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Titel
Adaptive filters: stable but divergent
Verfasser / Verfasserin Rupp, Markus
Erschienen in
EURASIP Journal on Advances in Signal Processing, 2015,, S. 1-15
Erschienen2015
Ausgabe
Published version
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)l2-stability / Adaptive gradient-type filters / Mean squared error / Small-gain theorem / Contraction mapping / Error bounds / Neural networks / Backpropagation / Proportionate normalized least-mean-square
URNurn:nbn:at:at-ubtuw:3-1145 Persistent Identifier (URN)
DOI10.1186/s13634-015-0289-8 
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Adaptive filters: stable but divergent [1.74 mb]
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Zusammenfassung (Englisch)

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 l2stability 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 l2stability conditions ensures the absence of divergence.

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