Contraction mapping: an important property in adaptive filters

Shows that many adaptive filters used for system identification are contraction mappings. Applying deterministic methods the authors give conditions under which algorithms, like least mean square, normalized least mean square, modified least mean square with delayed update, modified filtered-X least mean square, affine projection, and recursive least square are a contraction mapping contracting. Based on this result, the authors investigate the algorithms' convergence rate for initialization phase and tracking.<
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