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.

本文主要研究攻击下的分布式估计问题，主要用于估计未知参数。为了解决此问题，采用了基于校正的安全扩散最小均方（CS-dLMS）算法，该算法是由非合作LMS（nc-LMS）算法和基于校正的扩散最小均方组成的混合算法。提出了（C-dLMS）算法用于分布式估计。nc-LMS算法用于提供可靠的参考系统，该参考系统可以通过设置网络攻击下的阈值来检测可靠的邻居节点。基于校正的最小均方算法可以通过与邻居节点进行交互来估计未知参数。为了保证CS-dLMS算法在攻击下的平均性能，提出了充分的条件。最后，