Adaptive recursive order statistic filters

The ideas embodied by the recursive median filter are merged into a more general class of recursive LI-filters which includes both the infinite impulse response (IIR) filters and all the order statistic filters. The recursive LI-filter is a special case of a state-dependent system, and it can be seen as a more general IIR filter whose coefficients are picked up at every time step from a fixed set according to the order relationships existing among the elements of the observed window. An algorithm for adaptive computation of the coefficients of the recursive order statistic filters is derived. The algorithm is a steepest-descent search which follows an approach similar to that of the output-error formulation used in adaptive IIR filters. As a verification of convergence an example is shown in which the adaptive algorithm identifies successfully a recursive median filter and a recursive LI-filter. An example that shows how the recursive generalized filter has improved characteristics with respect to transient instabilities is also shown