Nonlinear Filters: Estimation and Applications
For a nonlinear filtering problem, the most heuristic and easiest approximation is to use the Taylor series expansion and apply the conventional linear recursive Kalman filter algorithm directly to the linearized nonlinear measurement and transition equations. First, it is discussed that the Taylor...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1993
|
| Ausgabe: | 1st ed. 1993 |
| Schriftenreihe: | Lecture Notes in Economics and Mathematical Systems
400 |
| Schlagworte: | |
| Online-Zugang: | BTU01 Volltext |
| Zusammenfassung: | For a nonlinear filtering problem, the most heuristic and easiest approximation is to use the Taylor series expansion and apply the conventional linear recursive Kalman filter algorithm directly to the linearized nonlinear measurement and transition equations. First, it is discussed that the Taylor series expansion approach gives us the biased estimators. Next, a Monte-Carlo simulation filter is proposed, where each expectation of the nonlinear functions is evaluated generating random draws. It is shown from Monte-Carlo experiments that the Monte-Carlo simulation filter yields the unbiased but inefficient estimator. Anotherapproach to the nonlinear filtering problem is to approximate the underlyingdensity functions of the state vector. In this monograph, a nonlinear and nonnormal filter is proposed by utilizing Monte-Carlo integration, in which a recursive algorithm of the weighting functions is derived. The densityapproximation approach gives us an asymptotically unbiased estimator. Moreover, in terms of programming and computational time, the nonlinear filter using Monte-Carlo integration can be easily extended to higher dimensional cases, compared with Kitagawa's nonlinear filter using numericalintegration |
| Beschreibung: | 1 Online-Ressource (XII, 203 p) |
| ISBN: | 9783662222379 |
| DOI: | 10.1007/978-3-662-22237-9 |
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| 520 | |a For a nonlinear filtering problem, the most heuristic and easiest approximation is to use the Taylor series expansion and apply the conventional linear recursive Kalman filter algorithm directly to the linearized nonlinear measurement and transition equations. First, it is discussed that the Taylor series expansion approach gives us the biased estimators. Next, a Monte-Carlo simulation filter is proposed, where each expectation of the nonlinear functions is evaluated generating random draws. It is shown from Monte-Carlo experiments that the Monte-Carlo simulation filter yields the unbiased but inefficient estimator. Anotherapproach to the nonlinear filtering problem is to approximate the underlyingdensity functions of the state vector. In this monograph, a nonlinear and nonnormal filter is proposed by utilizing Monte-Carlo integration, in which a recursive algorithm of the weighting functions is derived. The densityapproximation approach gives us an asymptotically unbiased estimator. Moreover, in terms of programming and computational time, the nonlinear filter using Monte-Carlo integration can be easily extended to higher dimensional cases, compared with Kitagawa's nonlinear filter using numericalintegration | ||
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Datensatz im Suchindex
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| author | Tanizaki, Hisashi |
| author_facet | Tanizaki, Hisashi |
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| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| doi_str_mv | 10.1007/978-3-662-22237-9 |
| edition | 1st ed. 1993 |
| format | Electronic eBook |
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| index_date | 2024-07-03T15:15:35Z |
| indexdate | 2024-07-10T08:56:07Z |
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| spelling | Tanizaki, Hisashi Verfasser aut Nonlinear Filters Estimation and Applications by Hisashi Tanizaki 1st ed. 1993 Berlin, Heidelberg Springer Berlin Heidelberg 1993 1 Online-Ressource (XII, 203 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Economics and Mathematical Systems 400 For a nonlinear filtering problem, the most heuristic and easiest approximation is to use the Taylor series expansion and apply the conventional linear recursive Kalman filter algorithm directly to the linearized nonlinear measurement and transition equations. First, it is discussed that the Taylor series expansion approach gives us the biased estimators. Next, a Monte-Carlo simulation filter is proposed, where each expectation of the nonlinear functions is evaluated generating random draws. It is shown from Monte-Carlo experiments that the Monte-Carlo simulation filter yields the unbiased but inefficient estimator. Anotherapproach to the nonlinear filtering problem is to approximate the underlyingdensity functions of the state vector. In this monograph, a nonlinear and nonnormal filter is proposed by utilizing Monte-Carlo integration, in which a recursive algorithm of the weighting functions is derived. The densityapproximation approach gives us an asymptotically unbiased estimator. Moreover, in terms of programming and computational time, the nonlinear filter using Monte-Carlo integration can be easily extended to higher dimensional cases, compared with Kitagawa's nonlinear filter using numericalintegration Economic Theory/Quantitative Economics/Mathematical Methods Statistics, general Control, Robotics, Mechatronics Economic theory Statistics Control engineering Robotics Mechatronics Schätztheorie (DE-588)4121608-8 gnd rswk-swf Nichtlineares Filter (DE-588)4451051-2 gnd rswk-swf Filtertheorie (DE-588)4154392-0 gnd rswk-swf Nichtlineare Filterung (DE-588)4171753-3 gnd rswk-swf Filter Stochastik (DE-588)4128590-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Nichtlineares Filter (DE-588)4451051-2 s Filter Stochastik (DE-588)4128590-6 s DE-604 Schätztheorie (DE-588)4121608-8 s Nichtlineare Filterung (DE-588)4171753-3 s Filtertheorie (DE-588)4154392-0 s Erscheint auch als Druck-Ausgabe 9783540567721 Erscheint auch als Druck-Ausgabe 9783662222386 https://doi.org/10.1007/978-3-662-22237-9 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Tanizaki, Hisashi Nonlinear Filters Estimation and Applications Economic Theory/Quantitative Economics/Mathematical Methods Statistics, general Control, Robotics, Mechatronics Economic theory Statistics Control engineering Robotics Mechatronics Schätztheorie (DE-588)4121608-8 gnd Nichtlineares Filter (DE-588)4451051-2 gnd Filtertheorie (DE-588)4154392-0 gnd Nichtlineare Filterung (DE-588)4171753-3 gnd Filter Stochastik (DE-588)4128590-6 gnd |
| subject_GND | (DE-588)4121608-8 (DE-588)4451051-2 (DE-588)4154392-0 (DE-588)4171753-3 (DE-588)4128590-6 (DE-588)4113937-9 |
| title | Nonlinear Filters Estimation and Applications |
| title_auth | Nonlinear Filters Estimation and Applications |
| title_exact_search | Nonlinear Filters Estimation and Applications |
| title_exact_search_txtP | Nonlinear Filters Estimation and Applications |
| title_full | Nonlinear Filters Estimation and Applications by Hisashi Tanizaki |
| title_fullStr | Nonlinear Filters Estimation and Applications by Hisashi Tanizaki |
| title_full_unstemmed | Nonlinear Filters Estimation and Applications by Hisashi Tanizaki |
| title_short | Nonlinear Filters |
| title_sort | nonlinear filters estimation and applications |
| title_sub | Estimation and Applications |
| topic | Economic Theory/Quantitative Economics/Mathematical Methods Statistics, general Control, Robotics, Mechatronics Economic theory Statistics Control engineering Robotics Mechatronics Schätztheorie (DE-588)4121608-8 gnd Nichtlineares Filter (DE-588)4451051-2 gnd Filtertheorie (DE-588)4154392-0 gnd Nichtlineare Filterung (DE-588)4171753-3 gnd Filter Stochastik (DE-588)4128590-6 gnd |
| topic_facet | Economic Theory/Quantitative Economics/Mathematical Methods Statistics, general Control, Robotics, Mechatronics Economic theory Statistics Control engineering Robotics Mechatronics Schätztheorie Nichtlineares Filter Filtertheorie Nichtlineare Filterung Filter Stochastik Hochschulschrift |
| url | https://doi.org/10.1007/978-3-662-22237-9 |
| work_keys_str_mv | AT tanizakihisashi nonlinearfiltersestimationandapplications |