non-Gaussian Impulsive Environments Research Articles

A Generalized Robust Logarithmic Family-Based Adaptive Filtering Algorithms

In recent years, algorithms based on the Maximum Versoria Criterion (MVC) and a relative logarithmic cost function have gained the attention of researchers because they improve the filtering accuracy and robustness towards non-Gaussian/impulsive noises. To further enhance the steady-state convergence behavior of these aforementioned algorithms in impulsive noise scenarios, we introduce a generalized, robust logarithmic family (GRLF) framework that underlies the relative logarithmic cost function and MVC, and the corresponding GRLF-based adaptive filters called least mean square based-GRLF (GRLF-LMS) and least absolute difference based-GRLF (GRLF-LAD) algorithms are designed. With an approximate solution using Taylors expansion, the steady-state behavior of the GRLF-LMS and GRLF-LAD methods is presented. Then, algorithms are used in practical simulation studies in system identification to compare the performance of GRLF-LMS and GRLF-LAD filtering in Gaussian and non-Gaussian impulsive environments in terms of accuracy and robustness to that of their competitors.

Kernel Least Mean $p$-Power Algorithm

This letter proposes a novel kernel least mean $p$ -power (KLMP) algorithm for nonlinear system identification in the presence of additive non-Gaussian impulsive noises, modeled by a symmetric $\alpha$ -stable distribution with heavy tail. The KLMP algorithm based on the fractional lower order statistics error criterion can effectively scale down the dynamic recursive weight coefficients affected by the impulsive estimation error to avoid the significant performance degradation. Simulation results demonstrate that the proposed algorithm has favorable convergence properties than the classical kernel least-mean-square algorithm using a conventional error criterion in the non-Gaussian impulsive environment.

Statistically-Efficient Filtering in Impulsive Environments: Weighted Myriad Filters

Linear filtering theory has been largely motivated by the characteristics of Gaussian signals. In the same manner, the proposed Myriad Filtering methods are motivated by the need for a flexible filter class with high statistical efficiency in non-Gaussian impulsive environments that can appear in practice. Myriad filters have a solid theoretical basis, are inherently more powerful than median filters, and are very general, subsuming traditional linear FIR filters. The foundation of the proposed filtering algorithms lies in the definition of the myriad as a tunable estimator of location derived from the theory of robust statistics. We prove several fundamental properties of this estimator and show its optimality in practical impulsive models such as the α-stable and generalized-t. We then extend the myriad estimation framework to allow the use of weights. In the same way as linear FIR filters become a powerful generalization of the mean filter, filters based on running myriads reach all of their potential when a weighting scheme is utilized. We derive the normal equations for the optimal myriad filter, and introduce a suboptimal methodology for filter tuning and design. The strong potential of myriad filtering and estimation in impulsive environments is illustrated with several examples.

Optimality of the myriad filter in practical impulsive-noise environments

Linear filtering theory has been largely motivated by the characteristics of Gaussian signals. In the same manner, the proposed myriad filtering methods are motivated by the need for a flexible filter class with high statistical efficiency in non-Gaussian impulsive environments that can appear in practice. We introduce several important properties of the myriad filter and prove its optimality in the family of /spl alpha/-stable distributions.

Nonlinear decorrelator for multiuser detection in non-Gaussian impulsive environments

A nonlinear decorrelator is proposed for robust multiuser detection in CDMA non-Gaussian channels. The new detector involves the use of a nonlinear front-end followed by a linear decorrelating stage. Simulation results show that the new detector exhibits good near-far resistance under both Gaussian and non-Gaussian impulsive noise environments.