Modified Sigmoid Function-Based Proportionate Diffusion Recursive Adaptive Filtering Algorithm Over Sensor Network

In recent years, the spotlight of research in the adaptive learning era has turned toward distributed adaptive filtering algorithms for sparse systems over wireless sensor networks (WSNs) leveraging error nonlinearity cost functions. This interest has been sparked by their exceptional efficiency in both Gaussian and non-Gaussian/impulsive noise environments, leading to the development of many adaptive filtering algorithms. Notably, among these approaches is the proportionate robust diffusion recursive exponential hyperbolic cosine (PR-DREHC) algorithm, a recent method based on the exponential hyperbolic cosine function (EHCF). While the PR-DREHC algorithm is robust against impulsive noise distortion, it remains afflicted by notable shortcomings such as pronounced computational burden and notable steady-state misalignment. To address these limitations, this study introduces a novel approach by introducing a new cost function termed the generalized correntropy-based modified sigmoid function (GCMSF). Our findings substantiate that the GCMSF holds the potential to engender robust algorithms distinguished by enhanced performance in terms of steady-state misalignment and expedited convergence. Capitalizing on this insight, we present novel robust diffusion recursive algorithms formulated through the maximization of the proposed GCMSF cost function. This ensemble encompasses the robust proportionate diffusion recursive GCMSF (RP-DRGCMSF) algorithm. The mean and mean square stability conditions of the introduced approach are also derived. Finally, the proposed algorithm is applied to practical simulation studies to examine its performance under different Gaussian and non-Gaussian noise environments and compare it to its respective competitors.