A class of order statistic LMS algorithms

Conventional gradient-based adaptive filters, as typified by the well-known LMS algorithm, use an instantaneous estimate of the error-surface gradient to update the filter coefficients. Such a strategy leaves the algorithm extremely vulnerable to impulsive interference. A class of adaptive algorithms employing order statistic filtering of the sampled gradient estimates is presented. These algorithms, dubbed order statistic least mean squares (OSLMS), are designed to facilitate adaptive filter performance close to the least squares optimum across a wide range of input environments from Gaussian to highly impulsive. Three specific OSLMS filters are defined: the median LMS, the average LMS, and the trimmed-mean LMS. The properties of these algorithms are investigated and the potential for improvement demonstrated. Finally, a general adaptive OSLMS scheme in which the nature of the order-statistic operator is also adapted in response to the statistics of the input signal is presented. It is shown that this can facilitate performance gains over a wide range of input data types