LAUSR

Under false data-injection (FDI) attacks, the data of some agents are tampered with by the FDI attackers, which causes that the distributed algorithm cannot estimate the ideal unknown parameter. Due to the concealment of the malicious data tampered with by the FDI attacks, many detection algorithms against FDI attacks often have poor detection results or low detection efficiencies. To solve these problems, a conveniently distributed diffusion least-mean-square (DLMS) algorithm with cross-verification (CV) is proposed against FDI attacks. The proposed DLMS with CV (DLMS-CV) algorithm is comprised of two subsystems: one subsystem provides a detection test of agents based on the CV mechanism, while the other provides a secure distribution estimation. In the CV mechanism, a smoothness strategy is introduced, which can improve the detection performance. The convergence performance of the proposed algorithm is analyzed, and then the design method of the adaptive threshold is also formulated. In particular, the probabilities of missing alarm and false alarm are examined, and they decay exponentially to zero under sufficiently small step size. Finally, simulation experiments are provided to illustrate the effectiveness and simplicity of the proposed DLMS-CV algorithm in comparison to other algorithms against FDI attacks.