A finite dimensional filter with exponential conditional density
In this paper we consider the continuous-time nonlinear filtering problem, which has an infinite-dimensional solution in general, as proved by Chaleyat-Maurel and Michel (1984). There are few examples of nonlinear systems for which the optimal filter is finite dimensional, in particular the Kalman,...
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| creator | Brigo, D. LeGland, F. |
| description | In this paper we consider the continuous-time nonlinear filtering problem, which has an infinite-dimensional solution in general, as proved by Chaleyat-Maurel and Michel (1984). There are few examples of nonlinear systems for which the optimal filter is finite dimensional, in particular the Kalman, Benes, and Daum filters. In the present paper, we construct new classes of scalar nonlinear systems admitting finite-dimensional filters. We consider a given (nonlinear) diffusion coefficient for the state equation, a given (nonlinear) observation function, and a given finite-dimensional exponential family of probability densities. We construct a drift for the state equation such that the resulting nonlinear system admits a finite-dimensional filter evolving in the prescribed exponential family, provided the coefficients of the exponential family include the observation function and its square. |
| doi_str_mv | 10.1109/CDC.1997.657749 |
| format | Conference Proceeding |
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There are few examples of nonlinear systems for which the optimal filter is finite dimensional, in particular the Kalman, Benes, and Daum filters. In the present paper, we construct new classes of scalar nonlinear systems admitting finite-dimensional filters. We consider a given (nonlinear) diffusion coefficient for the state equation, a given (nonlinear) observation function, and a given finite-dimensional exponential family of probability densities. We construct a drift for the state equation such that the resulting nonlinear system admits a finite-dimensional filter evolving in the prescribed exponential family, provided the coefficients of the exponential family include the observation function and its square.</description><identifier>ISSN: 0191-2216</identifier><identifier>ISBN: 0780341872</identifier><identifier>ISBN: 9780780341876</identifier><identifier>DOI: 10.1109/CDC.1997.657749</identifier><language>eng</language><publisher>IEEE</publisher><subject>Communities ; Ear ; Electronic mail ; Filtering ; Kalman filters ; Linear systems ; Nonlinear equations ; Nonlinear filters ; Nonlinear systems ; Risk management</subject><ispartof>Proceedings of the 36th IEEE Conference on Decision and Control, 1997, Vol.2, p.1643-1644 vol.2</ispartof><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/657749$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>309,310,776,780,785,786,2051,4035,4036,27904,54898</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/657749$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Brigo, D.</creatorcontrib><creatorcontrib>LeGland, F.</creatorcontrib><title>A finite dimensional filter with exponential conditional density</title><title>Proceedings of the 36th IEEE Conference on Decision and Control</title><addtitle>CDC</addtitle><description>In this paper we consider the continuous-time nonlinear filtering problem, which has an infinite-dimensional solution in general, as proved by Chaleyat-Maurel and Michel (1984). There are few examples of nonlinear systems for which the optimal filter is finite dimensional, in particular the Kalman, Benes, and Daum filters. In the present paper, we construct new classes of scalar nonlinear systems admitting finite-dimensional filters. We consider a given (nonlinear) diffusion coefficient for the state equation, a given (nonlinear) observation function, and a given finite-dimensional exponential family of probability densities. We construct a drift for the state equation such that the resulting nonlinear system admits a finite-dimensional filter evolving in the prescribed exponential family, provided the coefficients of the exponential family include the observation function and its square.</description><subject>Communities</subject><subject>Ear</subject><subject>Electronic mail</subject><subject>Filtering</subject><subject>Kalman filters</subject><subject>Linear systems</subject><subject>Nonlinear equations</subject><subject>Nonlinear filters</subject><subject>Nonlinear systems</subject><subject>Risk management</subject><issn>0191-2216</issn><isbn>0780341872</isbn><isbn>9780780341876</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>1997</creationdate><recordtype>conference_proceeding</recordtype><sourceid>6IE</sourceid><sourceid>RIE</sourceid><recordid>eNotj81Kw0AURgdUsK2uBVd5gcR7Z8b52VmiVaHgRtclydyLI-mkJAPat7cSVx8cDgc-IW4QKkTwd_VjXaH3tjL31mp_JpZgHSiNzspzsQD0WEqJ5lIsp-kLABwYsxAP64JjipmKEPeUpjikpj-hPtNYfMf8WdDPYUiUcjzxbkgh5tkJf3Y-XokLbvqJrv93JT42T-_1S7l9e36t19sySlS51M4r5wJx6DhoZ4LS2joD7AI3FrT3DK0PaJldC8S67QzrIGXbIbSk1Urczt1IRLvDGPfNeNzNZ9Uv7gZJqQ</recordid><startdate>1997</startdate><enddate>1997</enddate><creator>Brigo, D.</creator><creator>LeGland, F.</creator><general>IEEE</general><scope>6IE</scope><scope>6IL</scope><scope>CBEJK</scope><scope>RIE</scope><scope>RIL</scope></search><sort><creationdate>1997</creationdate><title>A finite dimensional filter with exponential conditional density</title><author>Brigo, D. ; LeGland, F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-i213t-489388defdcfd486d3447860f8dfa70499f0b9d17ff8b0ef4bc6f4d22bc10be43</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>1997</creationdate><topic>Communities</topic><topic>Ear</topic><topic>Electronic mail</topic><topic>Filtering</topic><topic>Kalman filters</topic><topic>Linear systems</topic><topic>Nonlinear equations</topic><topic>Nonlinear filters</topic><topic>Nonlinear systems</topic><topic>Risk management</topic><toplevel>online_resources</toplevel><creatorcontrib>Brigo, D.</creatorcontrib><creatorcontrib>LeGland, F.</creatorcontrib><collection>IEEE Electronic Library (IEL) Conference Proceedings</collection><collection>IEEE Proceedings Order Plan All Online (POP All Online) 1998-present by volume</collection><collection>IEEE Xplore All Conference Proceedings</collection><collection>IEEE Electronic Library (IEL)</collection><collection>IEEE Proceedings Order Plans (POP All) 1998-Present</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Brigo, D.</au><au>LeGland, F.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>A finite dimensional filter with exponential conditional density</atitle><btitle>Proceedings of the 36th IEEE Conference on Decision and Control</btitle><stitle>CDC</stitle><date>1997</date><risdate>1997</risdate><volume>2</volume><spage>1643</spage><epage>1644 vol.2</epage><pages>1643-1644 vol.2</pages><issn>0191-2216</issn><isbn>0780341872</isbn><isbn>9780780341876</isbn><abstract>In this paper we consider the continuous-time nonlinear filtering problem, which has an infinite-dimensional solution in general, as proved by Chaleyat-Maurel and Michel (1984). There are few examples of nonlinear systems for which the optimal filter is finite dimensional, in particular the Kalman, Benes, and Daum filters. In the present paper, we construct new classes of scalar nonlinear systems admitting finite-dimensional filters. We consider a given (nonlinear) diffusion coefficient for the state equation, a given (nonlinear) observation function, and a given finite-dimensional exponential family of probability densities. We construct a drift for the state equation such that the resulting nonlinear system admits a finite-dimensional filter evolving in the prescribed exponential family, provided the coefficients of the exponential family include the observation function and its square.</abstract><pub>IEEE</pub><doi>10.1109/CDC.1997.657749</doi><oa>free_for_read</oa></addata></record> |
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| ispartof | Proceedings of the 36th IEEE Conference on Decision and Control, 1997, Vol.2, p.1643-1644 vol.2 |
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| language | eng |
| recordid | cdi_ieee_primary_657749 |
| source | IEEE Electronic Library (IEL) Conference Proceedings |
| subjects | Communities Ear Electronic mail Filtering Kalman filters Linear systems Nonlinear equations Nonlinear filters Nonlinear systems Risk management |
| title | A finite dimensional filter with exponential conditional density |
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