A state estimation and malicious attack game in multi-sensor dynamic systems

In this paper, the problem of false information attack on and the Kalman filter's defense of state estimation in dynamic multi-sensor systems is investigated from a game theoretic perspective. The relationship between the Kalman filter and the adversary can be regarded as a two-person zero-sum game. Under which condition both sides of the game will reach the Nash equilibrium is investigated in the paper. The multisensor Kalman filter system and the adversary are supposed to be rational players. The Kalman filter and the adversary have to choose their respective subsets of sensors to perform system state estimation and false information injection. It is shown how both sides pick their strategies in order to gain more and lose less. The optimal solutions are achieved by solving the minimax problem. Numerical results are also provided in order to illustrate the effectiveness of the derived optimal strategies.