Information Geometric Nonlinear Filtering
| Autor: | Newton, Nigel J. |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Infinite Dimensional Analysis, Quantum Probability and Related Topics, 18 (2015), 1550014 (24 pages), World Scientific Publishing Company |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1142/S0219025715500149 |
| Popis: | 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. Comment: 30 pages. To be published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics |
| Databáze: | arXiv |
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