On the convergence of the ensemble Kalman filter

Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, the continuous mapping theorem gives convergence in probability of the ensemble members, and Lp bounds on the ensemble then give Lp convergence.

[1]  Michel Loève,et al.  Probability Theory I , 1977 .

[2]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[3]  G. Evensen,et al.  Analysis Scheme in the Ensemble Kalman Filter , 1998 .

[4]  Jeffrey L. Anderson.  An Ensemble Adjustment Kalman Filter for Data Assimilation , 2001 .

[5]  Eugenia Kalnay,et al.  Atmospheric Modeling, Data Assimilation and Predictability , 2002 .

[6]  J. Whitaker,et al.  Ensemble Square Root Filters , 2003, Statistical Methods for Climate Scientists.

[7]  A. Kemball,et al.  Time-dependent Reconstruction of Nonstationary Objects with Tomographic or Interferometric Measurements , 2005, astro-ph/0509472.

[8]  G. Evensen.  Data Assimilation: The Ensemble Kalman Filter , 2006 .

[9]  T. Bengtsson,et al.  Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants , 2007 .

[10]  Yan Li,et al.  Remote sensing data assimilation in environmental models , 2008, 2008 37th IEEE Applied Imagery Pattern Recognition Workshop.

[11]  Dongbin Xiu,et al.  On numerical properties of the ensemble Kalman filter for data assimilation , 2008 .

[12]  Jonathan D. Beezley,et al.  An Ensemble Kalman-Particle Predictor-Corrector Filter for Non-Gaussian Data Assimilation , 2008, ICCS.

[13]  Jonathan D. Beezley,et al.  HIGH-DIMENSIONAL DATA ASSIMILATION AND MORPHING ENSEMBLE KALMAN FILTERS WITH APPLICATIONS IN WILDFIRE MODELING , 2009 .

[14]  Richard A. Frazin,et al.  Tomographic Imaging of Dynamic Objects With the Ensemble Kalman Filter , 2009, IEEE Transactions on Image Processing.

[15]  F. Gland,et al.  Large sample asymptotics for the ensemble Kalman filter , 2009 .

[16]  J. Norris.  Appendix: probability and measure , 1997 .