Robust Polynomial Filters for Impulsive Environments

Linear combinations of polynomial terms yield poor performance in environments characterized by heavy-tailed distributions. Weighted myriad (WMy) filters, however, are well-known for their outlier suppression and detail preservation properties. It is shown here that the WMy methodology is naturally extended to the polynomial sample case, yielding filter structures that exploit the higher order statistics of the observed samples while simultaneously being robust to outliers for heavy-tailed distributions environments. Moreover, the introduced PWMy filter class is well motivated by analysis of cross and square term statistics of heavy-tailed distributions. The effectiveness of the proposed filter is evaluated through simulations.