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Consider the class of Ensemble Square Root filtering algorithms for the numerical approximation of the posterior distribution of nonlinear Markovian signals partially observed with linear observations corrupted with independent measurement noise.
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Wang, Xuguang, Bishop, Craig H., Julier, Simon J. Which is better, an ensemble of positive-negative pairs or centered spherical simplex ensemble? Monthly Weather Review, Vol. 132, 1590–1605, 2004
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Leuuwenburgh, Olwijn, Evensen, Geir, Bertino, Laurent, The impact of ensemble filter definition on the assimilation of temperature profiles in the tropical Pacific Quarterly Journal of the Royal Meteorological Society, Vol. 131, 3291–3300, 2005
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Livings, David M., Dance, Sarah L., Nichols, Nancy K., Unbiased Ensemble Square Root Filters. Physica D: Nonlinear Phenomena, Vol. 237, 1021–1028, 2008
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Le Gland, François, Monbet, Valérie, Tran, Vu-Duc, Large sample asymptotics for the ensemble Kalman filter. In: The Oxford handbook of nonlinear filtering, Eds. Crisan, et al., Oxford Univ. Press, Oxford, 598–631, 2011
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Mandel, Jan, Cobb, Loren, Beezley, Jonathan D., On the convergence of the ensemble Kalman filter. Applications of Mathematics, Vol. 56, No. 6, 533–541, 2011
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Bergemann, Kay, Reich, Sebastian, An ensemble Kalman-Bucy filter for continuous data assimilation. Meteorologische Zeitschrift, Vol. 21, No. 3, 213-219, 2012
Kwiatkowski, Evan, Mandel, Jan, Convergence of the Square Root Ensemble Kalman Filter in the Large Ensemble Limit. SIAM/ASA Journal on Uncertainty Quantification, Vol. 3, No. 1, 1–17, 2015
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de Wiljes, Jana, Reich, Sebastian, Stannat, Wilhelm, Long-time stability and accuracy of the ensemble Kalman–Bucy filter for fully observed processes and small measurement noise
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Bishop, Adrian N., Del Moral, Pierre, On the stability of matrix-valued Riccati diffusions. Electronic Journal of Probability, Vol. 24, No. 24, 2019
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Bishop, Adrian N., Del Moral, Pierre, Kamatani, Kengo, Remillard, Bruno, On one-dimensional Riccati diffusions. Annals of Applied Probability, Vol. 29, No. 2, 1127–1187, 2019
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Beyou, Sebastien, Cuzol, Anne, Subrahmanyam Gorthi, Sai, Mémin, Etienne, Weighted ensemble transform Kalman filter for image assimilation. Tellus A: Dynamic Meteorology and Oceanography, Vol. 65, No. 1, 18803, 2013
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Scheutzow, Michael, A stochastic Gronwall lemma. Infin. Dimens. Anal. Quantum Probab. Relat. Top., Vol. 16, 1350019, 4 pp, 2013
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2019
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Bishop, Adrian N., Del Moral, Pierre, Niclas, Angele, A perturbation analysis of stochastic matrix Riccati diffusions. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, Vol. 56, No. 2, 884–916, 2020
2020
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