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.

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gradientbased estimator curved exponential families deterministic optimization problem radio interferometric positioning system rips measurements statistical manifolds statistical inference distributed mote network localization problem natural gradient descent geometric interpretation methodology problem of nonlinear parameter estimation information geometry free mote location structure

Xuezhi Wang,.Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network Localization. 19 (7),.

Xuezhi Wang,"Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network Localization" 19

Xuezhi Wang,"Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network Localization"