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Real-Time Sensor Anomaly Detection and Recovery in Connected Automated Vehicle Sensors
Yiyang Wang, Neda Masoud, Anahita Khojandi
TL;DR
CAV sensor anomaly detection must separate faults and attacks from legitimate changes while coping with noise, missing data, and delays. The paper combines delayed car-following dynamics, AEKF filtering, and OCSVM detection; experiments find better performance than the traditional χ2-detector, while larger delays worsen detection.
Problem
CAV anomaly detection must distinguish faulty or malicious sensor readings from legitimate network changes, noise, missing values, and communication delays.
Method
The method combines an adaptive extended Kalman filter with a delayed nonlinear car-following model and OCSVM anomaly detection using leading-vehicle information.
Results
OCSVM consistently outperforms the χ2-detector, the IDM observer improves performance by up to 23% over AEKF without IDM, and larger delays deteriorate detection performance.
Takeaways & Limitations
Using leading-vehicle information and OCSVM improves the reported real-time detection of anomalous sensor values compared with approaches without those components.
Takeaways & Limitations
The study simulates vehicle states and anomalies because suitable ACC datasets with anomalous CAV data are scarce, and assumes the leading-vehicle input is non-anomalous.
Abstract
from arXiv · showhide
In this paper we propose a novel observer-based method to improve the safety and security of connected and automated vehicle (CAV) transportation. The proposed method combines model-based signal filtering and anomaly detection methods. Specifically, we use adaptive extended Kalman filter (AEKF) to smooth sensor readings of a CAV based on a nonlinear car-following motion model. Under the assumption of a car-following model, the subject vehicle utilizes its leading vehicle's information to detect sensor anomalies by employing previously-trained One Class Support Vector Machine (OCSVM) models. This approach allows the AEKF to estimate the state of a vehicle not only based on the vehicle's location and speed, but also by taking into account the state of the surrounding traffic. A communication time delay factor is considered in the car-following model to make it more suitable for real-world applications. Our experiments show that compared with the AEKF with a traditional $χ^2$-detector, our proposed method achieves a better anomaly detection performance. We also demonstrate that a larger time delay factor has a negative impact on the overall detection performance.
I. INTRODUCTION
CAV sensor anomaly detection must distinguish faults and attacks from legitimate network changes, noise, missing values, and communication delays. The paper proposes combining an adaptive extended Kalman filter with a delayed car-following model and a data-driven detector using leading-vehicle information.
- Sensor anomalies can indicate faulty sensors or malicious attacks, so anomalous data must be detected and excluded from decision making.
- False negatives may let falsified data affect trajectory planning, while false positives may cause vehicles to discard legitimate abrupt changes such as downstream braking.
- Real-time CAV detectors must distinguish network changes from anomalies while handling sensor noise, communication delay, missing values, and vehicle resource constraints.
- The paper models five anomaly types—short, noise, bias, gradual drift, and miss—but does not explicitly account for miss, which may partially resemble short or bias.
- The proposed framework combines AEKF, a car-following model, and OCSVM to detect anomalies while accounting for delayed environmental observations.
II. RELATED WORK
Prior CAV anomaly-detection work includes model-based, learning-based, and other fault-diagnosis approaches, but the literature remains limited. This paper combines AEKF, leading-vehicle information, delayed dynamics, and OCSVM to detect and recover anomalous sensor readings.
- Existing anomaly-detection methods include observer-based fault detection, parity relations, and parameter-estimation approaches.
- CAV sensor anomalies may arise from sensor failures, environmental effects, hardware problems, or malicious attacks that inject false information.
- The paper addresses a scarcity of CAV anomaly-detection techniques despite the severe consequences of undetected sensor anomalies.
- The proposed observer-based method combines AEKF filtering with OCSVM learning and leading-vehicle information to detect anomalies and recover corrupt signals.
- Unlike the authors’ prior CNN framework, this study uses a single sensor’s readings, incorporates the leading vehicle’s state, and replaces the traditional χ2-detector with OCSVM.
III. METHODS
The method formulates a delayed nonlinear car-following state-space model and combines AEKF signal smoothing with OCSVM anomaly detection. It also compares OCSVM against a traditional χ2-detector.
- The method represents vehicle motion with a delayed car-following state-transition model and sensor sampling with a discrete measurement model.
- AEKF and OCSVM are combined for anomaly detection, with the traditional χ2-detector included for performance comparison.
A. Car-Following Model with Time Delay
The car-following model describes the subject vehicle’s response to its leading vehicle while incorporating perception-reaction delay. Its state-space formulation maps vehicle states and leader information into actionable motion decisions.
- The model uses subject-vehicle acceleration, speed, location, distance gap, and relative speed to describe car-following dynamics.
- The parameter τ represents perception-reaction time between a leading vehicle’s action and the subject vehicle’s response.
- The continuous state vector contains vehicle location and speed, which can be extended to include historical observations.
- The model maps the subject vehicle’s state and the leading vehicle’s location and speed into an actionable decision.
B. Continuous State-Discrete Measurement State-Space Model
The model represents vehicle motion with continuous state transitions and discrete sensor measurements while incorporating delayed inputs. Because nonzero delays break the Markov property, bounded-acceleration assumptions support an approximate delayed state-transition model.
- B. Continuous State-Discrete Measurement State-Space Model: The state-space formulation combines continuous vehicle dynamics with discrete sensor measurements and process and observation noise.The measurement interval is defined as Δt, and the approximation error is included in the process noise.
- B. Continuous State-Discrete Measurement State-Space Model: When τ = 0, the state-space model is Markovian and permits application of the adaptive extended Kalman filter.
- B. Continuous State-Discrete Measurement State-Space Model: For nonzero τ, delayed state dependence prevents direct AEKF application because the state derivative depends on multiple previous states.
- B. Continuous State-Discrete Measurement State-Space Model: Assuming bounded acceleration between amin and amax yields lower and upper bounds for approximating the delayed vehicle velocity.The bounds incorporate the delayed state and acceleration limits over the delay interval.
- B. Continuous State-Discrete Measurement State-Space Model: The resulting delay differential equation approximates the original delayed dynamics before producing a continuous-time, discrete-measurement transition model.
C. Adaptive Extended Kalman Filter with Fault Detector
The method combines AEKF state estimation with a fault detector, addressing unknown noise covariances and delayed, biased innovations. OCSVMs replace the traditional χ2 detector because model approximation and non-Gaussian effects can increase false decisions.
- C. Adaptive Extended Kalman Filter with Fault Detector: AEKF estimates unknown process- and measurement-noise covariance matrices using a moving window of residuals and forgetting factors.The moving window reduces covariance fluctuations but delays adaptation to system changes.
- C. Adaptive Extended Kalman Filter with Fault Detector: The EKF pipeline initializes state estimates, predicts the next state and covariance, and updates them using the new measurement.The innovation is defined as the difference between the measurement and its prediction.
- C. Adaptive Extended Kalman Filter with Fault Detector: Figure 1 illustrates a nonzero-mean normalized innovation sequence at τ = 0.5 second under a χ2-detector threshold σ = 2.5.
- C. Adaptive Extended Kalman Filter with Fault Detector: The χ2 detector requires zero-mean Gaussian innovations, but delay, imperfect modeling, and non-Gaussian noise can violate these conditions.Under such conditions, the detector may generate higher false-positive and false-negative rates.
- C. Adaptive Extended Kalman Filter with Fault Detector: The proposed detector uses OCSVMs to learn adaptive innovation boundaries because delayed model approximation can bias the innovation sequence.
D. One Class Support Vector Machine
The OCSVM component learns normal normalized-innovation behavior and selects among models with different false-positive parameters. Windowed innovation magnitude determines whether stricter or more permissive outlier detection is used.
- D. One Class Support Vector Machine: OCSVM learns a decision boundary enclosing at least 1 − p of normal training data, with p controlling the false-positive rate and outlier fraction.
- D. One Class Support Vector Machine: The method trains multiple OCSVM models with different p values and selects among them using the average normalized innovation over a time window.
- D. One Class Support Vector Machine: Small average normalized innovation triggers a larger-p model to detect smaller variations, whereas large innovation selects smaller p to avoid unnecessary dismissals.
- D. One Class Support Vector Machine: The innovation histogram from normal data estimates its distribution and calibrates p through the tail area controlled by γ.The tail represents drastic changes, while the center represents smooth changes.
- D. One Class Support Vector Machine: The complete algorithm combines AEKF smoothing with OCSVM detection and replaces anomalous measurements with predictions for subsequent estimation.
E. Anomaly Model
The anomaly dataset is constructed by injecting synthetic sensor anomalies into normal CAV trajectory data. The experiments cover short, noise, bias, and gradual-drift behaviors under randomized onset, duration, and sensor selection.
- E. Anomaly Model: Because no public anomalous CAV trajectory dataset is available, the study generates data by adding synthetic anomalies to normal trajectories.
- E. Anomaly Model: The experiments model four anomaly types: short, noise, bias, and gradual drift.
- E. Anomaly Model: Short anomalies are single Gaussian perturbations, noise anomalies are multi-sample Gaussian sequences, and bias anomalies are temporary offsets.
- E. Anomaly Model: Gradual drift is generated by scaling a sequence in either increasing or decreasing direction using a random sign.
- E. Anomaly Model: The models assume sensor-anomaly onset is independent and do not explicitly train on interdependent failures or systemic cyberattacks.
- E. Anomaly Model: Anomalies begin at randomized times, persist for randomized durations when applicable, and affect randomly selected sensors at a specified anomaly rate.
IV. CASE STUDY BASED ON THE INTELLIGENT DRIVER MODEL
The case study evaluates IDM-informed AEKF anomaly detection with χ2 and OCSVM detectors across anomaly settings and communication delays. The IDM observer and OCSVM improve detection, while increasing delay degrades performance.
- Model and data: The IDM model represents delayed car-following dynamics using parameters for acceleration, braking, desired speed, spacing, and reaction time.The case study uses the IDM model with time delay τ and specified city-traffic parameter values.
- Model and data: Synthetic following-vehicle states are generated from SPMD leading-vehicle speed data under an IDM car-following assumption.The study adds bounded random uncertainty and Gaussian white noise to the generated data.
- Experimental design: The evaluation varies the motion model, detector, anomaly magnitude, and delay, using AUC to assess detection performance.Three scenarios compare χ2 and OCSVM with or without the IDM motion model, while anomaly parameters are varied across settings.
- Results: Up to 23% improvement is achieved by the IDM observer-based method over AEKF without the IDM model across time delays.The reported comparison covers the tested anomaly settings and delay values.
- Results: OCSVM consistently achieves better fault-detection performance than the χ2 detector in the evaluated scenarios.The experiments compare χ2 without IDM, χ2 with IDM, and OCSVM with IDM.
- Results: Increasing the time delay from 0 to 0.5 and 1.5 seconds systematically deteriorates overall detection performance.Tables I–III report AUC values for these three delay settings.
V. CONCLUSION
The paper combines IDM-informed AEKF filtering with OCSVM anomaly detection to identify and recover anomalous CAV sensor readings using leading-vehicle information. Experiments show better detection than traditional χ2-based AEKF detection, while larger signal delays reduce performance.
- Conclusion: The proposed method combines an adaptive extended Kalman filter, the IDM car-following model, and OCSVM anomaly detection.The AEKF uses onboard and leading-vehicle information to filter readings and detect anomalous information.
- Conclusion: The combined OCSVM and IDM approach outperforms traditional χ2-detector-based anomaly detection with AEKF.The paper evaluates χ2 without IDM, χ2 with IDM, and OCSVM with IDM.
- Conclusion: Larger communication or sensor delays deteriorate overall anomaly-detection performance.The study identifies delay as a performance-limiting factor in the car-following model.
- Limitations: The study relies on simulated following-vehicle states and anomalous sensor values because suitable anomalous ACC datasets are scarce.The authors identify real ACC data collection and model calibration as directions for improvement.