Constrained adaptive LMS L-filters

Two novel adaptive nonlinear filter structures are proposed which are based on linear combinations of order statistics. These adaptive schemes are modifications of the standard LMS (least mean square) algorithm and have the ability to incorporate constraints imposed on coefficients in order to permit location invariant and unbiased estimation of a constant signal in the presence of additive white noise. The convergence properties of the proposed filters are considered. Both of them can adapt well to a variety of noise probability distributions ranging from short-tailed to long-tailed ones. Simulation examples are given