Document Zbl 1087.93056

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It can handle the filtering, smoothing, and prediction fusion problems for state or signal. The optimal fusion rule weighted by matrices is re-derived as a weighted least squares (WLS) fuser, and is reviewed. An optimal fusion rule weighted by diagonal matrices is presented, which is equivalent to the optimal fusion rule weighted by scalars for components, and it realizes a decoupled fusion. The new algorithms of the steady-state Kalman estimator gains are presented. In order to compute the optimal weights, the formulas of computing the cross-covariances among local estimation errors by Lyapunov equations are presented. The exponential convergence of the iterative solution of Lyapunov equation is proved. It is proved that the optimal fusion estimators under three weighted fusion rules are locally optimal, but are globally suboptimal. The proposed steady-state Kalman fusers can reduce the on-line computational burden, and are suitable for real-time applications. A simulation example for the 3-sensor steady-state Kalman tracking fusion estimators shows their effectiveness and correctness, and gives the accuracy comparison of the fusion rules.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A2232487">Cited in <strong>40</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%3A62M10" title="MSC2020">62M10</a> </td> <td class="space"> Time series, auto-correlation, regression, etc. in statistics (GARCH) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62M20" title="MSC2020">62M20</a> </td> <td class="space"> Inference from stochastic processes and prediction </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Adistributed+fusion">distributed fusion</a>; <a href="/?q=ut%3Aweighted+fusion">weighted fusion</a>; <a href="/?q=ut%3Alinear+minimum+variance+fusion">linear minimum variance fusion</a>; <a href="/?q=ut%3Acovariance+information+fusion">covariance information fusion</a>; <a href="/?q=ut%3Afusion+rules">fusion rules</a>; <a href="/?q=ut%3Atrack+fusion">track fusion</a>; <a href="/?q=ut%3Ainformation+fusion+steady-state+Kalman+filter">information fusion steady-state Kalman filter</a>; <a href="/?q=ut%3AARMA+innovation+model">ARMA innovation model</a>; <a href="/?q=ut%3ALyapunov+equation">Lyapunov equation</a>; <a href="/?q=ut%3Amodern+time+series+analysis+method">modern time series analysis method</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 1087.93056" data-ciurl="/ci/02232487" data-biburl="/bibtex/02232487.bib" data-amsurl="/amsrefs/02232487.bib" data-xmlurl="/xml/02232487.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/02232487.pdf" title="Zbl 1087.93056 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.automatica.2005.04.020" aria-label="DOI for “New approach to information fusion steady-state Kalman filtering”" title="10.1016/j.automatica.2005.04.020">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">Anderson, B. 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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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