Attack-Aware Intrusion Risk Monitoring for Aerial Surveillance via Probabilistic Signal Temporal Logic

Abstract

This paper considers online intrusion-risk assessment and graded warning for unmanned aerial vehicles under bounded measurement attacks. To address this problem, we develop a monitoring framework that combines trusted state estimation, attack-aware risk assessment, and probabilistic signal temporal logic (PrSTL). Trusted observations support recursive state estimation, while potentially attacked observations inform integrity testing and intrusion-risk assessment. The key contribution is a confidence-set construction that combines normalized innovation statistics with physical attack bounds to characterize admissible measurement biases. The resulting family of bias-corrected Gaussian posteriors yields an upper bound on the probability of occupying a no-fly zone or its surrounding safety margin. Confidence guarantees and finite-cover numerical certificates quantify the reliability of this risk envelope, which is evaluated with or without an integrity alarm. The PrSTL monitor analyzes the resulting risk sequence to distinguish ordered, persistent, and repeated risk and produces graded warnings with explicit robustness margins and supporting windows. We validate the monitor in flight experiments with a Crazyflie quadrotor tracked by a Vicon motion capture system. Controlled comparisons quantify the contributions of individual monitoring components. Prescribed risk profiles verify the temporal semantics and illustrate how distinct risk patterns produce different warning levels.