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 δ, is proposed. We develop an optimal estimator for the new performance metric with a fixed δ, which is the Chebyshev center of a union of ellipsoids. We further provide an estimator that is optimal for every δ, for the special case where the sensors are homogeneous. Numerical examples are given to elaborate the results.