Diffusion ACNSAF Algorithm for Secure Distributed Estimation Under Complex-Valued Attacks

In order to protect the distributed network from complex-valued attack, a secure diffusion augmented complex-valued normalized subband adaptive filter algorithm is proposed in this article, which is derived from a novel complex-valued detection method. This complex-value detection method can be considered to consist of two parts. First, a non-cooperative augmented complex-valued normalized subband adaptive filter algorithm is used to provide reliable reference estimations under complex-valued attacks, and then the threshold test is constructed by using the reliable reference estimations to detect the trustworthy neighbors of each node. The second part is to reassemble the information from the trustworthy neighbors by using the diffusion augmented complex-valued normalized subband adaptive filter algorithm. Then, the theoretical analyses of the mean and mean-square performance of the proposed algorithm are derived based on the energy conservation framework. Finally, some experiments are performed to show the effectiveness of the proposed algorithm under non-time-varying and time-varying complex-valued attacks, respectively.