Quadratic filtering for linear stochastic non-Gaussian systems under false data injection attacks

Abstract

This paper addresses the quadratic filtering issue for a class of linear discrete-time systems in the presence of non-Gaussian noise under the false data injection attacks. The false data injection attacks are modeled with the simultaneously established additive and multiplicative false data. The majority of measurements are consistently inaccurate due to the presence of these two types of false data. To this end, a recursive quadratic filtering algorithm is proposed by constructing a quadratic system that combines the original system states with their second-order Kronecker powers. An upper bound for the filtering error covariance is derived recursively, and can be minimized by appropriately choosing the gain parameters. In addition, a sufficient condition is obtained to guarantee the mean-square boundedness of the upper bound. Finally, simulations are provided to validate the efficacy of the proposed quadratic filtering algorithm.