Geodesic
Large-scale Kalman filtering using the limited memory BFGS method
Electronic transactions on numerical analysis, Tome 35 (2009), pp. 217-233
The standard formulations of the Kalman filter (KF) and extended Kalman filter (EKF) require the storage and multiplication of matrices of size n $\times n$, where n is the size of the state space, and the inversion of matrices of size m $\times m$, where m is the size of the observation space. Thus when both m and n are large, implementation issues arise. In this paper, we advocate the use of the limited memory BFGS method (LBFGS) to address these issues. A detailed description of how to use LBFGS within both the KF and EKF methods is given.
Classification : 65K10, 15A29
Keywords: Kalman filter, Bayesian estimation, large-scale optimization 
@article{ETNA_2009__35__a2,
     author = {Auvinen,  H. and Bardsley,  J.M. and Haario,  H. and Kauranne,  T.},
     title = {Large-scale {Kalman} filtering using the limited memory {BFGS} method},
     journal = {Electronic transactions on numerical analysis},
     pages = {217--233},
     year = {2009},
     volume = {35},
     zbl = {1188.65084},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2009__35__a2/}
}
TY  - JOUR
AU  - Auvinen,  H.
AU  - Bardsley,  J.M.
AU  - Haario,  H.
AU  - Kauranne,  T.
TI  - Large-scale Kalman filtering using the limited memory BFGS method
JO  - Electronic transactions on numerical analysis
PY  - 2009
SP  - 217
EP  - 233
VL  - 35
UR  - http://geodesic.mathdoc.fr/item/ETNA_2009__35__a2/
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%0 Journal Article
%A Auvinen,  H.
%A Bardsley,  J.M.
%A Haario,  H.
%A Kauranne,  T.
%T Large-scale Kalman filtering using the limited memory BFGS method
%J Electronic transactions on numerical analysis
%D 2009
%P 217-233
%V 35
%U http://geodesic.mathdoc.fr/item/ETNA_2009__35__a2/
%G en
%F ETNA_2009__35__a2
Auvinen,  H.; Bardsley,  J.M.; Haario,  H.; Kauranne,  T. Large-scale Kalman filtering using the limited memory BFGS method. Electronic transactions on numerical analysis, Tome 35 (2009), pp. 217-233. http://geodesic.mathdoc.fr/item/ETNA_2009__35__a2/