On an algebraic method for derivatives estimation and parameter estimation for partial derivatives systems
Identifieur interne : 000088 ( France/Analysis ); précédent : 000087; suivant : 000089On an algebraic method for derivatives estimation and parameter estimation for partial derivatives systems
Auteurs : Rosane Ushirobira [France] ; Anja Korporal [France] ; Wilfrid Perruquetti [France]Source :
Abstract
— In this communication, we discuss two estimation problems dealing with partial derivatives systems. Namely, estimating partial derivatives of a multivariate noisy signal and identifying parameters of partial differential equations. The multivariate noisy signal is expressed as a truncated Taylor expression in a small time interval. An algebraic method can be then used to estimate its partial derivatives in the opera-tional domain. The same approach applies for the parameter identification problem. The main objects in the aforementioned algebraic method are particular differential operators called annihilators. Stafford's theorem can be applied to formalize the left ideal in the Weyl algebra formed by the annihilators. In the spatial domain, iterated integrals present in the estimates yield noise filtering.
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59655 Villeneuve d'Ascq Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.univ-lille1.fr/</ref></desc></org></tutelle><tutelle active="#struct-120930" type="indirect"><org type="institution" xml:id="struct-120930" status="VALID"><orgName>Ecole Centrale de Lille</orgName><desc><address><addrLine>Cité Scientifique - CS 20048 59651 Villeneuve d'Ascq Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.ec-lille.fr/</ref></desc></org></tutelle><tutelle active="#struct-301700" type="indirect"><org type="institution" xml:id="struct-301700" status="VALID"><idno type="IdRef">026404524</idno><idno type="ISNI">0000000121517701</idno><orgName>Université de Lille, Sciences Humaines et Sociales</orgName><desc><address><addrLine>Domaine universitaire du "Pont de Bois"Rue du Barreau BP 60149 59653 Villeneuve d'Ascq Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.univ-lille3.fr/</ref></desc></org></tutelle><tutelle name="UMR9189" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="IdRef">02636817X</idno><idno type="ISNI">0000000122597504</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country></affiliation></author><author><name sortKey="Perruquetti, Wilfrid" sort="Perruquetti, Wilfrid" uniqKey="Perruquetti W" first="Wilfrid" last="Perruquetti">Wilfrid Perruquetti</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-432039" status="VALID"><orgName>Non-Asymptotic estimation for online systems</orgName><orgName type="acronym">NON-A</orgName><date type="start">2015-01-01</date><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/non-a</ref></desc><listRelation><relation active="#struct-104752" type="direct"></relation><relation active="#struct-300009" type="indirect"></relation><relation active="#struct-410272" type="direct"></relation><relation active="#struct-92973" type="indirect"></relation><relation active="#struct-120930" type="indirect"></relation><relation active="#struct-301700" type="indirect"></relation><relation name="UMR9189" active="#struct-441569" type="indirect"></relation></listRelation><tutelles><tutelle active="#struct-104752" type="direct"><org type="laboratory" xml:id="struct-104752" status="VALID"><orgName>INRIA Lille - Nord Europe</orgName><desc><address><addrLine>Parc Scientifique de la Haute Borne 40, avenue Halley Bât.A, Park Plaza 59650 Villeneuve d'Ascq</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/lille/</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle active="#struct-410272" type="direct"><org type="laboratory" xml:id="struct-410272" status="VALID"><idno type="IdRef">18388695X</idno><idno type="RNSR">201521249L</idno><orgName>Centre de Recherche en Informatique, Signal et Automatique de Lille</orgName><orgName type="acronym">CRIStAL</orgName><date type="start">2015-01-01</date><desc><address><addrLine>Bâtiment M3, Université Lille 1, 59655 Villeneuve d'Ascq Cedex FRANCE </addrLine><country key="FR"></country></address><ref type="url">http://www.cristal.univ-lille.fr</ref></desc><listRelation><relation active="#struct-92973" type="direct"></relation><relation active="#struct-120930" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation active="#struct-301700" type="direct"></relation><relation name="UMR9189" active="#struct-441569" type="direct"></relation></listRelation></org></tutelle><tutelle active="#struct-92973" type="indirect"><org type="institution" xml:id="struct-92973" status="VALID"><idno type="IdRef">026404184</idno><orgName>Université de Lille, Sciences et Technologies</orgName><desc><address><addrLine>Cité Scientifique - 59655 Villeneuve d'Ascq Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.univ-lille1.fr/</ref></desc></org></tutelle><tutelle active="#struct-120930" type="indirect"><org type="institution" xml:id="struct-120930" status="VALID"><orgName>Ecole Centrale de Lille</orgName><desc><address><addrLine>Cité Scientifique - CS 20048 59651 Villeneuve d'Ascq Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.ec-lille.fr/</ref></desc></org></tutelle><tutelle active="#struct-301700" type="indirect"><org type="institution" xml:id="struct-301700" status="VALID"><idno type="IdRef">026404524</idno><idno type="ISNI">0000000121517701</idno><orgName>Université de Lille, Sciences Humaines et Sociales</orgName><desc><address><addrLine>Domaine universitaire du "Pont de Bois"Rue du Barreau BP 60149 59653 Villeneuve d'Ascq Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.univ-lille3.fr/</ref></desc></org></tutelle><tutelle name="UMR9189" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="IdRef">02636817X</idno><idno type="ISNI">0000000122597504</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country></affiliation></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">— In this communication, we discuss two estimation problems dealing with partial derivatives systems. Namely, estimating partial derivatives of a multivariate noisy signal and identifying parameters of partial differential equations. The multivariate noisy signal is expressed as a truncated Taylor expression in a small time interval. An algebraic method can be then used to estimate its partial derivatives in the opera-tional domain. The same approach applies for the parameter identification problem. The main objects in the aforementioned algebraic method are particular differential operators called annihilators. Stafford's theorem can be applied to formalize the left ideal in the Weyl algebra formed by the annihilators. In the spatial domain, iterated integrals present in the estimates yield noise filtering.</div></front></TEI><affiliations><list><country><li>France</li></country></list><tree><country name="France"><noRegion><name sortKey="Ushirobira, Rosane" sort="Ushirobira, Rosane" uniqKey="Ushirobira R" first="Rosane" last="Ushirobira">Rosane Ushirobira</name></noRegion><name sortKey="Korporal, Anja" sort="Korporal, Anja" uniqKey="Korporal A" first="Anja" last="Korporal">Anja Korporal</name><name sortKey="Perruquetti, Wilfrid" sort="Perruquetti, Wilfrid" uniqKey="Perruquetti W" first="Wilfrid" last="Perruquetti">Wilfrid Perruquetti</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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