Secure estimation against complex-valued attacks

Arash Mohammadi, Konstantinos N. Plataniotis

Abstract: Motivated by recent evolution of cutting-edge sensor technologies with complex-valued measurements, the paper exposes complex-valued (non-circular) false data injection attacks. We propose an attack model where an adversary applies widely-linear transformations on the sensor measurements to introduce correlations between the real and imaginary parts of the reported observations. Existing state estimators and attack detectors assume the measurements to have statistical properties similar to real-valued signals making them highly vulnerable to such complex-valued attacks. As a countermeasure, we propose to transform the attack detection problem into the problem of comparing the statistical distance between the Gaussian representation of the innovation sequence under attack and its counterpart with the optimal profile. Our Monte Carlo simulations illustrate the destructive nature of complex-valued attacks and validate the effectiveness of the proposed detection concept.