Robust Adaptive Volterra Filtering Based on a Generalized Gaussian Mixture Model Framework

Abstract

In complex and impulse noise environments, traditional adaptive filtering algorithms often fail to achieve satisfactory performance due to the non-Gaussian characteristics of the noise. For the adaptive filtering problem of linear systems, existing research has applied the generalized Gaussian mixture model (GGMM) to residual modeling, leading to the development of robust filtering methods that improve performance in non-Gaussian noise environments. However, in practical applications, systems often exhibit significant nonlinearity, making it difficult for linear filters to accurately characterize the complex mapping between input and output. Building on this foundation, this paper extends the GGMM framework to nonlinear Volterra filters, proposing a robust adaptive Volterra filtering method based on the GGMM. The proposed method captures high-order nonlinear characteristics of the system through Volterra expansion. Under the maximum likelihood framework, it utilizes GGMM probability modeling to characterize the residual distribution. Meanwhile, the distribution parameters are iteratively estimated via the expectation-maximization (EM) algorithm, achieving synergistic adaptive updates of filter coefficients and noise models. Theoretical analysis and simulation results demonstrate that in non-Gaussian noise environment, the method not only maintains fast convergence and low steady-state error, but also significantly outperforms traditional linear robust filtering methods for nonlinear system identification.