On the convergence of the ensemble Kalman filter

Applications of Mathematics

Volumn 56, Issue 6, 2011, Pages 533-541

  Mandel, Jan ^a   Cobb, Loren ^a   Beezley, Jonathan D ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

asymptotics; convergence; data assimilation; ensemble; exchangeable random variables; filtering

Indexed keywords

ASYMPTOTICS; CONTINUOUS MAPPING THEOREM; CONVERGENCE; CONVERGENCE IN PROBABILITY; DATA ASSIMILATION; ENSEMBLE; ENSEMBLE KALMAN FILTER; LAW OF LARGE NUMBERS;

FILTRATION; RANDOM VARIABLES;

KALMAN FILTERS;

EID: 84860717050     PISSN: 08627940     EISSN: 15729109     Source Type: Journal    
DOI: 10.1007/s10492-011-0031-2     Document Type: Article

References (17)

1. B.D.O. Anderson, J.B. Moore: Optimal Filtering. Prentice-Hall, Englewood Cliffs, 1979.
2. J. L. Anderson: An ensemble adjustment Kalman filter for data assimilation. Monthly Weather Review 129 (1999), 2884-2903.
3. J.D. Beezley: High-dimensional data assimilation and morphing ensemble Kalman filters with applications in wildfire modeling. PhD. Thesis. Department of Mathematical and Statistical Sciences, University of Colorado Denver, 2009, http://math.cudenver.edu/~jbeezley/jbeezley thesis.pdf.
4. P. Billingsley: Probability and Measure, 3rd edition. John Wiley & Sons Inc., New York, 1995.
5. G. Burgers, P. J. van Leeuwen, G. Evensen: Analysis scheme in the ensemble Kalman filter. Monthly Weather Review 126 (1998), 1719-1724. (Pubitemid 128597660)
6. M.D. Butala, R.A. Frazin, Y. Chen, F. Kamalabadi: Tomographic imaging of dynamic objects with the ensemble Kalman filter. IEEE Trans. Image Proces. 18 (2009), 1573-1587.
7. G. Evensen: Data Assimilation: The Ensemble Kalman Filter. Springer, Berlin, 2007.
8. R.A. Frazin, M.D. Butala, A. Kemball, F. Kamalabadi: Time-dependent reconstruction of nonstationary objects with tomographic or interferometric measurements. Astrophys. J. 635 (2005), L197-L200. (Pubitemid 43082957)
9. R. Furrer, T. Bengtsson: Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants. J. Multivariate Anal. 98 (2007), 227-255. (Pubitemid 44660963)
10. E. Kalnay: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press, Cambridge, 2003.
11. F. Le Gland, V. Monbet, V.-D. Tran: Large Sample Asymptotics for the Ensemble Kalman Filter. Research Report RR-7014, INRIA, August 2009. http://hal.inria.fr/inria-00409060/en/.
12. J. Li, D. Xiu: On numerical properties of the ensemble Kalman filter for data assimilation. Comput. Methods Appl. Mech. Eng. 197 (2008), 3574-3583.
13. J. Mandel, J.D. Beezley: An ensemble Kalman-particle predictor-corrector filter for non-Gaussian data assimilation. ICCS 2009. Lecture Notes in Computer Science, Vol. 5545 (G. Allen, J. Nabrzyski, E. Seidel, G.D. van Albada, J. Dongarra, P.M.A. Sloot, eds.). Springer, 2009, pp. 470-478.
14. J. Mandel, L. Cobb, J.D. Beezley: On the convergence of the ensemble Kalman filter. University of Colorado Denver CCM Report 278, January 2009. http://www.arXiv.org/abs/0901.2951.
15. M.K. Tippett, J. L. Anderson, C.H. Bishop, T.M. Hamill, J. S. Whitaker: Ensemble square root filters. Monthly Weather Review 131 (2003), 1485-1490. (Pubitemid 36953823)
16. A.W. Van der Vaart: Asymptotic Statistics. Cambridge University Press, Cambridge, 2000.
17. A. Vodacek, Y. Li, A. J. Garrett: Remote sensing data assimilation in environmental models. In: AIPR ′08: Proceedings of the 2008 37th IEEE Applied Imagery Pattern Recognition Workshop. IEEE Computer Society, Washington, 2008, pp. 1-5.