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

Abstract: In this paper, firstly, manifold PD(n) consisting of all n× n symmetric positive-definite matrices is introduced based on matrix information geometry; Secondly, the geometrical structures of information submanifold of PD(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.