Diffusion random Fourier adaptive filtering algorithm based on logistic distance metric for distributed estimation

Distributed adaptive filtering over networks can improve filtering performance by fusing information from nodes within the same neighbor. In nonlinear estimation, adaptive filters derived from a linear framework usually suffer from large misalignment. To solve the above problem, this work develops a diffusion kernel filtering algorithm based on the random Fourier approximation method. To promote robustness to impulsive noise, the minimum logistic distance metric (LDM) is employed as a loss function. Compared to traditional kernel algorithms, the presented algorithm uses a fixed-length filter and is suitable for online distributed adaptive filtering tasks. In addition, this work also conducts a performance analysis based on Isserlis' and Price's theorems with several statistical assumptions. Simulations are conducted to exhibit the robustness of the proposed method to impulsive noise and to examine the accuracy of the theory on performance analysis.