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This paper studies static state estimation in multi-sensor settings, with acaveat that an unknown subset of the sensors are compromised by an adversary,whose measurements can be manipulated arbitrarily. The attacker is able tocompromise $q$ out of $m$ sensors. A new performance metric, which quantifiesthe asymptotic decay rate for the probability of having an estimation errorlarger than $\delta$, is proposed. We develop an optimal estimator for the newperformance metric with a fixed $\delta$, which is the Chebyshev center of aunion of ellipsoids. We further provide an estimator that is optimal for every$\delta$, for the special case where the sensors are homogeneous. Numericalexamples are given to elaborate the results.

Secure State Estimation with Byzantine Sensors: A Probabilistic Approach