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Global optimal feedbacks for stochastic quantized nonlinear event systems
On the consistency of ensemble transform filter formulations
1. | Universität Potsdam, Institut für Mathematik, Am Neuen Palais 10, D-14469 Potsdam, Germany |
2. | Korea Institute of Atmospheric Prediction Systems, 4F Korea Computer Bldg., 35 Boramae-ro 5-gil, Dongjak-gu, Seoul 156-849, South Korea |
References:
[1] |
J. Amezcua, E. Kalnay, K. Ide and S. Reich, Ensemble transform Kalman-Bucy filters,, Q. J. Royal Meteorological Soc., (2013).
doi: 10.1002/qj.2186. |
[2] |
J. Anderson and S. Anderson, A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts,, Mon. Wea. Rev., 127 (1999), 2741.
doi: 10.1175/1520-0493(1999)127<2741:AMCIOT>2.0.CO;2. |
[3] |
A. Bain and D. Crisan, Fundamentals of Stochastic Filtering, vol. 60 of Stochastic modelling and applied probability,, Springer-Verlag, (2009).
|
[4] |
K. Bergemann, G. Gottwald and S. Reich, Ensemble propagation and continuous matrix factorization algorithms,, Q. J. R. Meteorological Soc., 135 (2009), 1560.
doi: 10.1002/qj.457. |
[5] |
K. Bergemann and S. Reich, A localization technique for ensemble Kalman filters,, Q. J. R. Meteorological Soc., 136 (2010), 701.
doi: 10.1002/qj.591. |
[6] |
K. Bergemann and S. Reich, A mollified ensemble Kalman filter,, Q. J. R. Meteorological Soc., 136 (2010), 1636.
doi: 10.1002/qj.672. |
[7] |
K. Bergemann and S. Reich, An ensemble Kalman-Bucy filter for continuous data assimilation,, Meteorolog. Zeitschrift, 21 (2012), 213.
doi: 10.1127/0941-2948/2012/0307. |
[8] |
D. Crisan and J. Xiong, Approximate McKean-Vlasov representation for a class of SPDEs,, Stochastics, 82 (2010), 53.
doi: 10.1080/17442500902723575. |
[9] |
D. Crisan and J. Xiong, Numerical solution for a class of SPDEs over bounded domains,, Stochastics, (2013).
doi: 10.1051/proc:071916. |
[10] |
G. Evensen, Data Assimilation. The Ensemble Kalman Filter,, Springer-Verlag, (2006).
doi: 10.1007/978-3-642-03711-5. |
[11] |
A. Jazwinski, Stochastic Processes and Filtering Theory,, Academic Press, (1970). Google Scholar |
[12] |
J. Lei and P. Bickel, A moment matching ensemble filter for nonlinear and non-Gaussian data assimilation,, Mon. Weath. Rev., 139 (2011), 3964.
doi: 10.1175/2011MWR3553.1. |
[13] |
E. Lorenz, Deterministic non-periodic flows,, J. Atmos. Sci., 20 (1963), 130. Google Scholar |
[14] |
S. Reich, A dynamical systems framework for intermittent data assimilation,, BIT Numer Math, 51 (2011), 235.
doi: 10.1007/s10543-010-0302-4. |
[15] |
S. Reich, A Gaussian mixture ensemble transform filter,, Q. J. R. Meterolog. Soc., 138 (2012), 222.
doi: 10.1002/qj.898. |
[16] |
M. Tippett, J. Anderson, G. Bishop, T. Hamill and J. Whitaker, Ensemble square root filters,, Mon. Wea. Rev., 131 (2003), 1485.
doi: 10.1175/1520-0493(2003)131<1485:ESRF>2.0.CO;2. |
[17] |
C. Villani, Topics in Optimal Transportation,, American Mathematical Society, (2003).
doi: 10.1007/b12016. |
[18] |
X. Xiong, I. Navon and B. Uzungoglu, A note on the particle filter with posterior Gaussian resampling,, Tellus, 58 (2006), 456.
doi: 10.1111/j.1600-0870.2006.00185.x. |
[19] |
T. Yang, P. Mehta and S. Meyn, Feedback particle filter,, IEEE Trans. on Automatic Control, 58 (2013), 2465.
doi: 10.1109/TAC.2013.2258825. |
show all references
References:
[1] |
J. Amezcua, E. Kalnay, K. Ide and S. Reich, Ensemble transform Kalman-Bucy filters,, Q. J. Royal Meteorological Soc., (2013).
doi: 10.1002/qj.2186. |
[2] |
J. Anderson and S. Anderson, A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts,, Mon. Wea. Rev., 127 (1999), 2741.
doi: 10.1175/1520-0493(1999)127<2741:AMCIOT>2.0.CO;2. |
[3] |
A. Bain and D. Crisan, Fundamentals of Stochastic Filtering, vol. 60 of Stochastic modelling and applied probability,, Springer-Verlag, (2009).
|
[4] |
K. Bergemann, G. Gottwald and S. Reich, Ensemble propagation and continuous matrix factorization algorithms,, Q. J. R. Meteorological Soc., 135 (2009), 1560.
doi: 10.1002/qj.457. |
[5] |
K. Bergemann and S. Reich, A localization technique for ensemble Kalman filters,, Q. J. R. Meteorological Soc., 136 (2010), 701.
doi: 10.1002/qj.591. |
[6] |
K. Bergemann and S. Reich, A mollified ensemble Kalman filter,, Q. J. R. Meteorological Soc., 136 (2010), 1636.
doi: 10.1002/qj.672. |
[7] |
K. Bergemann and S. Reich, An ensemble Kalman-Bucy filter for continuous data assimilation,, Meteorolog. Zeitschrift, 21 (2012), 213.
doi: 10.1127/0941-2948/2012/0307. |
[8] |
D. Crisan and J. Xiong, Approximate McKean-Vlasov representation for a class of SPDEs,, Stochastics, 82 (2010), 53.
doi: 10.1080/17442500902723575. |
[9] |
D. Crisan and J. Xiong, Numerical solution for a class of SPDEs over bounded domains,, Stochastics, (2013).
doi: 10.1051/proc:071916. |
[10] |
G. Evensen, Data Assimilation. The Ensemble Kalman Filter,, Springer-Verlag, (2006).
doi: 10.1007/978-3-642-03711-5. |
[11] |
A. Jazwinski, Stochastic Processes and Filtering Theory,, Academic Press, (1970). Google Scholar |
[12] |
J. Lei and P. Bickel, A moment matching ensemble filter for nonlinear and non-Gaussian data assimilation,, Mon. Weath. Rev., 139 (2011), 3964.
doi: 10.1175/2011MWR3553.1. |
[13] |
E. Lorenz, Deterministic non-periodic flows,, J. Atmos. Sci., 20 (1963), 130. Google Scholar |
[14] |
S. Reich, A dynamical systems framework for intermittent data assimilation,, BIT Numer Math, 51 (2011), 235.
doi: 10.1007/s10543-010-0302-4. |
[15] |
S. Reich, A Gaussian mixture ensemble transform filter,, Q. J. R. Meterolog. Soc., 138 (2012), 222.
doi: 10.1002/qj.898. |
[16] |
M. Tippett, J. Anderson, G. Bishop, T. Hamill and J. Whitaker, Ensemble square root filters,, Mon. Wea. Rev., 131 (2003), 1485.
doi: 10.1175/1520-0493(2003)131<1485:ESRF>2.0.CO;2. |
[17] |
C. Villani, Topics in Optimal Transportation,, American Mathematical Society, (2003).
doi: 10.1007/b12016. |
[18] |
X. Xiong, I. Navon and B. Uzungoglu, A note on the particle filter with posterior Gaussian resampling,, Tellus, 58 (2006), 456.
doi: 10.1111/j.1600-0870.2006.00185.x. |
[19] |
T. Yang, P. Mehta and S. Meyn, Feedback particle filter,, IEEE Trans. on Automatic Control, 58 (2013), 2465.
doi: 10.1109/TAC.2013.2258825. |
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