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Open AccessArticle

Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks

by Hao Xu 1, Huafei Sun 1,2,* and Aung Naing Win 1
1
The School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
2
Beijing Key Laboratory on MCAACI, Beijing 100081, China
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(3), 131; https://doi.org/10.3390/e19030131
Received: 30 December 2016 / Revised: 1 March 2017 / Accepted: 16 March 2017 / Published: 17 March 2017
(This article belongs to the Special Issue Information Geometry II)
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. View Full-Text
Keywords: symmetric positive-definite matrices; information submanifold; geodesic distance; information resolution symmetric positive-definite matrices; information submanifold; geodesic distance; information resolution
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Xu, H.; Sun, H.; Win, A.N. Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks. Entropy 2017, 19, 131.

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