Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network Localization
Information geometry enables a deeper understanding of the methods of statistical inference. In this paper, the problem of nonlinear parameter estimation is considered from a geometric viewpoint using a natural gradient descent on statistical manifolds. It is demonstrated that the nonlinear estimati...
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doaj-6123596aa3574838a3377fcfd31c5b3b2020-11-24T23:03:34ZengMDPI AGEntropy1099-43002017-06-0119730810.3390/e19070308e19070308Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network LocalizationYongqiang Cheng0Xuezhi Wang1Bill Moran2School of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, ChinaSchool of Engineering, RMIT University, Melbourne 3000, AustraliaSchool of Engineering, RMIT University, Melbourne 3000, AustraliaInformation geometry enables a deeper understanding of the methods of statistical inference. In this paper, the problem of nonlinear parameter estimation is considered from a geometric viewpoint using a natural gradient descent on statistical manifolds. It is demonstrated that the nonlinear estimation for curved exponential families can be simply viewed as a deterministic optimization problem with respect to the structure of a statistical manifold. In this way, information geometry offers an elegant geometric interpretation for the solution to the estimator, as well as the convergence of the gradient-based methods. The theory is illustrated via the analysis of a distributed mote network localization problem where the Radio Interferometric Positioning System (RIPS) measurements are used for free mote location estimation. The analysis results demonstrate the advanced computational philosophy of the presented methodology.http://www.mdpi.com/1099-4300/19/7/308information geometrystatistical manifoldsnonlinear estimationnatural gradientmaximum likelihood estimation |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Yongqiang Cheng Xuezhi Wang Bill Moran |
spellingShingle |
Yongqiang Cheng Xuezhi Wang Bill Moran Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network Localization Entropy information geometry statistical manifolds nonlinear estimation natural gradient maximum likelihood estimation |
author_facet |
Yongqiang Cheng Xuezhi Wang Bill Moran |
author_sort |
Yongqiang Cheng |
title |
Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network Localization |
title_short |
Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network Localization |
title_full |
Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network Localization |
title_fullStr |
Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network Localization |
title_full_unstemmed |
Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network Localization |
title_sort |
optimal nonlinear estimation in statistical manifolds with application to sensor network localization |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2017-06-01 |
description |
Information geometry enables a deeper understanding of the methods of statistical inference. In this paper, the problem of nonlinear parameter estimation is considered from a geometric viewpoint using a natural gradient descent on statistical manifolds. It is demonstrated that the nonlinear estimation for curved exponential families can be simply viewed as a deterministic optimization problem with respect to the structure of a statistical manifold. In this way, information geometry offers an elegant geometric interpretation for the solution to the estimator, as well as the convergence of the gradient-based methods. The theory is illustrated via the analysis of a distributed mote network localization problem where the Radio Interferometric Positioning System (RIPS) measurements are used for free mote location estimation. The analysis results demonstrate the advanced computational philosophy of the presented methodology. |
topic |
information geometry statistical manifolds nonlinear estimation natural gradient maximum likelihood estimation |
url |
http://www.mdpi.com/1099-4300/19/7/308 |
work_keys_str_mv |
AT yongqiangcheng optimalnonlinearestimationinstatisticalmanifoldswithapplicationtosensornetworklocalization AT xuezhiwang optimalnonlinearestimationinstatisticalmanifoldswithapplicationtosensornetworklocalization AT billmoran optimalnonlinearestimationinstatisticalmanifoldswithapplicationtosensornetworklocalization |
_version_ |
1725633262751055872 |