Analysis and generalization of a median adaptive filter

A class of gradient based adaptive algorithms is presented which employs order-statistical transformations of the gradient estimates over a short window. These algorithms, called order-statistical least mean squares (OSLMS), are designed to facilitate adaptive filter performance close to the least-squares optimum in impulsive and other non-Gaussian input environments. Three specific OSLMS filters are defined: the median LMS, the averaged LMS, and the trimmed-mean LMS. For the median LMS some simple convergence results are given. Simulations of all three algorithms, conducted using a generalized exponential density, are presented