`a`
Inverse Problems and Imaging (IPI)
 

Stabilized BFGS approximate Kalman filter
Pages: 1003 - 1024, Issue 4, November 2015

doi:10.3934/ipi.2015.9.1003      Abstract        References        Full text (504.4K)           Related Articles

Alexander Bibov - LUT Mafy - Department of Mathematics and Physics, Lappeenranta University Of Technology, P.O. Box 20 FI-53851, Finland (email)
Heikki Haario - Department of Mathematics and Physics, Lappeenranta University of Technology, P.O.Box 20, FIN-53851 Lappeenranta, Finland (email)
Antti Solonen - Lappeenranta University of Technology, Department of Mathematics and Physics, Lappeenranta, P.O. Box 20 FI-53851, Finland (email)

1 J. L. Anderson, An adaptive covariance inflation error correction algorithm for ensemble filters, Tellus-A, 59 (2006), 210-224.
2 H. Auvinen, J. Bardsley, H. Haario and T. Kauranne, Large-scale Kalman filtering using the limited memory BFGS method, Electronic Transactions on Numerical Analysis, 35 (2009), 217-233.       
3 H. Auvinen, J. Bardsley, H. Haario and T. Kauranne, The variational Kalman filter and an efficient implementation using limited memory BFGS, International Journal on Numerical methods in Fluids, 64 (2009), 314-335.       
4 J. Bardsley, A. Parker, A. Solonen and M. Howard, Krylov space approximate Kalman filtering, Numerical Linear Algebra with Applications, 20 (2013), 171-184.
5 A. Barth, A. Alvera-Azcárate, K.-W. Gurgel, J. Staneva, A. Port, J.-M. Beckers and E. Stanev, Ensemble perturbation smoother for optimizing tidal boundary conditions by assimilation of high-frequency radar surface currents - application to the German bight, Ocean Science, 6 (2010), 161-178.
6 A. Ben-Israel, A note on iterative method for generalized inversion of matrices, Math. Computation, 20 (1966), 439-440.
7 G. J. Bierman, Factorization Methods for Discrete Sequential Estimation, Vol. 128, Academic Press, 1977.       
8 R. Bucy and P. Joseph, Filtering for Stochastic Processes with Applications to Guidance, John Wiley & Sons, New York, 1968.       
9 R. Byrd, J. Nocedal and R. Schnabel, Representations of quasi-Newton matrices and their use in limited memory methods, Mathematical Programming, 63 (1994), 129-156.       
10 M. Cane, A. Kaplan, R. Miller, B. Tang, E. Hackert and A. Busalacchi, Mapping tropical pacific sea level: Data assimilation via reduced state Kalman filter, Journal of Geophysical Research, 101 (1996), 22599-22617.
11 L. Canino, J. Ottusch, M. Stalzer, J. Visher and S. Wandzura, Numerical solution of the Helmholtz equation in 2d and 3d using a high-order Nyström discretization, Journal of Computational Physics, 146 (1998), 627-663.       
12 J. L. Crassidis and J. L. Junkins, Optimal Estimation of Dynamic Systems, 2nd edition, CRC Press, 2012.       
13 D. Dee, Simplification of the Kalman filter for meteorological data assimilation, Quarterly Journal of the Royal Meteorological Society, 117 (1991), 365-384.
14 J. Dennis and J. Moré, Quasi-Newton methods, motivation and theory, SIAM Review, 19 (1977), 46-89.       
15 J. Dennis and R. Schnabel, Least change secant updates for quasi-Newton methods, SIAM Review, 21 (1979), 443-459.       
16 J. Dennis and R. Schnabel, A new derivation of symmetric positive definite secant updates, in Nonlinear Programming (Madison, Wis., 1980), 4, Academic Press, New York-London, 1981, 167-199.       
17 L. Evans, Partial Differential Equations, Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 1998.       
18 G. Evensen, Sequential data assimilation with a non-linear quasi-geostrophic model using monte carlo methods to forecast error statistics, Journal of Geophysical Research, 99 (1994), 143-162.
19 C. Fandry and L. Leslie, A two-layer quasi-geostrophic model of summer trough formation in the australian subtropical easterlies, Journal of the Atmospheric Sciences, 41 (1984), 807-818.
20 M. Fisher, Development of a Simplified Kalman Filter, ECMWF Technical Memorandum, 260, ECMWF, 1998.
21 M. Fisher, An Investigation of Model Error in a Quasi-Geostrophic, Weak-Constraint, 4D-Var Analysis System, Oral presentation, ECMWF, 2009.
22 M. Fisher and E. Adresson, Developments in 4D-var and Kalman Filtering, ECMWF Technical Memorandum, 347, ECMWF, 2001.
23 R. Kalman, A new approach to linear filtering and prediction problems, Transactions of the ASME - Journal of Basic Engineering, 82 (1960), 35-45.
24 R. Leveque, Finite Difference Methods for Ordinary and Partial Differential Equations. Steady-State and Time-Dependent Problems, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2007.       
25 J. Nocedal and S. Wright, Limited-memory BFGS in Numerical Optimization, Springer-Verlag, New York, 1999, 224-227.
26 J. Nocedal and S. Wright, Numerical Optimization, Springer-Verlag, New York, 1999.       
27 V. Pan and R. Schreiber, An improved newton iteration for the generalized inverse of a matrix, with applications, SIAM Journal on Scientific and Statistical Computing, 12 (1991), 1109-1130.       
28 J. Pedlosky, Geostrophic motion, in Geophysical Fluid Dynamics, Springer-Verlag, New York, 1987, 22-57.
29 K. Riley, M. Hobson and S. Bence, Partial differential equations: Separation of variables and other methods, in Mathematical Methods for Physics and Engineering, Cambridge University Press, Cambridge, 2004, 671-676.
30 D. Simon, The discrete-time Kalman filter, in Optimal State Estimation, Kalman, $H_\infty$, and Nonlinear Approaches, Wiley-Interscience, Hoboken, 2006, 123-145.
31 A. Staniforth and J. Côté, Semi-lagrangian integration schemes for atmospheric models review, Monthly Weather Review, 119 (1991), 2206-2223.
32 Y. Trémolet, Incremental 4d-var convergence study, Tellus, 59A (2007), 706-718.
33 Y. Tremolet and A. Hofstadler, OOPS as a common framework for Research and Operations, Presentation 14th Workshop on meteorological operational systems, ECMWF, 2013.
34 A. Voutilainen, T. Pyhälahti, K. Kallio, H. Haario and J. Kaipio, A filtering approach for estimating lake water quality from remote sensing data, International Journal of Applied Earth Observation and Geoinformation, 9 (2007), 50-64.
35 D. Zupanski, A general weak constraint applicable to operational 4dvar data assimilation systems, Monthly Weather Review, 125 (1996), 2274-2292.

Go to top