This paper studies static state estimation based on measurements from a set of sensors, a subset of which can be compromised by an attacker. The measurements from a compromised sensor can be manipulated arbitrarily by the adversary. A new notion is adopted to indicate the performance of an estimator, that is, the asymptotic exponential rate, with which the worst-case probability of estimate lying outside certain ball centered at the true underlying state goes to zero. An optimal estimator, which computes Chebyshev centers and only utilizes the information contained in the averaged measurements, is proposed. Numerical examples are given to elaborate the results.