On false-data attacks in robust multi-sensor-based estimation

State estimation in critical networked infrastructure such as the transportation and electricity (smart grid) networks is becoming increasingly important. Consequently, the security of state estimation algorithms has been identified as an important design factor in order to safeguard critical infrastructure. In this paper we study false-data attacks on robust state estimation in multi-sensor-based systems. Specifically, we suppose there is a group of attacking entities that want to compromise the integrity of the state estimator by hijacking certain sensors and distorting their outputs. We consider an underlying class of uncertain (discrete-time) systems and we outline a decentralized set-valued state estimation algorithm that recursively produces an ellipsoidal set of all those state estimates consistent with the measurements and modelling assumptions. We then show that in order for the attack to go undetected, the distorted measurements need to be carefully designed. In particular, we compute a set of those measurements which are consistent with the modelling assumptions. This set then forms the basis for a test to detect false-data attacks and provides a quantitative measure of the resilience of the system to false-data attacks. We also briefly discuss how an attacker can design their false-data attack in some optimal fashion while ensuring it goes undetected.