Diffusion Laguerre Fourier Hierarchical Algorithm for Distributed Censored Regression Over Networks

System modeling in distributed adaptive networks remains challenging under sensor aging-induced nonlinear data censoring and non-Gaussian interference. This brief proposes a robust hierarchical control framework that incorporates a Laguerre-based random Fourier filter to capture network nonlinearities. To address censored measurements and impulsive noise, a robust Laguerre RFF Diffusion Hierarchical (LRFF-DH) algorithm is developed. It leverages maximum likelihood estimation to correct bias and introduces a connectivity-adaptive robustness strategy based on node connectivity, enhancing edge-node resilience while reducing computational load on critical nodes. Simulations on a 20-node ad-hoc network verify the algorithm's effectiveness in interference suppression and mean squared error reduction under complex nonlinear conditions.