A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking
A new sparse Gauss-Hermite cubature rule is designed to avoid dimension explosion caused by the traditional full tensor-product based Gauss-Hermite cubature rule. Although Smolyak’s quadrature rule can successfully generate sparse cubature points for high dimensional integral, it has a potential dra...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Modelling and Simulation in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2017/2783781 |
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| author | Lijun Peng Xiaojun Duan Jubo Zhu |
| author_facet | Lijun Peng Xiaojun Duan Jubo Zhu |
| author_sort | Lijun Peng |
| collection | DOAJ |
| description | A new sparse Gauss-Hermite cubature rule is designed to avoid dimension explosion caused by the traditional full tensor-product based Gauss-Hermite cubature rule. Although Smolyak’s quadrature rule can successfully generate sparse cubature points for high dimensional integral, it has a potential drawback that some cubature points generated by Smolyak’s rule have negative weights, which may result in instability for the computation. A relative-weight-ratio criterion based sparse Gauss-Hermite rule is presented in this paper, in which cubature points are kept symmetric in the input space and corresponding weights are guaranteed to be positive. The generation of the new sparse cubature points set is simple and meaningful for practice. The difference between our new sparse Gauss-Hermite cubature rule and other cubature rules is analysed. Simulation results show that, compared with Kalman filter with those types of full tensor-product based Gauss-Hermite rules, our new sparse Gauss-Hermite cubature rule based Kalman filter can lead to a substantially reduced number of cubature points, more stable computation capability, and maintaining the accuracy of integration at the same time. |
| format | Article |
| id | doaj-art-83f46432dbb846d88d0c45a01a9729d8 |
| institution | Kabale University |
| issn | 1687-5591 1687-5605 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Modelling and Simulation in Engineering |
| spelling | doaj-art-83f46432dbb846d88d0c45a01a9729d82025-02-03T05:59:43ZengWileyModelling and Simulation in Engineering1687-55911687-56052017-01-01201710.1155/2017/27837812783781A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target TrackingLijun Peng0Xiaojun Duan1Jubo Zhu2College of Science, National University of Defense Technology, Changsha, Hunan 410073, ChinaCollege of Science, National University of Defense Technology, Changsha, Hunan 410073, ChinaCollege of Science, National University of Defense Technology, Changsha, Hunan 410073, ChinaA new sparse Gauss-Hermite cubature rule is designed to avoid dimension explosion caused by the traditional full tensor-product based Gauss-Hermite cubature rule. Although Smolyak’s quadrature rule can successfully generate sparse cubature points for high dimensional integral, it has a potential drawback that some cubature points generated by Smolyak’s rule have negative weights, which may result in instability for the computation. A relative-weight-ratio criterion based sparse Gauss-Hermite rule is presented in this paper, in which cubature points are kept symmetric in the input space and corresponding weights are guaranteed to be positive. The generation of the new sparse cubature points set is simple and meaningful for practice. The difference between our new sparse Gauss-Hermite cubature rule and other cubature rules is analysed. Simulation results show that, compared with Kalman filter with those types of full tensor-product based Gauss-Hermite rules, our new sparse Gauss-Hermite cubature rule based Kalman filter can lead to a substantially reduced number of cubature points, more stable computation capability, and maintaining the accuracy of integration at the same time.http://dx.doi.org/10.1155/2017/2783781 |
| spellingShingle | Lijun Peng Xiaojun Duan Jubo Zhu A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking Modelling and Simulation in Engineering |
| title | A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking |
| title_full | A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking |
| title_fullStr | A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking |
| title_full_unstemmed | A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking |
| title_short | A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking |
| title_sort | new sparse gauss hermite cubature rule based on relative weight ratios for bearing ranging target tracking |
| url | http://dx.doi.org/10.1155/2017/2783781 |
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