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From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality
Joint Authors
Pannekoucke, Olivier
Cébron, Pierrick
Oger, Niels
Arbogast, Philippe
Source
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-11-30
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Pannekoucke, Olivier& Cébron, Pierrick& Oger, Niels& Arbogast, Philippe. 2016. From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality. Advances in Meteorology،Vol. 2016, no. 2016, pp.1-18.
https://search.emarefa.net/detail/BIM-1095723
Modern Language Association (MLA)
Pannekoucke, Olivier…[et al.]. From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality. Advances in Meteorology No. 2016 (2016), pp.1-18.
https://search.emarefa.net/detail/BIM-1095723
American Medical Association (AMA)
Pannekoucke, Olivier& Cébron, Pierrick& Oger, Niels& Arbogast, Philippe. From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality. Advances in Meteorology. 2016. Vol. 2016, no. 2016, pp.1-18.
https://search.emarefa.net/detail/BIM-1095723
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1095723