Optimal Myopic Attacks on Nonlinear Estimation

Prior works have analyzed the security of estimation and control (E&C) for linear, time-invariant systems; however, there are few analyses of nonlinear systems despite their broad safety-critical use. We define two attack objectives on nonlinear E&C and illustrate that realizing the optimal attacks against the widely-adopted extended Kalman filter with industry-standard χ
²
anomaly detection is equivalent to solving convex quadratically-constrained quadratic programs. Although these require access to the true state of the system, we provide practical relaxations on the optimal attacks to allow for execution at runtime given a specified amount of attacker knowledge. We show that the difference between the optimal and relaxed attacks is bounded by the attacker knowledge.