Doctor of Philosophy
Carl R Elks
The impact of false information injection is investigated for linear dynamic systems with multiple sensors. First, it is assumed that the system is unaware of the existence of false information and the adversary is trying to maximize the negative effect of the false information on Kalman filter's estimation performance under a power constraint. The false information attack under different conditions is mathematically characterized. For the adversary, many closed-form results for the optimal attack strategies that maximize the Kalman filter's estimation error are theoretically derived. It is shown that by choosing the optimal correlation coefficients among the false information and allocating power optimally among sensors, the adversary could significantly increase the Kalman filter's estimation errors.
In order to detect the false information injected by an adversary, we investigate the strategies for the Bayesian estimator to detect the false information and defend itself from such attacks. We assume that the adversary attacks the system with certain probability, and that he/she adopts the worst possible strategy that maximizes the mean squared error (MSE) if the attack is undetected. An optimal Bayesian detector is designed which minimizes the average system estimation error instead of minimizing the probability of detection error, as a conventional Bayesian detector typically does.
The case that the adversary attacks the system continuously is also studied. In this case, sparse attack strategies in multi-sensor dynamic systems are investigated from the adversary's point of view. It is assumed that the defender can perfectly detect and remove the sensors once they are corrupted by false information injected by an adversary. The adversary's goal is to maximize the covariance matrix of the system state estimate by the end of attack period under the constraint that the adversary can only attack the system a few times over the sensor and over the time, which leads to an integer programming problem. In order to overcome the prohibitive complexity of the exhaustive search, polynomial-time algorithms, such as greedy search and dynamic programming, are proposed to find the suboptimal attack strategies. As for greedy search, it starts with an empty set， and one sensor is added at each iteration, whose elimination will lead to the maximum system estimation error. The process terminates when the cardinality of the active set reaches to the sparsity constraint. Greedy search based approaches such as sequential forward selection (SFS), sequential backward selection (SBS), and simplex improved sequential forward selection (SFS-SS) are discussed and corresponding attack strategies are provided. Dynamic programming is also used in obtaining the sub-optimal attack strategy. The validity of dynamic programming lies on a straightforward but important nature of dynamic state estimation systems: the credibility of the state estimate at current step is in accordance with that at previous step.
The problem of false information attack on and the Kalman filter's defense of state estimation in dynamic multi-sensor systems is also investigated from a game theoretic perspective. The relationship between the Kalman filter and the adversary can be regarded as a two-person zero-sum game. The condition under which both sides of the game will reach a Nash equilibrium is investigated.
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