Document Zbl 0847.93060

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Non-recursive optimal state estimators are given, whose recursive version gives a steady-state Kalman filter, and a new algorithm to obtain the Kalman filter gain is proposed. Two new algorithms for the Kalman predictor gain are also derived. Local asymptotic stability of the Kalman filter is proved. To illustrate, three simulation examples are given.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A231">Wang Cheng-Shu (Denver)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A867758">Cited in <strong>18</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%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%3A93C55" title="MSC2020">93C55</a> </td> <td class="space"> Discrete-time control/observation systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AARMA">ARMA</a>; <a href="/?q=ut%3Ainnovation+model">innovation model</a>; <a href="/?q=ut%3Aestimation">estimation</a>; <a href="/?q=ut%3AKalman+filter">Kalman filter</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 0847.93060" data-ciurl="/ci/00867758" data-biburl="/bibtex/00867758.bib" data-amsurl="/amsrefs/00867758.bib" data-xmlurl="/xml/00867758.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/00867758.pdf" title="Zbl 0847.93060 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/10.1016/0005-1098(96)85549-X" aria-label="DOI for “Optimal and self-tuning white noise estimators with applications to deconvolution and filtering problems”" title="10.1016/0005-1098(96)85549-X">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">Ahlen, A.; Sternad, M., Optimal deconvolution based on polynomial method, IEEE Trans. Acoust. Speech Sig. Process., ASSP-37, 217-226 (1989)</td> </tr><tr> <td>[2]</td> <td class="space">Ahlen, A.; Sternad, M., Wiener filter design using polynomial equations, IEEE Trans. Sig. Process., SP-39, 2387-2398 (1991) · <a href="/0758.93069" class="nowrap">Zbl 0758.93069</a></td> </tr><tr> <td>[3]</td> <td class="space">Anderson, A. J.; Moir, T. J., Evaluation of the gain for an adaptive deconvolution smoother, Sig. Process., 22, 209-213 (1991)</td> </tr><tr> <td>[4]</td> <td class="space">Anderson, B. D.O.; Moore, J. B., (Optimal Filtering (1979), Prentice-Hall: Prentice-Hall London) · <a href="/0688.93058" class="nowrap">Zbl 0688.93058</a></td> </tr><tr> <td>[5]</td> <td class="space">Box, G. E.P.; Jenkins, G. M., (Time Series Analysis, Forecasting and Control (1976), Holden-Day: Holden-Day San Francisco) · <a href="/0363.62069" class="nowrap">Zbl 0363.62069</a></td> </tr><tr> <td>[6]</td> <td class="space">Chisci, L.; Mosca, E., Polynomial equations for the linear MMSE state estimation, IEEE Trans. Autom. Control, AC-37, 623-626 (1992) · <a href="/0756.93070" class="nowrap">Zbl 0756.93070</a></td> </tr><tr> <td>[7]</td> <td class="space">Dabis, H. S.; Moir, T. J., A unified approach to optimal estimation using diophantine equations, Int. J. Control, 57, 577-598 (1993) · <a href="/0780.93086" class="nowrap">Zbl 0780.93086</a></td> </tr><tr> <td>[8]</td> <td class="space">Deng, Z. L., Multivariate self tuning filter and smoother, (Preprints 6th IFAC Symp. on Identification and System Parameter Estimation. Preprints 6th IFAC Symp. on Identification and System Parameter Estimation, Washington, DC (1982)), 879-883</td> </tr><tr> <td>[9]</td> <td class="space">Deng, Z. L., White-noise filter and smoother with application to seismic data deconvolution, (Preprints 7th IFAC/IFORS Symp. on Identification and System Parameter Estimation. Preprints 7th IFAC/IFORS Symp. on Identification and System Parameter Estimation, York U.K. (1985)), 621-624</td> </tr><tr> <td>[10]</td> <td class="space">Deng, Z. L., Self-tuning white noise estimators with application to seismic data deconvolution, Acta Automatica Sinica, 12, 155-161 (1986) · <a href="/0592.93058" class="nowrap">Zbl 0592.93058</a></td> </tr><tr> <td>[11]</td> <td class="space">Deng, Z. L.; Guo, Y. X., (Modern Time Series Analysis and Its Applications, Modelling, Filtering, Deconvolution, Prediction and Control (1989), Knowledge Press: Knowledge Press Beijing)</td> </tr><tr> <td>[12]</td> <td class="space">Deng, Z. L.; Li, B. X., A self-tuning α-β tracking filter, Acta Automatica Sinica, 18, 720-723 (1992) · <a href="/0775.93002" class="nowrap">Zbl 0775.93002</a></td> </tr><tr> <td>[13]</td> <td class="space">Deng, Z. L.; Li, B. X., A self-tuning filter for nonstationary ARMA signals and applications, Chinese J. Automation, 4, 207-214 (1992)</td> </tr><tr> <td>[14]</td> <td class="space">Deng, Z. L.; Zhang, H. S., Multivariable self-tuning recursive deconvolution filter, Control and Decision, 9, 205-210 (1994)</td> </tr><tr> <td>[15]</td> <td class="space">Deng, Z. L.; Zhang, H. S., A self-tuning deconvolution filter for nonstationary ARMA signals, Chinese J. Automation, 6, 143-148 (1994)</td> </tr><tr> <td>[16]</td> <td class="space">Fung, P. T.K.; Grimble, M. J., Dynamic ship positioning using a self-tuning Kalman filter, IEEE Trans. Autom. Control, AC-28, 339-349 (1983) · <a href="/0508.93052" class="nowrap">Zbl 0508.93052</a></td> </tr><tr> <td>[17]</td> <td class="space">Gevers, M.; Wouters, W. R.E., An innovations approach to the discrete-time stochastic realization problem, Journal A, 19, 90-109 (1978) · <a href="/0381.93041" class="nowrap">Zbl 0381.93041</a></td> </tr><tr> <td>[18]</td> <td class="space">Goodwin, G. C.; Doan, H. B.; Cantoni, A., Application of ARMA models to automatic channel equalization, Inf. Sci., 22, 107-129 (1980)</td> </tr><tr> <td>[19]</td> <td class="space">Guan, Z. Z.; Chen, H. F., (Controllability and Observability of Linear Control Systems (1975), Science Press: Science Press Beijing)</td> </tr><tr> <td>[20]</td> <td class="space">Hagander, P.; Wittenmark, B., A self-tuning filter for fixed-lag smoothing, IEEE Trans. Inf. Theory, IT-23, 377-384 (1977) · <a href="/0382.93060" class="nowrap">Zbl 0382.93060</a></td> </tr><tr> <td>[21]</td> <td class="space">Jazwinski, A. H., (Stochastic Processes and Filtering Theory (1970), Academic Press: Academic Press New York) · <a href="/0203.50101" class="nowrap">Zbl 0203.50101</a></td> </tr><tr> <td>[22]</td> <td class="space">Jezek, J.; Kučera, V., Efficient algorithm for matrix spectral factorization, Automatica, 21, 663-669 (1985) · <a href="/0585.93015" class="nowrap">Zbl 0585.93015</a></td> </tr><tr> <td>[23]</td> <td class="space">Kailath, T., (Linear Systems (1980), Prentice Hall: Prentice Hall Englewood Cliffs, NJ) · <a href="/0458.93025" class="nowrap">Zbl 0458.93025</a></td> </tr><tr> <td>[24]</td> <td class="space">Kormylo, J. J.; Mendel, J. M., Maximum likelihood detection and estimation of Bernoulli-Gaussian processes, IEEE Trans. Inf. Theory, IT-28, 482-488 (1982) · <a href="/0481.60049" class="nowrap">Zbl 0481.60049</a></td> </tr><tr> <td>[25]</td> <td class="space">Lee, T. T., A direct approach to identify the noise covariances of Kalman filtering, IEEE Trans. Autom. Control, AC-25, 841-842 (1980) · <a href="/0445.93035" class="nowrap">Zbl 0445.93035</a></td> </tr><tr> <td>[26]</td> <td class="space">Ljung, L., (System Identification: Theory for the User (1987), Prentice Hall: Prentice Hall Englewood Cliffs, NJ) · <a href="/0615.93004" class="nowrap">Zbl 0615.93004</a></td> </tr><tr> <td>[27]</td> <td class="space">Mehra, R. K., On the identification of variances and adaptive Kalman filtering, IEEE Trans. Autom. Control, AC-15, 175-184 (1970)</td> </tr><tr> <td>[28]</td> <td class="space">Mendel, J. M., White noise estimators for seismic data processing in oil exploration, IEEE Trans. Autom. Control, AC-22, 694-706 (1977) · <a href="/0362.93026" class="nowrap">Zbl 0362.93026</a></td> </tr><tr> <td>[29]</td> <td class="space">Mendel, J. M., Minimum-variance deconvolution, IEEE Trans. Geosci. Rem. Sensing, GE-19, 161-171 (1981)</td> </tr><tr> <td>[30]</td> <td class="space">Moir, T. J., Optimal deconvolution smoother, (Proc. IEE Pt D, 133 (1986)), 13-18 · <a href="/0588.93067" class="nowrap">Zbl 0588.93067</a></td> </tr><tr> <td>[31]</td> <td class="space">Moir, T.; Grimble, M. J., Optimal self-tuning filtering, prediction, and smoothing for discrete multivariable processes, IEEE Trans. Autom. Control, AC-29, 128-137 (1984) · <a href="/0537.93063" class="nowrap">Zbl 0537.93063</a></td> </tr><tr> <td>[32]</td> <td class="space">Moir, T. J.; Vishwanath, T. G.; Campbell, D. R., Real-time self-tuning deconvolution filter and smoother, Int. J. Control, 45, 969-985 (1987)</td> </tr><tr> <td>[33]</td> <td class="space">Moir, T. J.; Campbell, D. R.; Dabis, H. S., A polynomial approach to optimal and adaptive filtering with application to speech enhancement, IEEE Trans. Sig. Process., SP-39, 1221-1224 (1991)</td> </tr><tr> <td>[34]</td> <td class="space">Priestley, M. B., (Spectral Analysis and Time Series (1981), Academic Press: Academic Press New York) · <a href="/0537.62075" class="nowrap">Zbl 0537.62075</a></td> </tr><tr> <td>[35]</td> <td class="space">Shieh, L. S.; Tsay, Y. T., Transformation of class of mulivariable control systems to block companion forms, IEEE Trans. Autom. Control, AC-27, 199-302 (1982) · <a href="/0471.93016" class="nowrap">Zbl 0471.93016</a></td> </tr><tr> <td>[36]</td> <td class="space">Strejc, V., (State Space Theory of Discrete Linear Control (1981), Wiley: Wiley New York) · <a href="/0567.93050" class="nowrap">Zbl 0567.93050</a></td> </tr><tr> <td>[37]</td> <td class="space">Tajima, K., Estimation of steady-state Kalman filter gain, IEEE Trans. Autom. Control, AC-23, 944-946 (1978) · <a href="/0387.93050" class="nowrap">Zbl 0387.93050</a></td> </tr><tr> <td>[38]</td> <td class="space">Wang, Y., (Basic Mathematics in Automatic Control (1987), Science Press: Science Press Beijing)</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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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