Normalised order statistic LMS adaptive filtering

Normalised order statistic adaptive filtering is proposed to overcome the practical problem of spike clustering. The family of Order Statistic Least Mean Square (OSLMS) adaptive filter algorithms is substantially more robust to single, well-spaced, outlier values present within the signals which form the input to an adaptive filter than the established Least Mean Square (LMS) algorithm. Normalisation of the LMS algorithm is another, not so generally appreciated, mechanism which affords such robustness in an adaptive algorithm. Moreover, for outliers which cluster it is computationally more efficient to combine the benefits of an order statistic adaptive algorithm with normalisation. This leads to the notion of Normalised Order Statistic Least Mean Square (NOSLMS) adaptive filtering. In particular, the Normalised Averaged Least Mean Square (NALMS) and Normalised Median Least Mean Square (NMLMS) algorithms are developed and their performance is demonstrated by application to a parameter estimation problem