Correction-based diffusion LMS algorithms for secure distributed estimation under attacks

In this paper, we mainly study the distributed estimation problem under attacks, which is mainly used to estimate an unknown parameter. To solve this problem, a correction-based secure diffusion least mean square (CS-dLMS) algorithm, which is a hybrid algorithm that composes of a non-cooperative LMS (nc-LMS) algorithm and a correction-based diffusion least-mean squares (C-dLMS) algorithm, is proposed for distributed estimation. The nc-LMS algorithm is used to provide a reliable reference system, which can detect reliable neighbor nodes by setting a threshold under network attacks. The correction-based least mean square algorithm can estimate an unknown parameter by interacting with neighbor nodes. In order to guarantee the mean performance of the CS-dLMS algorithm under attacks, a sufficient condition is proposed. Finally, simulation results are provided to verify the effectiveness of the proposed algorithm and it outperforms the C-dLMS algorithm and nc-LMS algorithm.