Mean-Square Estimation of Nonlinear Functionals via Kalman Filtering
This paper focuses on estimation of a nonlinear functional of state vector (NFS) in discrete-time linear stochastic systems. The NFS represents a nonlinear multivariate functional of state variables, which can indicate useful information of a target system for control. The optimal mean-square estima...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/10/11/630 |
| _version_ | 1818002014986043392 |
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| author | Won Choi Vladimir Shin Il Young Song |
| author_facet | Won Choi Vladimir Shin Il Young Song |
| author_sort | Won Choi |
| collection | DOAJ |
| description | This paper focuses on estimation of a nonlinear functional of state vector (NFS) in discrete-time linear stochastic systems. The NFS represents a nonlinear multivariate functional of state variables, which can indicate useful information of a target system for control. The optimal mean-square estimator of a general NFS represents a function of the Kalman estimate and its error covariance. The polynomial functional of state vector is studied in detail. In this case an optimal estimation algorithm has a closed-form computational procedure. The novel mean-square quadratic estimator is derived. For a general NFS we propose to use the unscented transformation to calculate an optimal estimate. The obtained results are demonstrated on theoretical and practical examples with different types of NFS. Comparative analysis with suboptimal estimators for NFS is presented. The subsequent application of the proposed estimators to linear discrete-time systems demonstrates their practical effectiveness. |
| first_indexed | 2024-04-14T03:40:32Z |
| format | Article |
| id | doaj.art-6abb6bfe2f1a4b3782e530cb3773ddfb |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T03:40:32Z |
| publishDate | 2018-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-6abb6bfe2f1a4b3782e530cb3773ddfb2022-12-22T02:14:32ZengMDPI AGSymmetry2073-89942018-11-01101163010.3390/sym10110630sym10110630Mean-Square Estimation of Nonlinear Functionals via Kalman FilteringWon Choi0Vladimir Shin1Il Young Song2Department of Mathematics, Incheon National University, 119 Academy-ro, Yeonsu-gu, Incheon 406-772, KoreaDepartment of Information and Statistics, Research Institute of Natural Science, Gyeongsang National University, 501 Jinjudaero, Jinju, Gyeongsangnam-do 660-701, KoreaLaser & Sensor System Team, Hanwha Daejeon Plant, 305 Pangyo-ro, Bundang-gu, Seongnam-si 13488, KoreaThis paper focuses on estimation of a nonlinear functional of state vector (NFS) in discrete-time linear stochastic systems. The NFS represents a nonlinear multivariate functional of state variables, which can indicate useful information of a target system for control. The optimal mean-square estimator of a general NFS represents a function of the Kalman estimate and its error covariance. The polynomial functional of state vector is studied in detail. In this case an optimal estimation algorithm has a closed-form computational procedure. The novel mean-square quadratic estimator is derived. For a general NFS we propose to use the unscented transformation to calculate an optimal estimate. The obtained results are demonstrated on theoretical and practical examples with different types of NFS. Comparative analysis with suboptimal estimators for NFS is presented. The subsequent application of the proposed estimators to linear discrete-time systems demonstrates their practical effectiveness.https://www.mdpi.com/2073-8994/10/11/630nonlinear functionalquadratic functionalmean square errordiscrete-time systemKalman filteringmultivariate normal distribution |
| spellingShingle | Won Choi Vladimir Shin Il Young Song Mean-Square Estimation of Nonlinear Functionals via Kalman Filtering Symmetry nonlinear functional quadratic functional mean square error discrete-time system Kalman filtering multivariate normal distribution |
| title | Mean-Square Estimation of Nonlinear Functionals via Kalman Filtering |
| title_full | Mean-Square Estimation of Nonlinear Functionals via Kalman Filtering |
| title_fullStr | Mean-Square Estimation of Nonlinear Functionals via Kalman Filtering |
| title_full_unstemmed | Mean-Square Estimation of Nonlinear Functionals via Kalman Filtering |
| title_short | Mean-Square Estimation of Nonlinear Functionals via Kalman Filtering |
| title_sort | mean square estimation of nonlinear functionals via kalman filtering |
| topic | nonlinear functional quadratic functional mean square error discrete-time system Kalman filtering multivariate normal distribution |
| url | https://www.mdpi.com/2073-8994/10/11/630 |
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