-
Previous Article
Modularity revisited: A novel dynamics-based concept for decomposing complex networks
- JCD Home
- This Issue
-
Next Article
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. |
[1] |
Junyoung Jang, Kihoon Jang, Hee-Dae Kwon, Jeehyun Lee. Feedback control of an HBV model based on ensemble kalman filter and differential evolution. Mathematical Biosciences & Engineering, 2018, 15 (3) : 667-691. doi: 10.3934/mbe.2018030 |
[2] |
Alexander Bibov, Heikki Haario, Antti Solonen. Stabilized BFGS approximate Kalman filter. Inverse Problems & Imaging, 2015, 9 (4) : 1003-1024. doi: 10.3934/ipi.2015.9.1003 |
[3] |
Russell Johnson, Carmen Núñez. The Kalman-Bucy filter revisited. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4139-4153. doi: 10.3934/dcds.2014.34.4139 |
[4] |
Xiaoying Han, Jinglai Li, Dongbin Xiu. Error analysis for numerical formulation of particle filter. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1337-1354. doi: 10.3934/dcdsb.2015.20.1337 |
[5] |
Andrea Arnold, Daniela Calvetti, Erkki Somersalo. Vectorized and parallel particle filter SMC parameter estimation for stiff ODEs. Conference Publications, 2015, 2015 (special) : 75-84. doi: 10.3934/proc.2015.0075 |
[6] |
Qifeng Cheng, Xue Han, Tingting Zhao, V S Sarma Yadavalli. Improved particle swarm optimization and neighborhood field optimization by introducing the re-sampling step of particle filter. Journal of Industrial & Management Optimization, 2019, 15 (1) : 177-198. doi: 10.3934/jimo.2018038 |
[7] |
Laura Martín-Fernández, Gianni Gilioli, Ettore Lanzarone, Joaquín Míguez, Sara Pasquali, Fabrizio Ruggeri, Diego P. Ruiz. A Rao-Blackwellized particle filter for joint parameter estimation and biomass tracking in a stochastic predator-prey system. Mathematical Biosciences & Engineering, 2014, 11 (3) : 573-597. doi: 10.3934/mbe.2014.11.573 |
[8] |
Alexandre J. Chorin, Fei Lu, Robert N. Miller, Matthias Morzfeld, Xuemin Tu. Sampling, feasibility, and priors in data assimilation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4227-4246. doi: 10.3934/dcds.2016.36.4227 |
[9] |
Qiyu Jin, Ion Grama, Quansheng Liu. Convergence theorems for the Non-Local Means filter. Inverse Problems & Imaging, 2018, 12 (4) : 853-881. doi: 10.3934/ipi.2018036 |
[10] |
Hai Huyen Dam, Kok Lay Teo. Variable fractional delay filter design with discrete coefficients. Journal of Industrial & Management Optimization, 2016, 12 (3) : 819-831. doi: 10.3934/jimo.2016.12.819 |
[11] |
Débora A. F. Albanez, Maicon J. Benvenutti. Continuous data assimilation algorithm for simplified Bardina model. Evolution Equations & Control Theory, 2018, 7 (1) : 33-52. doi: 10.3934/eect.2018002 |
[12] |
Z. G. Feng, Kok Lay Teo, N. U. Ahmed, Yulin Zhao, W. Y. Yan. Optimal fusion of sensor data for Kalman filtering. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 483-503. doi: 10.3934/dcds.2006.14.483 |
[13] |
Valerii Maltsev, Michael Pokojovy. On a parabolic-hyperbolic filter for multicolor image noise reduction. Evolution Equations & Control Theory, 2016, 5 (2) : 251-272. doi: 10.3934/eect.2016004 |
[14] |
Kody Law, Abhishek Shukla, Andrew Stuart. Analysis of the 3DVAR filter for the partially observed Lorenz'63 model. Discrete & Continuous Dynamical Systems - A, 2014, 34 (3) : 1061-1078. doi: 10.3934/dcds.2014.34.1061 |
[15] |
Yi Xu, Wenyu Sun. A filter successive linear programming method for nonlinear semidefinite programming problems. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 193-206. doi: 10.3934/naco.2012.2.193 |
[16] |
Abdel-Rahman Hedar, Alaa Fahim. Filter-based genetic algorithm for mixed variable programming. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 99-116. doi: 10.3934/naco.2011.1.99 |
[17] |
Issam S. Strub, Julie Percelay, Olli-Pekka Tossavainen, Alexandre M. Bayen. Comparison of two data assimilation algorithms for shallow water flows. Networks & Heterogeneous Media, 2009, 4 (2) : 409-430. doi: 10.3934/nhm.2009.4.409 |
[18] |
Yuan Pei. Continuous data assimilation for the 3D primitive equations of the ocean. Communications on Pure & Applied Analysis, 2019, 18 (2) : 643-661. doi: 10.3934/cpaa.2019032 |
[19] |
Juan Carlos De los Reyes, Estefanía Loayza-Romero. Total generalized variation regularization in data assimilation for Burgers' equation. Inverse Problems & Imaging, 2019, 13 (4) : 755-786. doi: 10.3934/ipi.2019035 |
[20] |
Joshua Hudson, Michael Jolly. Numerical efficacy study of data assimilation for the 2D magnetohydrodynamic equations. Journal of Computational Dynamics, 2019, 6 (1) : 131-145. doi: 10.3934/jcd.2019006 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]