An adaptive cubature Kalman filter for nonlinear systems against randomly occurring injection attacks

Abstract

The problem of state estimation for nonlinear dynamic systems in the presence of randomly occurring injection attacks (ROIAs) is investigated. This paper requires no prior statistical information of the attacks, which relaxes the assumption of the existing result that the attack probability and the probability density function of attack signals need to be known. With the distribution of the attack probability and attack signals modeled as Beta distribution and Gaussian mixture distribution, a variational Bayesian based adaptive cubature Kalman filter is proposed to approximate the joint posterior distribution of the system state vector and unknown parameters. In addition, the update rules of the state and the statistical parameters of attacks are analytically derived by employing the fixed-point iteration approach. Finally, the effectiveness of the proposed filter is validated through numerical results.