Title: Adaptive filters: stable but divergent
Language: English
Authors: Rupp, Markus 
Category: Review Article
Issue Date: 2015
Journal: EURASIP Journal on Advances in Signal Processing
ISSN: 1687-6180
The pros and cons of a quadratic error measure in the context of various applications have often been discussed. In this tutorial, we argue that it is not only a suboptimal but definitely the wrong choice when describing the stability behavior of adaptive filters. We take a walk through the past and recent history of adaptive filters and present 14 canonical forms of adaptive algorithms and even more variants thereof contrasting their mean-square with their l2−stability conditions. In particular, in safety critical applications, the convergence in the mean-square sense turns out to provide wrong results, often not leading to stability at all. Only the robustness concept with its l2−stability conditions ensures the absence of divergence.
Keywords: l2-stability; Adaptive gradient-type filters; Mean squared error; Small-gain theorem; Contraction mapping; Error bounds; Neural networks; Backpropagation; Proportionate normalized least-mean-square
DOI: 10.1186/s13634-015-0289-8
Library ID: AC11359681
URN: urn:nbn:at:at-ubtuw:3-1145
Organisation: E389 - Institute of Telecommunications 
Publication Type: Article
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