Convergence of adaptive algorithms with order statistic based gradient estimates

Order statistic Least Mean Square (OSLMS) algorithms are a class of adaptive algorithms which modify the ordinary Least Mean Square (LMS) algorithm by applying an order statistic (OS) filtering operation to the instantaneous gradient estimate. Adaptive filter performance may be improved by OSLMS since it effectively reduces effects of gradient noise at filter convergence. In this paper, the convergence analysis has been established for OSLMS. It is shown that OSLMS will converge on average, with noise corrupting both the filter input and the desired signal, and this result is confirmed via simulations. The optimal selection of the OS filter in the algorithm is also discussed. The OS filter is chosen to produce a minimum variance gradient estimate at the filter convergence point; a reduction of the mean squared coefficient error is shown to accrue from this choice of filter