Jackal as a target system [27]. A new adaptive cruise control (ACC) function is implemented in the target system. The operation of the physical systems can change with time while ACC driving. For the sake of simplicity, we assume that our target system performs uniform linear motion, as the Jackal UGV continues to move on a straight line with a constant velocity. During the ACC operation, states of the moving physical system might not depend on dynamics and be linear during a certain period. Figure 1 shows the real variables measured from a left encoder of the Jackal UGV. Although it drives on a straight line in a normal situation without any major fault of the sensors, we observe many anomalies for about 50 s. In other words, due to the environment uncertainty, we can see that there are frequently sensed data with noise while driving but they only show a small difference from the normal data. In the existing model-based detection applied to the Jackal UGV, after the residual is generated using these measurements as shown in Figure 1, the difference between the magnitudes of them are examined only with the fixed threshold. The cyber system, therefore, concludes that the target system may go into the abnormal state as some faults of the encoder are detected, even though Jackal is actually in a normal state. It is no wonder that a false positive rate related to these anomalies could increase dramatically over time. This is because the fixed threshold does not respond to a changing environment where some anomalies occur naturally with uncertainty while driving.