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Local Decomposition of Kalman Filters and Its Application for Secure State Estimation

par Liu, Xinghua;Mo, Yilin;Garone, Emanuele
Référence IEEE transactions on automatic control
Publication Publié, 2020-12-01

Article révisé par les pairs

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Résumé :

This technical note is concerned with the secure state estimation problem of a linear discrete-time Gaussian system in the presence of sparse integrity attacks. m sensors are deployed to monitor the state and p of them can potentially be compromised by an adversary, whose data can be arbitrarily manipulated by the attacker. We show that the optimal Kalman estimate can be decomposed as a weighted sum of local state estimates. Based on these local estimates, we propose a convex optimization based approach to generate a more secure state estimate. It is proved that our proposed estimator coincides with the Kalman estimator with a certain probability when all sensors are benign. Besides, we establish a sufficient condition under which the proposed estimator is stable against the (p, m)-sparse attack. A numerical example is provided to validate the secure state estimation scheme.