Document Zbl 1467.93313

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J. Adapt. Control Signal Process.</a> <a href="/?q=in%3A449483" title="Articles in this Issue">34, No. 2, 151-182 (2020)</a>. </div> <div class="abstract">Summary: In this paper, the weighted fusion robust steady-state Kalman filtering problem is studied for a class of multisensor networked systems with mixed uncertainties. The uncertainties include same multiplicative noises in system parameter matrices, uncertain noise variances, as well as the one-step random delay and inconsecutive packet dropouts, which modeled by sequences of Bernoulli variables with different probabilities. By defining a new observation vector and applying the augmented method, the system under study is converted into one with only uncertain noise variances. The sufficient conditions for the existence of steady-state estimators are given. According to the minimax robust estimation principle, based on the worst-case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady-state Kalman estimators (predictor, filter, and smoother) are proposed. Applying the optimal fusion algorithm weighted by matrices and the covariance intersection fusion algorithm, the two kinds of robust fusion steady-state Kalman estimators are derived in a unified framework. The robustness of the proposed fusion estimators is proved by applying the permutation matrices and the global Lyapunov equations method, such that, for all admissible uncertainties, the actual steady-state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fusion steady-state Kalman estimators are proved. An example with application to autoregressive moving average signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7371876">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A93E10" title="MSC2020">93E10</a> </td> <td class="space"> Estimation and detection in stochastic control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B35" title="MSC2020">93B35</a> </td> <td class="space"> Sensitivity (robustness) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B70" title="MSC2020">93B70</a> </td> <td class="space"> Networked control </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ainconsecutive+packet+dropouts">inconsecutive packet dropouts</a>; <a href="/?q=ut%3ALyapunov+equation+approach">Lyapunov equation approach</a>; <a href="/?q=ut%3Aminimax+robust+estimation+principle">minimax robust estimation principle</a>; <a href="/?q=ut%3Aone-step+random+delay">one-step random delay</a>; <a href="/?q=ut%3Arobust+fusion+steady-state+estimators">robust fusion steady-state estimators</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 1467.93313" data-ciurl="/ci/07371876" data-biburl="/bibtex/07371876.bib" data-amsurl="/amsrefs/07371876.bib" data-xmlurl="/xml/07371876.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07371876.pdf" title="Zbl 1467.93313 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/10.1002/acs.3076" aria-label="DOI for “Weighted fusion robust steady-state estimators for multisensor networked systems with one-step random delay and inconsecutive packet dropouts”" title="10.1002/acs.3076">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">Deng, ZL; Gao, Y.; Mao, L.; Li, Y.; Hao, G., New approach to information fusion steady‐state Kalman filtering, Automatica, 41, 10, 1695-1707, 2005 · <a href="/1087.93056" class="nowrap">Zbl 1087.93056</a></td> </tr><tr> <td>[2]</td> <td class="space">Sun, SL; Deng, ZL, Multi‐sensor optimal information fusion Kalman filter, Automatica, 40, 6, 1017-1024, 2004 · <a href="/1075.93037" class="nowrap">Zbl 1075.93037</a></td> </tr><tr> <td>[3]</td> <td class="space">Julier, SJ; Uhlman, JK, A non‐divergent estimation algorithm in the presence of unknown correlations. 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This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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