Covert Vehicle Misguidance and Its Detection: A Hypothesis Testing Game over Continuous-Time Dynamics

TL;DR

This paper models a continuous-time stochastic game between an attacker aiming to covertly mislead a vehicle and a detector trying to identify such attacks, deriving optimal strategies and error exponents.

Contribution

It introduces a novel game-theoretic framework for vehicle attack detection using stochastic calculus and derives optimal attack and detection strategies.

Findings

Constant bias injection is the optimal attack strategy.

Likelihood ratio test is the optimal detection method.

Derived error exponents quantify detection performance.

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.