Document Zbl 1349.93415

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Franklin Inst.</a> <a href="/?q=in%3A360880" title="Articles in this Issue">353, No. 17, 4500-4525 (2016)</a>. </div> <div class="abstract">Summary: The least mean $p$th power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filter have been successfully developed for nonlinear system identification in $\alpha$-stable noise environments. However, there exists an inherent tradeoff between the convergence rate and steady-state performance. To address this compromise, a collaborative adaptive Volterra filter based on the convex combination scheme is proposed under the $\alpha$-stable noise in this paper. By utilizing the convex combination which performs at least as well as the best component filter, the proposed algorithms achieve fast convergence rate and small misadjustment. Furthermore, by following a frame of the generalized combination scheme, two novel combination structures of Volterra filter are presented. Simulations in nonlinear system identification contexts demonstrate that the performance of the proposed algorithms is superior to the existing algorithms under the $\alpha$-stable noise in terms of the convergence speed and steady state kernel error.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6655692">Cited in <strong>6</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E24" title="MSC2020">93E24</a> </td> <td class="space"> Least squares and related methods for stochastic control systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E11" title="MSC2020">93E11</a> </td> <td class="space"> Filtering in stochastic control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C40" title="MSC2020">93C40</a> </td> <td class="space"> Adaptive control/observation systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C10" title="MSC2020">93C10</a> </td> <td class="space"> Nonlinear systems in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B30" title="MSC2020">93B30</a> </td> <td class="space"> System identification </td> </tr><tr> <td class="mono"> 93B40 </td> <td class="space"> Computational methods in systems theory (MSC2010) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aleast+mean+%5C%28p%5C%29th+power+%28LMP%29+algorithm">least mean $p$th power (LMP) algorithm</a>; <a href="/?q=ut%3Anormalized+LMP+%28NLMP%29+algorithm">normalized LMP (NLMP) algorithm</a>; <a href="/?q=ut%3Aadaptive+Volterra+filter">adaptive Volterra filter</a>; <a href="/?q=ut%3Anonlinear+system+identification">nonlinear system identification</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1349.93415" data-ciurl="/ci/06655692" data-biburl="/bibtex/06655692.bib" data-amsurl="/amsrefs/06655692.bib" data-xmlurl="/xml/06655692.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06655692.pdf" title="Zbl 1349.93415 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.jfranklin.2016.08.025" aria-label="DOI for “Collaborative adaptive Volterra filters for nonlinear system identification in $\alpha$-stable noise environments”" title="10.1016/j.jfranklin.2016.08.025">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Mathews, V. 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