Gradient-based adaptive filters for non-Gaussian noise environments

Convergence properties are studied for a class of gradient-based adaptive algorithms known as order statistic least mean square (OSLMS) algorithms. These algorithms apply an order statistic filtering operation to the gradient estimate of the standard least mean square (LMS) algorithm. The order statistic operation in OSLMS can reduce the variance of the gradient estimate (relative to LMS) when operating in non-Gaussian noise environments. A consequence is that in steady state the excess mean square error can be reduced. It is shown that the coefficient estimates for a class of OSLMS algorithms converge when the input signals are i.i.d. and symmetrically distributed.<>