Information-Theoretic Disturbance Minimization for Unified Secure or Robust Distributed Estimation in Presence of Impulsive FDI Attack or Impulsive Noise

In this paper, an information-theoretic and statistical viewpoint of distributed estimation problem is considered as the contribution of the work. So, a novel minimum information-theoretic disturbance diffusion least-mean-square (LMS) algorithm is presented for both robust distributed estimation against impulsive noise and secure distributed estimation in the presence of False Data Injection (FDI) attacks. Throughout the paper, for the novelty of the paper, information-theoretic disturbance measure, specifically the Kullback-Leibler (KL) divergence, is formulated in a convenient and structured manner. It is considered as the generalization of Mean Square Error (MSE) disturbance measure. By some manipulations, it is seen that the proposed information-theoretic disturbance is equivalent to MSE disturbance plus an extra term that depends on the variance of the output variable. So, this KL divergence measure captures the variance information of the output variable. The optimal adaptation and combination coefficients in the sense of minimum KL disturbance is derived in closed-form formulas that provides the computational convenience of the proposed algorithm. Simulation results demonstrate the advantages of the proposed algorithm over some competing algorithms, while suggesting the impulsive FDI attacks shows its potential in lower detectability than Gaussian FDI attacks.