Design of constrained adaptive LMS L-filters

Two adaptive nonlinear filter structures are proposed which are based on linear combinations of order statistics. These adaptive schemes are modifications of the standard LMS 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 in the mean of the filter coefficients is proven. The proposed filters can adapt well to a variety of noise probability distributions ranging from short-tailed to long-tailed distributions