Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks
In this paper, firstly, manifoldPD(n)consisting of alln×nsymmetric positive-definite matrices is introduced based on matrix information geometry; Secondly, the geometrical structures of information submanifold ofPD(n)are presented including metric, geodesic and geodesic distance; Thirdly, the inform...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-03-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/19/3/131 |
| _version_ | 1818035802149486592 |
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| author | Hao Xu Huafei Sun Aung Naing Win |
| author_facet | Hao Xu Huafei Sun Aung Naing Win |
| author_sort | Hao Xu |
| collection | DOAJ |
| description | In this paper, firstly, manifoldPD(n)consisting of alln×nsymmetric positive-definite matrices is introduced based on matrix information geometry; Secondly, the geometrical structures of information submanifold ofPD(n)are presented including metric, geodesic and geodesic distance; Thirdly, the information resolution with sensor networks is presented by three classical measurement models based on information submanifold; Finally, the bearing-only tracking by single sensor is introduced by the Fisher information matrix. The preliminary analysis results introduced in this paper indicate that information submanifold is able to offer consistent and more comprehensive means to understand and solve sensor network problems for targets resolution and tracking, which are not easily handled by some conventional analysis methods. |
| first_indexed | 2024-12-10T07:00:50Z |
| format | Article |
| id | doaj.art-0d439dc6b9094eada83027a4fa726676 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-12-10T07:00:50Z |
| publishDate | 2017-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0d439dc6b9094eada83027a4fa7266762022-12-22T01:58:20ZengMDPI AGEntropy1099-43002017-03-0119313110.3390/e19030131e19030131Information Submanifold Based on SPD Matrices and Its Applications to Sensor NetworksHao Xu0Huafei Sun1Aung Naing Win2The School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, ChinaThe School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, ChinaThe School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, ChinaIn this paper, firstly, manifoldPD(n)consisting of alln×nsymmetric positive-definite matrices is introduced based on matrix information geometry; Secondly, the geometrical structures of information submanifold ofPD(n)are presented including metric, geodesic and geodesic distance; Thirdly, the information resolution with sensor networks is presented by three classical measurement models based on information submanifold; Finally, the bearing-only tracking by single sensor is introduced by the Fisher information matrix. The preliminary analysis results introduced in this paper indicate that information submanifold is able to offer consistent and more comprehensive means to understand and solve sensor network problems for targets resolution and tracking, which are not easily handled by some conventional analysis methods.http://www.mdpi.com/1099-4300/19/3/131symmetric positive-definite matricesinformation submanifoldgeodesic distanceinformation resolution |
| spellingShingle | Hao Xu Huafei Sun Aung Naing Win Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks Entropy symmetric positive-definite matrices information submanifold geodesic distance information resolution |
| title | Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks |
| title_full | Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks |
| title_fullStr | Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks |
| title_full_unstemmed | Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks |
| title_short | Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks |
| title_sort | information submanifold based on spd matrices and its applications to sensor networks |
| topic | symmetric positive-definite matrices information submanifold geodesic distance information resolution |
| url | http://www.mdpi.com/1099-4300/19/3/131 |
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