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Secure Estimation in the Presence of Integrity Attacks

Mo, Yilin and Sinopoli, Bruno (2015) Secure Estimation in the Presence of Integrity Attacks. IEEE Transactions on Automatic Control, 60 (4). pp. 1145-1151. ISSN 0018-9286.

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We consider the estimation of a scalar state based on m measurements that can be potentially manipulated by an adversary. The attacker is assumed to have full knowledge about the true value of the state to be estimated and about the value of all the measurements. However, the attacker has limited resources and can only manipulate up to l of the m measurements. The problem is formulated as a minimax optimization, where one seeks to construct an optimal estimator that minimizes the “worst-case” expected cost against all possible manipulations by the attacker. We show that if the attacker can manipulate at least half the measurements (l ≥ m/2), then the optimal worst-case estimator should ignore all measurements and be based solely on the a-priori information. We provide the explicit form of the optimal estimator when the attacker can manipulate less than half the measurements (l < m/2), which is based on (m/2l) local estimators. We further prove that such an estimator can be reduced into simpler forms for two special cases, i.e., either the estimator is symmetric and monotone or m = 2l + 1. Finally we apply the proposed methodology in the case of Gaussian measurements.

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Mo, Yilin0000-0001-7937-6737
Additional Information:© 2014 IEEE. This research is supported in part by grants CNS-1135895 and ECCS-0955111 from NSF.
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Issue or Number:4
Record Number:CaltechAUTHORS:20150114-093629156
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Official Citation:Yilin Mo; Sinopoli, B., "Secure Estimation in the Presence of Integrity Attacks," Automatic Control, IEEE Transactions on , vol.60, no.4, pp.1145,1151, April 2015 doi: 10.1109/TAC.2014.2350231 doi: 10.1109/TAC.2014.2350231 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:53678
Deposited By: Tony Diaz
Deposited On:14 Jan 2015 17:50
Last Modified:31 Jan 2020 17:37

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