False information detection with minimum mean squared errors for Bayesian estimation

In this paper, for a Bayesian estimator whose sensors could be attacked by false information injected by an adversary, we investigate the strategies for the Bayesian estimator to detect the false information and defend itself from such attacks. We assume that the adversary attacks the system with certain probability, and that he/she adopts the worst possible strategy which maximizes the mean squared error (MSE) if the attack is undetected. The defender´s goal is to minimize the average system estimation MSE instead of minimizing the probability of error, as a conventional Bayesian detector typically does. The cost functions are based on the traces of the MSE matrices of the estimation error. Numerical results show that the new detection-estimation structure outperforms that based on the traditional detectors such as the conventional Bayesian detector and the chisquared detector significantly in term of the average MSE. One proposed detection-estimation strategy, discarding sensor data when the presence of attack is declared, is very robust even when the attacker uses an attack strategy significantly different from the one assumed by the defender.