Robust Linear-in-the-Parameters Nonlinear Graph Diffusion Adaptive Filter Over Sensor Network

In recent years, there has been a growing interest in graph signal processing due to its capability to model and analyze irregular data generated by wireless sensor networks (WSNs). Nevertheless, it is still an open problem to model graph nonlinear systems in non-Gaussian noise environments. Since common nonlinear adaptive filtering algorithms are developed based on the linear-in-the-parameters (LIPs) model, this article uses this model to design a family of nonlinear graph diffusion adaptive filtering algorithms to model graph nonlinear systems. In addition, taking into account the presence of non-Gaussian noise, this article introduces the maximum mixture correntropy criterion (MMCC), which is generated by convex combination of two Gaussian kernel functions and exhibits more flexibility than the single kernel maximum correntropy criterion (MCC), and results in the nonlinear graph diffusion MMCC (NGD-MMCC) algorithm. The convergence conditions, mean-square transient behavior, and mean-square steady-state behavior of the proposed algorithm are also obtained under some common assumptions. Finally, we verify the correctness of the theoretical analysis and the effectiveness of the proposed algorithm for modeling nonlinear systems in a non-Gaussian environment by simulated and measured data, respectively.