Error analysis of recursive algorithms for computing the correlation matrix of the order statistics

摘要

The computation of the expected values and moments of the order statistics has received much attention since the mid-1950's, because of the prominent position order statistics in the field of robust estimation [1]-[6],[9]. The computation of the second-order and product moments appearing in the correlation matrix of the order statistics is of fundamental importance, because the correlation matrix of the order statistics is involved in the de sign of L-filters both single-channel [7,8,10] as well as multichannel ones [13]. Furthermore, a need for computing the correlation matrix of the order statistics is also arisen when the assessment of the performance of adaptive nonlinear filters based on Least Mean Squares (LMS) or Recursive Least Squares algorithms is to be pursued [11,12]. For example, the stability as well as the rate of convergence of LMS adaptive L-filters depend on the extreme eigenvalues of the correlation matrix of the order statistics.