Secure State Estimation with Byzantine Sensors: A Probabilistic Approach
For multi-sensor systems vulnerable to cyber-attacks, this work provides a probabilistic framework and optimal estimators for secure state estimation.
This paper addresses static state estimation with Byzantine sensors, where an unknown subset of sensors are compromised. It proposes a new performance metric and develops optimal estimators that minimize the asymptotic decay rate of the probability of large estimation errors.
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.