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Information geometric nonlinear filtering

Newton, NJ (2015) 'Information geometric nonlinear filtering.' Infinite Dimensional Analysis, Quantum Probability and Related Topics, 18 (2). ISSN 0219-0257

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© 2015 World Scientific Publishing Company. This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on a Hilbert information manifold. This supports the Fisher metric as a pseudo-Riemannian metric. Flows of Shannon information are shown to be connected with the quadratic variation of the process of posterior distributions in this metric. Apart from providing a suitable setting in which to study such information-theoretic properties, the Hilbert manifold has an appropriate topology from the point of view of multi-objective filter approximations. A general class of finite-dimensional exponential filters is shown to fit within this framework, and an intrinsic evolution equation, involving Amari's -1-covariant derivative, is developed for such filters. Three example systems, one of infinite dimension, are developed in detail.

Item Type: Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Jim Jamieson
Date Deposited: 10 Jul 2015 09:43
Last Modified: 23 Jan 2019 05:16

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