Reduced sigma point filters for the propagation of means and covariances through nonlinear transformations
The Unscented Transform (UT) approximates the result of applying a specified nonlinear transformation to a given mean and covariance estimate. The UT works by constructing a set of points, referred to as sigma points, which has the same known statistics, e.g., first and second and possibly higher mo...
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| creator | Julier, S.J. Uhlmann, J.K. |
| description | The Unscented Transform (UT) approximates the result of applying a specified nonlinear transformation to a given mean and covariance estimate. The UT works by constructing a set of points, referred to as sigma points, which has the same known statistics, e.g., first and second and possibly higher moments, as the given estimate. The given nonlinear transformation Is applied to the set, and the unscented estimate is obtained by computing the statistics of the transformed set of sigma points. For example, the mean and covariance of the transformed set approximates the nonlinear transformation of the original mean and covariance estimate. The computational efficiency of the UT therefore depends on the number of sigma points required to capture the known statistics of the original estimate. In this paper we examine methods for minimizing the number of sigma points for real-time control, estimation, and filtering applications. We demonstrate results in a 3D localization example. |
| doi_str_mv | 10.1109/ACC.2002.1023128 |
| format | Conference Proceeding |
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The UT works by constructing a set of points, referred to as sigma points, which has the same known statistics, e.g., first and second and possibly higher moments, as the given estimate. The given nonlinear transformation Is applied to the set, and the unscented estimate is obtained by computing the statistics of the transformed set of sigma points. For example, the mean and covariance of the transformed set approximates the nonlinear transformation of the original mean and covariance estimate. The computational efficiency of the UT therefore depends on the number of sigma points required to capture the known statistics of the original estimate. In this paper we examine methods for minimizing the number of sigma points for real-time control, estimation, and filtering applications. We demonstrate results in a 3D localization example.</description><identifier>ISSN: 0743-1619</identifier><identifier>ISBN: 0780372980</identifier><identifier>ISBN: 9780780372986</identifier><identifier>EISSN: 2378-5861</identifier><identifier>DOI: 10.1109/ACC.2002.1023128</identifier><language>eng</language><publisher>Piscataway NJ: IEEE</publisher><subject>Applied sciences ; Computational efficiency ; Computer science; control theory; systems ; Control theory. Systems ; Degradation ; Exact sciences and technology ; Filtering ; Jacobian matrices ; Linear approximation ; Monte Carlo methods ; Particle filters ; Sampling methods ; Statistical distributions ; Statistics</subject><ispartof>Proceedings of the 2002 American Control Conference (IEEE Cat. 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We demonstrate results in a 3D localization example.</description><subject>Applied sciences</subject><subject>Computational efficiency</subject><subject>Computer science; control theory; systems</subject><subject>Control theory. Systems</subject><subject>Degradation</subject><subject>Exact sciences and technology</subject><subject>Filtering</subject><subject>Jacobian matrices</subject><subject>Linear approximation</subject><subject>Monte Carlo methods</subject><subject>Particle filters</subject><subject>Sampling methods</subject><subject>Statistical distributions</subject><subject>Statistics</subject><issn>0743-1619</issn><issn>2378-5861</issn><isbn>0780372980</isbn><isbn>9780780372986</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2002</creationdate><recordtype>conference_proceeding</recordtype><sourceid>6IE</sourceid><sourceid>RIE</sourceid><recordid>eNpFkMtLAzEYxIMPsK3eBS-5eNz6JenmcSyLLygIoueSJl_alG12SbaC_72LFTzNYX4zDEPILYM5Y2Aelk0z5wB8zoALxvUZmXChdFVryc7JFJQGobjRcEEmoBaiYpKZKzItZQ_AjJEwIft39EeHnpa4PVjadzENNMR2wFxo6DIddkj73PV2a4fYJdoFekCbCrXJU9d92RxtclhGMHfH7Y6mLrUxoR2jeeTGjsNvslyTy2Dbgjd_OiOfT48fzUu1ent-bZarynHDh0pZZABSSrMRQm4MC1ppg2jAgQpaoLdCeM-9NFJ7Vi-QBwUuLESthGBMzMj9qbe3xdk2jCtcLOs-x4PN32tWK1bXmo_c3YmLiPhvn74UPz6qZvg</recordid><startdate>2002</startdate><enddate>2002</enddate><creator>Julier, S.J.</creator><creator>Uhlmann, J.K.</creator><general>IEEE</general><scope>6IE</scope><scope>6IH</scope><scope>CBEJK</scope><scope>RIE</scope><scope>RIO</scope><scope>IQODW</scope></search><sort><creationdate>2002</creationdate><title>Reduced sigma point filters for the propagation of means and covariances through nonlinear transformations</title><author>Julier, S.J. ; Uhlmann, J.K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c292t-7ae1006669b336b91f8789ee90c07f83eda33dd2d6968d154e2f70cf435733113</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2002</creationdate><topic>Applied sciences</topic><topic>Computational efficiency</topic><topic>Computer science; control theory; systems</topic><topic>Control theory. Systems</topic><topic>Degradation</topic><topic>Exact sciences and technology</topic><topic>Filtering</topic><topic>Jacobian matrices</topic><topic>Linear approximation</topic><topic>Monte Carlo methods</topic><topic>Particle filters</topic><topic>Sampling methods</topic><topic>Statistical distributions</topic><topic>Statistics</topic><toplevel>online_resources</toplevel><creatorcontrib>Julier, S.J.</creatorcontrib><creatorcontrib>Uhlmann, J.K.</creatorcontrib><collection>IEEE Electronic Library (IEL) Conference Proceedings</collection><collection>IEEE Proceedings Order Plan (POP) 1998-present by volume</collection><collection>IEEE Xplore All Conference Proceedings</collection><collection>IEEE Electronic Library (IEL)</collection><collection>IEEE Proceedings Order Plans (POP) 1998-present</collection><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Julier, S.J.</au><au>Uhlmann, J.K.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Reduced sigma point filters for the propagation of means and covariances through nonlinear transformations</atitle><btitle>Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301)</btitle><stitle>ACC</stitle><date>2002</date><risdate>2002</risdate><volume>2</volume><spage>887</spage><epage>892 vol.2</epage><pages>887-892 vol.2</pages><issn>0743-1619</issn><eissn>2378-5861</eissn><isbn>0780372980</isbn><isbn>9780780372986</isbn><abstract>The Unscented Transform (UT) approximates the result of applying a specified nonlinear transformation to a given mean and covariance estimate. The UT works by constructing a set of points, referred to as sigma points, which has the same known statistics, e.g., first and second and possibly higher moments, as the given estimate. The given nonlinear transformation Is applied to the set, and the unscented estimate is obtained by computing the statistics of the transformed set of sigma points. For example, the mean and covariance of the transformed set approximates the nonlinear transformation of the original mean and covariance estimate. The computational efficiency of the UT therefore depends on the number of sigma points required to capture the known statistics of the original estimate. In this paper we examine methods for minimizing the number of sigma points for real-time control, estimation, and filtering applications. We demonstrate results in a 3D localization example.</abstract><cop>Piscataway NJ</cop><pub>IEEE</pub><doi>10.1109/ACC.2002.1023128</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002, Vol.2, p.887-892 vol.2 |
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| source | IEEE Electronic Library (IEL) Conference Proceedings |
| subjects | Applied sciences Computational efficiency Computer science control theory systems Control theory. Systems Degradation Exact sciences and technology Filtering Jacobian matrices Linear approximation Monte Carlo methods Particle filters Sampling methods Statistical distributions Statistics |
| title | Reduced sigma point filters for the propagation of means and covariances through nonlinear transformations |
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