Full Length Article: Information geometry of target tracking sensor networks

Authors:
Yongqiang Cheng;Xuezhi Wang;Mark Morelande;Bill Moran
Affiliations:
School of Electronic Science and Engineering, National University of Defence Technology, Changsha, Hunan, China;Department of Electrical and Electronic Engineering, University of Melbourne, Australia;Department of Electrical and Electronic Engineering, University of Melbourne, Australia;Department of Electrical and Electronic Engineering, University of Melbourne, Australia
Venue:
Information Fusion
Year:
2013

Citing 11
Cited 0

Information geometry of the EM and em algorithms for neural networks

Neural Networks
Natural gradient works efficiently in learning

Neural Computation
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements

Journal of Mathematical Imaging and Vision
2008 Special Issue: Principal whitened gradient for information geometry

Neural Networks
Graphical Models, Exponential Families, and Variational Inference

Graphical Models, Exponential Families, and Variational Inference
FINE: Fisher Information Nonparametric Embedding

IEEE Transactions on Pattern Analysis and Machine Intelligence
Review of "Methods of information geometry" by Shunichi Amari and Hiroshi Nagaoka, American Mathematical Society and Oxford University Press, 2000

IEEE Transactions on Information Theory
Covariance, subspace, and intrinsic Crame´r-Rao bounds

IEEE Transactions on Signal Processing
Statistical inference under multiterminal rate restrictions: a differential geometric approach

IEEE Transactions on Information Theory
Information geometry on hierarchy of probability distributions

IEEE Transactions on Information Theory
Information geometry of Boltzmann machines

IEEE Transactions on Neural Networks

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, the connections between information geometry and performance of sensor networks for target tracking are explored to pursue a better understanding of placement, planning and scheduling issues. Firstly, the integrated Fisher information distance (IFID) between the states of two targets is analyzed by solving the geodesic equations and is adopted as a measure of target resolvability by the sensor. The differences between the IFID and the well known Kullback-Leibler divergence (KLD) are highlighted. We also explain how the energy functional, which is the ''integrated, differential'' KLD, relates to the other distance measures. Secondly, the structures of statistical manifolds are elucidated by computing the canonical Levi-Civita affine connection as well as Riemannian and scalar curvatures. We show the relationship between the Ricci curvature tensor field and the amount of information that can be obtained by the network sensors. Finally, an analytical presentation of statistical manifolds as an immersion in the Euclidean space for distributions of exponential type is given. The significance and potential to address system definition and planning issues using information geometry, such as the sensing capability to distinguish closely spaced targets, calculation of the amount of information collected by sensors and the problem of optimal scheduling of network sensor and resources, etc., are demonstrated. The proposed analysis techniques are presented via three basic sensor network scenarios: a simple range-bearing radar, two bearings-only passive sonars, and three ranges-only detectors, respectively.