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Information geometric nonlinear filtering

Newton, Nigel J (2015) 'Information geometric nonlinear filtering.' Infinite Dimensional Analysis Quantum Probability and related topics, 18 (02). ISSN 0219-0257

1502.04638.pdf - Submitted Version

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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
Uncontrolled Keywords: Information geometry, information theory, nonlinear filtering, Fisher metric, quadratic variation
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: 06 Oct 2020 11:15

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