From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality

Pannekoucke, O; Cébron, P; Oger, N; Arbogast, P

From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality

Pannekoucke, O Cébron, P Oger, N Arbogast, P

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Publisher:: Hindawi Limited
Publication Type:: Journal Article
Citation:: Advances in Meteorology, 2016, 2016, pp. 1-18
Issue Date:: 2016-01-01

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Field	Value	Language
dc.contributor.author	Pannekoucke, O
dc.contributor.author	Cébron, P
dc.contributor.author	Oger, N
dc.contributor.author	Arbogast, P
dc.date.accessioned	2022-03-21T00:09:24Z
dc.date.available	2022-03-21T00:09:24Z
dc.date.issued	2016-01-01
dc.identifier.citation	Advances in Meteorology, 2016, 2016, pp. 1-18
dc.identifier.issn	1687-9309
dc.identifier.issn	1687-9317
dc.identifier.uri	http://hdl.handle.net/10453/155395
dc.description.abstract	<jats:p>The aim of this contribution is to provide a description of the difference between Kalman filter and particle filter when the state space is of high dimension. In the Gaussian framework, KF and PF give the same theoretical result. However, in high dimension and using finite sampling for the Gaussian distribution, the PF is not able to reproduce the solution produced by the KF. This discrepancy is highlighted from the convergence property of the Gaussian law toward a hypersphere: in high dimension, any finite sample of a Gaussian law lies within a hypersphere centered in the mean of the Gaussian law and of radius square-root of the trace of the covariance matrix. This concentration of probability suggests the use of norm as a criterium that discriminates whether a forecast sample can be compatible or not with a given analysis state. The contribution illustrates important characteristics that have to be considered for the high dimension but does not introduce a new approach to face the curse of dimensionality.</jats:p>
dc.language	en
dc.publisher	Hindawi Limited
dc.relation.ispartof	Advances in Meteorology
dc.relation.isbasedon	10.1155/2016/9372786
dc.rights	info:eu-repo/semantics/restrictedAccess
dc.subject	0401 Atmospheric Sciences
dc.title	From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality
dc.type	Journal Article
utslib.citation.volume	2016
utslib.for	0401 Atmospheric Sciences
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Life Sciences
utslib.copyright.status	recently_added	*
dc.date.updated	2022-03-21T00:09:23Z
pubs.publication-status	Published
pubs.volume	2016

Abstract:

The aim of this contribution is to provide a description of the difference between Kalman filter and particle filter when the state space is of high dimension. In the Gaussian framework, KF and PF give the same theoretical result. However, in high dimension and using finite sampling for the Gaussian distribution, the PF is not able to reproduce the solution produced by the KF. This discrepancy is highlighted from the convergence property of the Gaussian law toward a hypersphere: in high dimension, any finite sample of a Gaussian law lies within a hypersphere centered in the mean of the Gaussian law and of radius square-root of the trace of the covariance matrix. This concentration of probability suggests the use of norm as a criterium that discriminates whether a forecast sample can be compatible or not with a given analysis state. The contribution illustrates important characteristics that have to be considered for the high dimension but does not introduce a new approach to face the curse of dimensionality.

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http://hdl.handle.net/10453/155395