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Entropy 2017, 19(2), 54; doi:10.3390/e19020054

Information Geometric Approach to Recursive Update in Nonlinear Filtering

School of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China
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Academic Editor: Geert Verdoolaege
Received: 25 November 2016 / Revised: 14 January 2017 / Accepted: 20 January 2017 / Published: 26 January 2017
(This article belongs to the Special Issue Information Geometry II)
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Abstract

The measurement update stage in the nonlinear filtering is considered in the viewpoint of information geometry, and the filtered state is considered as an optimization estimation in parameter space has been corresponded with the iteration in the statistical manifold, then a recursive method is proposed in this paper. This method is derived based on the natural gradient descent on the statistical manifold, which constructed by the posterior probability density function (PDF) of state conditional on the measurement. The derivation procedure is processing in the geometric viewpoint, and gives a geometric interpretation for the iteration update. Besides, the proposed method can be seen as an extended for the Kalman filter and its variants. For the one step in our proposed method, it is identical to the Extended Kalman filter (EKF) in the nonlinear case, while traditional Kalman filter in the linear case. Benefited from the natural gradient descent used in the update stage, our proposed method performs better than the existing methods, and the results have showed in the numerical experiments. View Full-Text
Keywords: information geometry; nonlinear filtering; Kalman filter; Bayesian filtering; natural gradient descent information geometry; nonlinear filtering; Kalman filter; Bayesian filtering; natural gradient descent
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Li, Y.; Cheng, Y.; Li, X.; Hua, X.; Qin, Y. Information Geometric Approach to Recursive Update in Nonlinear Filtering. Entropy 2017, 19, 54.

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