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Advances in Meteorology
Volume 2016, Article ID 9372786, 18 pages
http://dx.doi.org/10.1155/2016/9372786
Research Article

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

1CNRM, UMR 3589, 42 Av. Coriolis, 31057 Toulouse, France
2INPT-ENM, 42 Av. Coriolis, 31057 Toulouse, France

Received 28 June 2016; Accepted 20 October 2016

Academic Editor: James Cleverly

Copyright © 2016 Olivier Pannekoucke et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. Bengtsson, P. Bickel, and B. Li, “Curseof-dimensionality revisited: collapse of the particle filter in very large scale systems,” in Collections, pp. 316–334, Institute of Mathematical Statistics Collections, 2008. View at Publisher · View at Google Scholar
  2. C. Snyder, T. Bengtsson, P. Bickel, and J. L. Anderson, “Obstacles to high-dimensional particle filtering,” Monthly Weather Review, vol. 136, no. 12, pp. 4629–4640, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. R. Bellman, Adaptive Control Processes: A Guided Tour, Princeton University Press, 1961. View at MathSciNet
  4. M. Bocquet, C. A. Pires, and L. Wu, “Beyond gaussian statistical modeling in geophysical data assimilation,” Monthly Weather Review, vol. 138, no. 8, pp. 2997–3023, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Doucet, N. de Freita, N. Gordon, and A. Smith, Sequential Monte Carlo Methods in Practice, Springer, Berlin, Germany, 2001.
  6. P. J. van Leeuwen, “A variance-minimizing filter for large-scale applications,” Monthly Weather Review, vol. 131, no. 9, pp. 1175–2084, 2003. View at Publisher · View at Google Scholar
  7. G. Evensen, “Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics,” Journal of Geophysical Research, vol. 99, no. 5, pp. 10143–10162, 1994. View at Publisher · View at Google Scholar
  8. N. J. Gordon, D. J. Salmond, and A. F. M. Smith, “Novel approach to nonlinear/non-gaussian Bayesian state estimation,” IEE Proceedings, Part F: Radar and Signal Processing, vol. 140, no. 2, pp. 107–113, 1993. View at Publisher · View at Google Scholar · View at Scopus
  9. P. Del Moral, Feynman-Kac Formulae: Ge-Nealogical and Interacting Particle Systems with Applications, Springer, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  10. F. Le Gland, V. Monbet, and V.-D. Tran, “Large sample asymptotics for the ensemble Kalman filter,” I. N. R. I. A 7014, 2009. View at Google Scholar
  11. J. Mandel, L. Cobb, and J. D. Beezley, “On the convergence of the ensemble Kalman filter,” Applications of Mathematics, vol. 56, no. 6, pp. 533–541, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. A. Chorin and M. Morzfeld, “Conditions for successful data assimilation,” Journal Geophysical Research, vol. 118, pp. 522–533, 2013. View at Google Scholar
  13. M. Talagrand, “A new look at independence,” The Annals of Probability, vol. 24, no. 1, pp. 1–34, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  14. R. N. Hoffman and E. Kalnay, “Lagged average forecasting, an alternative to Monte Carlo forecasting,” Tellus A, vol. 35, no. 2, pp. 100–118, 1983. View at Google Scholar · View at Scopus
  15. A. R. Lawrence and J. A. Hansen, “A transformed lagged ensemble forecasting technique for increasing ensemble size,” Monthly Weather Review, vol. 135, no. 4, pp. 1424–1438, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. Z. Ben Bouallègue, S. E. Theis, and C. Gebhardt, “Enhancing COSMO-DE ensemble forecasts by inexpensive techniques,” Meteorologische Zeitschrift, vol. 22, no. 1, pp. 49–59, 2013. View at Publisher · View at Google Scholar · View at Scopus
  17. L. Descamps, C. Labadie, A. Joly, E. Bazile, P. Arbogast, and P. Cébron, “PEARP, the Météo-France short-range ensemble prediction system,” Quarterly Journal of the Royal Meteorological Society, vol. 141, no. 690, pp. 1671–1685, 2015. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Milan, D. Schüttemeyer, T. Bick, and C. Simmer, “A sequential ensemble prediction system at convection-permitting scales,” Meteorology and Atmospheric Physics, vol. 123, no. 1-2, pp. 17–31, 2014. View at Publisher · View at Google Scholar · View at Scopus
  19. L. Raynaud, O. Pannekoucke, P. Arbogast, and F. Bouttier, “Application of a Bayesian weighting for short-range lagged ensemble forecasting at the convective scale,” Quarterly Journal of the Royal Meteorological Society, vol. 141, no. 687, pp. 459–468, 2015. View at Publisher · View at Google Scholar · View at Scopus
  20. D. J. Patil, B. R. Hunt, E. Kalnay, J. A. Yorke, and E. Ott, “Local low dimensionality of atmospheric dynamics,” Physical Review Letters, vol. 86, no. 26, pp. 5878–5881, 2001. View at Publisher · View at Google Scholar · View at Scopus
  21. A. Weaver and P. Courtier, “Correlation modelling on the sphere using a generalized diffusion equation,” Quarterly Journal Royal Meteorological Society, vol. 127, no. 575, pp. 1815–1846, 2001. View at Publisher · View at Google Scholar
  22. O. Pannekoucke and S. Massart, “Estimation of the local diffusion tensor and normalization for heterogeneous correlation modelling using a diffusion equation,” Quarterly Journal of the Royal Meteorological Society, vol. 134, no. 635, pp. 1425–1438, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. O. Pannekoucke, L. Berre, and G. Desroziers, “Background-error correlation length-scale estimates and their sampling statistics,” Quarterly Journal of the Royal Meteorological Society, vol. 134, no. 631, pp. 497–508, 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. P. L. Houtekamer and H. L. Mitchell, “Data assimilation using an ensemble Kalman filter technique,” Monthly Weather Review, vol. 126, no. 3, pp. 796–811, 1998. View at Publisher · View at Google Scholar · View at Scopus
  25. G. Evensen, Data Assimilation: The Ensemble Kalman Filter, Springer, Berlin, Germany, 2nd edition, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. G. Burgers, P. J. van Leeuwen, and G. Evensen, “Analysis scheme in the ensemble Kalman filter,” Monthly Weather Review, vol. 126, no. 6, pp. 1719–1724, 1998. View at Publisher · View at Google Scholar · View at Scopus
  27. C. Snyder, “Particle filters, the ‘optimal’ proposal and high-dimensional systems,” in Proceedings of the ECMWF Seminar on Data Assimilation for Atmosphere and Ocean, ECMWF, Ed., pp. 1–10, ECMWF, Reading, UK, 2011.
  28. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Stochastic Modelling and Applied Probability, Springer, 1998.
  29. S. M. Berman, Sojourners and Extremes of Stochastic Processes, Wadsworth, Reading, Mass, USA, 1989.