Understanding the Ensemble Kalman Filter

References

• Alspach, D. L., and Sorenson, H. W. (1972), “Nonlinear Bayesian Estimation Using Gaussian Sum Approximations,” IEEE Transactions on Automatic Control, 17, 439–448.
   Web of Science ®Google Scholar
• Anderson, J., Hoar, T., Raeder, K., Liu, H., Collins, N., Torn, R., and Avellano, A. (2009), “The Data Assimilation Research Testbed: A Community Facility,” Bulletin of the American Meteorological Society, 90, 1283–1296.
   Web of Science ®Google Scholar
• Anderson, J. L. (2001), “An Ensemble Adjustment Kalman Filter for Data Assimilation,” Monthly Weather Review, 129, 2884–2903.
   Web of Science ®Google Scholar
• ——— (2007a), “An Adaptive Covariance Inflation Error Correction Algorithm for Ensemble Filters,” Tellus A, 59, 210–224.
   Google Scholar
• ——— (2007b), “Exploring the Need for Localization in Ensemble Data Assimilation Using an Hierarchical Ensemble Filter,” Physica D, 230, 99–111.
   Web of Science ®Google Scholar
• ——— (2009), “Ensemble Kalman Filters for Large Geophysical Applications,” IEEE Control Systems Magazine, 29, 66–82.
   Web of Science ®Google Scholar
• Anderson, J. L., and Anderson, S. L. (1999), “A Monte Carlo Implementation of the Nonlinear Filtering Problem to Produce Ensemble Assimilations and Forecasts,” Monthly Weather Review, 127, 2741–2758.
   Web of Science ®Google Scholar
• Bengtsson, T., Snyder, C., and Nychka, D. (2003), “Toward a Nonlinear Ensemble Filter for High-Dimensional Systems,” Journal of Geophysical Research, 108, 8775.
   Web of Science ®Google Scholar
• Bishop, C., Etherton, B., and Majumdar, S. (2001), “Adaptive Sampling With the Ensemble Transform Kalman Filter. Part I: Theoretical Aspects,” Monthly Weather Review, 129, 420–436.
   Web of Science ®Google Scholar
• Bocquet, M., Pires, C. A., and Wu, L. (2010), “Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation,” Monthly Weather Review, 138, 2997–3023.
   Web of Science ®Google Scholar
• Burgers, G., van Leeuwen, P. J., and Evensen, G. (1998), “Analysis Scheme in the Ensemble Kalman Filter,” Monthly Weather Review, 126, 1719–1724.
   Web of Science ®Google Scholar
• Evensen, G. (1994), “Sequential Data Assimilation With a Nonlinear Quasi-Geostrophic Model Using Monte Carlo Methods to Forecast Error Statistics,” Journal of Geophysical Research, 99, 10143–10162.
   Web of Science ®Google Scholar
• Evensen, G., and van Leeuwen, P. J. (2000), “An Ensemble Kalman Smoother for Nonlinear Dynamics,” Monthly Weather Review, 128, 1852–1867.
   Web of Science ®Google Scholar
• Fahrmeir, L. (1992), “Posterior Mode Estimation by Extended Kalman Filtering for Multivariate Dynamic Generalized Linear Models,” Journal of the American Statistical Association, 87, 501–509.
   Web of Science ®Google Scholar
• Frei, M., and Künsch, H. R. (2012), “Sequential State and Observation Noise Covariance Estimation Using Combined Ensemble Kalman and Particle Filters,” Monthly Weather Review, 140, 1476–1495.
   Web of Science ®Google Scholar
• Furrer, R., and Bengtsson, T. (2007), “Estimation of High-Dimensional Prior and Posterior Covariance Matrices in Kalman Filter Variants,” Journal of Multivariate Analysis, 98, 227–255.
   Web of Science ®Google Scholar
• Furrer, R., Genton, M. G., and Nychka, D. (2006), “Covariance Tapering for Interpolation of Large Spatial Datasets,” Journal of Computational and Graphical Statistics, 15, 502–523.
   Web of Science ®Google Scholar
• Gaspari, G., and Cohn, S. E. (1999), “Construction of Correlation Functions in Two and Three Dimensions,” Quarterly Journal of the Royal Meteorological Society, 125, 723–757.
   Web of Science ®Google Scholar
• Goldstein, M., and Wooff, D. (2007), Bayes Linear Statistics, Theory & Methods ( Vol. 716), New York: Wiley.
   Google Scholar
• Gordon, N., Salmond, D., and Smith, A. (1993), “Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation,” IEE Proceedings F Radar and Signal Processing,, 140, 107–113.
   Web of Science ®Google Scholar
• Hartigan, J. (1969), “Linear Bayesian Methods,” Journal of the Royal Statistical Society, Series B, 3, 446–454.
   Google Scholar
• Hoteit, I., Pham, D.-T., Gharamti, M., and Luo, X. (2015), “Mitigating Observation Perturbation Sampling Errors in the Stochastic EnKF,” Monthly Weather Review.
   Web of Science ®Google Scholar
• Hoteit, I., Pham, D. T., Triantafyllou, G., and Korres, G. (2008), “A New Approximate Solution of the Optimal Nonlinear Filter for Data Assimilation in Meteorology and Oceanography,” Monthly Weather Review, 136, 317–334.
   Web of Science ®Google Scholar
• Houtekamer, P. L., and Mitchell, H. L. (1998), “Data Assimilation Using an Ensemble Kalman Filter Technique,” Monthly Weather Review, 126, 796–811.
   Web of Science ®Google Scholar
• ——— (2001), “A Sequential Ensemble Kalman Filter for Atmospheric Data Assimilation,” Monthly Weather Review, 129, 123–137.
   Web of Science ®Google Scholar
• Journel, A. G. (1974), “Geostatistics for Conditional Simulation of Ore Bodies,” Economic Geology, 69, 673–687.
   Web of Science ®Google Scholar
• Kalman, R. (1960), “A New Approach to Linear Filtering and Prediction Problems,” Journal of Basic Engineering, 82, 35–45.
   Google Scholar
• Lei, J., Bickel, P., and Snyder, C. (2010), “Comparison of Ensemble Kalman Filters Under Non-Gaussianity,” Monthly Weather Review, 138, 1293–1306.
   Web of Science ®Google Scholar
• Mitchell, H. L., and Houtekamer, P. L. (2000), “An Adaptive Ensemble Kalman Filter,” Monthly Weather Review, 128, 416–433.
   Web of Science ®Google Scholar
• Nychka, D., and Anderson, J. L. (2010), “Data Assimilation,” in Handbook of Spatial Statistics, eds. A. Gelfand, P. Diggle, P. Guttorp, and M. Fuentes, New York, NY: Chapman & Hall/CRC, pp. 477–492.
   Google Scholar
• O’Hagan, A. (1987), “Bayes Linear Estimators for Randomized Response Models,” Journal of the American Statistical Association, 82, 580–585.
   Web of Science ®Google Scholar
• Omre, H. (1987), “Bayesian Kriging merging Observations and Qualified Guesses in Kriging,” Mathematical Geology, 19, 25–39.
   Google Scholar
• Ott, E., Hunt, B. R., Szunyogh, I., Zimin, A. V., Kostelich, E. J., Corazza, M., Kalnay, E., Patil, D. J., and Yorke, J. A. (2004), “A Local Ensemble Kalman Filter for Atmospheric Data Assimilation,” Tellus, 56A, 415–428.
   Google Scholar
• Sherman, J., and Morrison, W. (1950), “Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix,” Annals of Mathematical Statistics, 21, 124–127.
   Google Scholar
• Shumway, R. H., and Stoffer, D. S. (2006), Time Series Analysis and its Applications With R Examples ( 2nd ed.), New York: Springer.
   Google Scholar
• Snyder, C., Bengtsson, T., Bickel, P., and Anderson, J. L. (2008), “Obstacles to High-dimensional Particle Filtering,” Monthly Weather Review, 136, 4629–4640.
   Web of Science ®Google Scholar
• Stordal, A. S., Karlsen, H. A., Nævdal, G., Skaug, H. J., and Vallès, B. (2011), “Bridging the Ensemble Kalman Filter and Particle Filters: The Adaptive Gaussian Mixture Filter,” Computational Geosciences, 15, 293–305.
   Web of Science ®Google Scholar
• Stroud, J. R., and Bengtsson, T. (2007), “Sequential State and Variance Estimation Within the Ensemble Kalman Filter,” Monthly Weather Review, 135, 3194–3208.
   Web of Science ®Google Scholar
• Stroud, J. R., Stein, M. L., Lesht, B. M., Schwab, D. J., and Beletsky, D. (2010), “An Ensemble Kalman Filter and Smoother for Satellite Data Assimilation,” Journal of the American Statistical Association, 105, 978–990.
   Web of Science ®Google Scholar
• Tippett, M. K., Anderson, J. L., Bishop, C. H., Hamill, T. M., and Whitaker, J. S. (2003), “Ensemble Square-Root Filters,” Monthly Weather Review, 131, 1485–1490.
   Web of Science ®Google Scholar
• Tukey, J. W. (1962), “The Future of Data Analysis,” The Annals of Mathematical Statistics, 33, 1–67.
   Google Scholar
• West, M., Harrison, P. J., and Migon, H. S. (1985), “Dynamic Generalized Linear Models and Bayesian Forecasting,” Journal of the American Statistical Association, 80, 73–83.
   Web of Science ®Google Scholar
• Wikle, C. K., and Berliner, L. M. (2007), “A Bayesian Tutorial for Data Assimilation,” Physica D: Nonlinear Phenomena, 230, 1–16.
   Web of Science ®Google Scholar
• Woodbury, M. (1950), “Inverting Modified Matrices,” Memorandum Report 42, Statistical Research Group, Princeton University, Princeton, NJ.
   Google Scholar