Adaptation in rapidly time-varying environments using coefficient filters

Analysis of archetypical adaptation algorithms such as LMS (least mean square) or RLS shows that their tracking behavior can be described with a learning filter that is linear and of first order. Therefore, the trade-off between tracking fidelity and noise suppression is controlled via a single parameter, the cut-off frequency of this filter. To facilitate the incorporation of prior knowledge about the expected time variations, the algorithm structure is extended with coefficient filters. This allows one to tailor the tracking behavior in response to `hypermodels´ of the coefficient evolution. A series of proposals for coefficient filters (covering leakage, momentum LMS, coefficient prediction and smoothness priors, multi-step algorithms and post-filtering techniques) is put into perspective on the basis of the unifying joint recursive optimality criterion