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Secure state estimation against sensor attacks in the presence of noise
We consider the problem of estimating the state of a noisy linear dynamical system when an unknown subset of sensors is arbitrarily corrupted by an adversary. We propose a secure state estimation algorithm, and derive (optimal) bounds on the achievable state estimation error given an upper bound on the number of attacked sensors. The proposed state estimator involves Kalman filters operating over subsets of sensors to search for a sensor subset which is reliable for state estimation. To further improve the subset search time, we propose Satisfiability Modulo Theory-based techniques to exploit the combinatorial nature of searching over sensor subsets. Finally, as a result of independent interest, we give a coding theoretic view of attack detection and state estimation against sensor attacks in a noiseless dynamical system
Secure State Estimation: Optimal Guarantees against Sensor Attacks in the Presence of Noise
Motivated by the need to secure cyber-physical systems against attacks, we
consider the problem of estimating the state of a noisy linear dynamical system
when a subset of sensors is arbitrarily corrupted by an adversary. We propose a
secure state estimation algorithm and derive (optimal) bounds on the achievable
state estimation error. In addition, as a result of independent interest, we
give a coding theoretic interpretation for prior work on secure state
estimation against sensor attacks in a noiseless dynamical system.Comment: A shorter version of this work will appear in the proceedings of ISIT
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Securing state reconstruction under sensor and actuator attacks: Theory and design
This paper discusses the problem of reconstructing the state of a linear time invariant system when some of its actuators and sensors are compromised by an adversarial agent. In the model considered in this paper, the adversarial agent attacks an input (output) by manipulating its value arbitrarily, i.e., we impose no constraints (statistical or otherwise) on how control commands (sensor measurements) are changed by the adversary other than a bound on the number of attacked actuators and sensors In the first part of this paper, we introduce the notion of sparse strong observability and we show that is a necessary and sufficient condition for correctly reconstructing the state despite the considered attacks. In the second half of this work, we propose an observer to harness the complexity of this intrinsically combinatorial problem, by leveraging satisfiability modulo theory solving. Numerical simulations illustrate the effectiveness and scalability of our observer
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