Covert Vehicle Misguidance and Its Detection: A Hypothesis Testing Game over Continuous-Time Dynamics
Takashi Tanaka, Kenji Sawada, Yohei Watanabe, Mitsugu Iwamoto
TL;DR
This work models covert vehicle misguidance as a continuous-time stochastic zero-sum game between an attacker inserting a constant drift and a detector performing a likelihood-ratio test on the trajectory. Using Girsanov’s theorem and the generalized Neyman–Pearson lemma, it establishes a unique saddle point: a constant bias attack $\theta^*(t)=\bar{\theta}$ and a detector $\phi^*(x)$ that depends only on the terminal state, with an explicit expression for the minimal misdetection probability. The paper derives the first- and second-order exponents of the Type II error as horizon $T$ grows, linking the first-order rate to a relative-entropy term and providing finite-horizon refinements. It also shows that allowing adversarial feedback disrupts the saddle point and discusses extensions to higher-dimensional/nonlinear settings and non-asymptotic analysis, highlighting implications for robust attack detection in continuous-time systems.
Abstract
We formulate a stochastic zero-sum game over continuous-time dynamics to analyze the competition between the attacker, who tries to covertly misguide the vehicle to an unsafe region, versus the detector, who tries to detect the attack signal based on the observed trajectory of the vehicle. Based on Girsanov's theorem and the generalized Neyman-Pearson lemma, we show that a constant bias injection attack as the attacker's strategy and a likelihood ratio test as the detector's strategy constitute the unique saddle point of the game. We also derive the first-order and the second-order exponents of the type II error as a function of the data length.