Secure State Estimation with Byzantine Sensors: A Probabilistic Approach

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