References
- Ades M. , van Leeuwen P. J . An exploration of the equivalent weights particle filter. Q. J. Roy. Meteorol. Soc. 2012; 139: 820–840.
- Anderson J. L. , Anderson S. L . A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts. Mon. Weather Rev. 1999; 127: 2741.
- Beyou S. , Cuzol A. , Gorthi S. S. , Mémin E . Weighted ensemble transform Kalman filter for image assimilation. Tellus A. 2013; 65: 1–17.
- Bishop C. H. , Etherton R. J. , Majumdar S. J . Adaptive sampling with the ensemble transform Kalman filter. Part I: theoretical aspects. Mon. Weather Rev. 2001; 129: 420–436.
- Bishop C. M . Pattern Recognition and Machine Learning. 2006; Springer, New York.
- Candy J. V . Bayesian Signal Processing–Classical, Modern, and Particle Filtering Methods. 2009; John Wiley, Hoboken..
- Chorin A. J. , Morzfeld M. , Tu X . Implicit particle filters for data assimilation. Commun. Appl. Math. Comput. 2010; 5: 221–240.
- Doucet A. , Godsill S. , Andrieu C . On sequential Monte Carlo sampling methods for Bayesian filtering. Stat. Comput. 2000; 10: 197–208.
- Evensen G . Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res. 1994; 99(C5): 10143.
- Evensen G . The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dynam. 2003; 53: 343.
- Gordon N. J. , Salmond D. J. , Smith A. F. M . Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings F. 1993; 140: 107.
- Hoteit I. , Luo X. , Pham D.-T . Particle Kalman filtering: a nonlinear Bayesian framework for ensemble Kalman filters. Mon. Weather Rev. 2012; 140: 528–542.
- Hoteit I. , Pham D.-T. , Triantafyllou G. , Korres G . A new approximate solution of the optimal nonlinear filter for data assimilation in meteorology and oceanography. Mon. Weather Rev. 2008; 136: 317–334.
- Hunt B. R. , Kostelich E. J. , Szunyogh I . Efficient data assimilation for spatiotemporal chaos: a local ensemble transform Kalman filter. Physica D. 2007; 230: 112–126.
- Julier S. J . The spherical simplex unscented transformation. Proc. Am. Contr. Conf. 2003; 2430–2434.
- Kitagawa G . Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. J. Comp. Graph. Stat. 1996; 5: 1.
- Kotecha J. H. , Djurić P. M . Gaussian particle filtering. IEEE Trans. Signal Process. 2003; 51: 2592.
- Lawson W. G. , Hansen J. A . Implications of stochastic and deterministic filters as ensemble-based data assimilation methods in varying regimes of error growth. Mon. Weather Rev. 2004; 132: 1966–1981.
- Lei J. , Bickel P . A moment matching ensemble filter for nonlinear non-Gaussian data assimilation. Mon. Weather Rev. 2011; 139: 3964–3973.
- Liu J. S . Monte Carlo Strategies in Scientific Computing. 2001; Springer-Verlag, New York..
- Liu J. S. , Chen R . Blind deconvolution via sequential imputations. J. Am. Stat. Assoc. 1995; 90: 567–576.
- Livings D. M. , Dance S. L. , Nichols N. K . Unbiased ensemble square root filters. Physica D. 2008; 237: 1021–1028.
- Lorenz E. N. , Emanuel K. A . Optimal sites for supplementary weather observations: simulations with a small model. J. Atmos. Sci. 1998; 55: 399.
- Morzfeld M. , Tu X. , Atkins E. , Chorin A. J . A random map implementation of implicit filters. J. Comput. Phys. 2012; 231: 2049–2066.
- Musso C. , Oudjane N. , Le Gland F . Doucet A. , de Freitas N. , Gordon N . Improving regularized particle filters. Sequential Monte Carlo Methods in Practice.
- Musso C. , Oudjane N. , Le Gland F . Doucet A. , de Freitas N. , Gordon N . Improving regularized particle filters. Sequential Monte Carlo Methods in Practice.
- Ott E. , Hunt B. R. , Szunyogh I. , Zimin A. V. , Kostelich E. J. , co-authors . A local ensemble Kalman filter for atmospheric data assimilation. Tellus A. 2004; 56: 415.
- Papadakis N. , Mémin E. , Cuzol A. , Gengembre N . Data assimilation with the weighted ensemble Kalman filter. Tellus A. 2010; 62: 673–697.
- Pham D. T . Stochastic methods for sequential data assimilation in strongly nonlinear systems. Mon. Weather Rev. 2001; 129: 1194–1207.
- Pitt M. K. , Shephard N . Filtering via simulation: auxiliary particle filter. J Am Stat Assoc. 1999; 94: 590.
- Rao C. R . Linear Statistical Inference and its Applications. 1973; 2nd ed, John Wiley, New York. Chapter 8.
- Roweis S. , Ghahramani Z . A unifying review of linear Gaussian models. Neural Comput. 1999; 11: 305–345.
- Sakov P. , Oke P. R . Implications of the form of the ensemble transformation in the ensemble square root filters. Mon. Weather Rev. 2008; 136: 1042.
- Smith K. W . Cluster ensemble Kalman filter. Tellus A. 2007; 59: 749–757.
- Snyder C. , Bengtsson T. , Bickel P. , Anderson J . Obstacles to high-dimensional particle filtering. Mon. Weather Rev. 2008; 136: 4629.
- Song H. , Hoteit I. , Cornuelle B. D. , Subramanian A. C . An adaptive approach to mitigate background covariance limitations in the ensemble Kalman filter. Mon. Weather Rev. 2010; 138: 2825.
- Tippett M. K. , Anderson J. L. , Bishop C. H. , Hamill T. M. , Whitaker J. S . Ensemble square root filters. Mon. Weather Rev. 2003; 131: 1485–1490.
- Tipping M. E. , Bishop C. M . Probabilistic principal component analysis. J. Roy. Stat. Soc. B. 1999; 61: 611–622.
- van Leeuwen P. J . Particle filtering in geophysical systems. Mon. Weather Rev. 2009; 137: 4089–4114.
- van Leeuwen P. J . Nonlinear data assimilation in geosciences: an extremely efficient particle filter. Q. J. R. Meteorol. Soc. 2010; 136: 1991–1999.
- van Leeuwen P. J . Efficient nonlinear data-assimilation in geophysical fluid dynamics. Comput. Fluid. 2011; 46: 52–58.
- Wang X. , Bishop C. H. , Julier S. J . Which is better, an ensemble of positive–negative pairs or a centered spherical simplex ensemble?. Mon. Weather Rev. 2004; 132: 1590–1605.
- Xiong X. , Navon I. M. , Uzunoglu B . A note on particle filter with posterior Gaussian resampling. Tellus A. 2006; 58: 456.