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M. Rupp:
"Adaptive Filters: Stable but not Convergent";
EURASIP Journal on Advances in Signal Processing, 1 (2015), 104.

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.

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.

adaptive filter

http://dx.doi.org/10.1186/s13634-015-0289-8

http://www.asp.eurasipjournals.com/content/pdf/s13634-015-0289-8.pdf

Project Head Markus Rupp:
Signal and Information Processing in Science and Engineering II: Theory and Implementation of Distributed Algorithms