From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality
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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Meteorology |
| Online Access: | http://dx.doi.org/10.1155/2016/9372786 |
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| author | Olivier Pannekoucke Pierrick Cébron Niels Oger Philippe Arbogast |
| author_facet | Olivier Pannekoucke Pierrick Cébron Niels Oger Philippe Arbogast |
| author_sort | Olivier Pannekoucke |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-de523f2e4ffb4987a7a25a16ff39fb7e |
| institution | OA Journals |
| issn | 1687-9309 1687-9317 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Meteorology |
| spelling | doaj-art-de523f2e4ffb4987a7a25a16ff39fb7e2025-08-20T02:21:21ZengWileyAdvances in Meteorology1687-93091687-93172016-01-01201610.1155/2016/93727869372786From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of DimensionalityOlivier Pannekoucke0Pierrick Cébron1Niels Oger2Philippe Arbogast3CNRM, UMR 3589, 42 Av. Coriolis, 31057 Toulouse, FranceCNRM, UMR 3589, 42 Av. Coriolis, 31057 Toulouse, FranceCNRM, UMR 3589, 42 Av. Coriolis, 31057 Toulouse, FranceCNRM, UMR 3589, 42 Av. Coriolis, 31057 Toulouse, FranceThe 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.http://dx.doi.org/10.1155/2016/9372786 |
| spellingShingle | Olivier Pannekoucke Pierrick Cébron Niels Oger Philippe Arbogast From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality Advances in Meteorology |
| title | From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality |
| title_full | From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality |
| title_fullStr | From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality |
| title_full_unstemmed | From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality |
| title_short | From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality |
| title_sort | from the kalman filter to the particle filter a geometrical perspective of the curse of dimensionality |
| url | http://dx.doi.org/10.1155/2016/9372786 |
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