Attack-Resilient $\mathcal H_2$, $\mathcal H_\infty$, and $\ell _1$ State Estimator

This paper considers the secure state estimation problem for noisy systems in the presence of sparse sensor integrity attacks. We show a fundamental limitation, that is, 2ρ-detectability is necessary for achieving bounded estimation errors, where ρ is the number of attacks. This condition is weaker than the 2ρ-observability condition typically assumed in the literature. Conversely, we propose a real-time state estimator that achieves the fundamental limitation. The proposed state estimator is inspired by robust control and fault detection and isolation, that is, it consists of local Luenberger estimators, local residual detectors, and a global fusion process. We show its performance guarantees for
H
₂
,
H
_∞
, and ℓ
₁
systems. Finally, numerical examples show that it has relatively low estimation errors among existing algorithms and average computation time for systems with a sufficiently small number of compromised sensors.