Geodesic
Large-scale Kalman filtering using the limited memory BFGS method
Electronic transactions on numerical analysis, Tome 35 (2009), pp. 217-233.

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Summary: 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},
     publisher = {mathdoc},
     volume = {35},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2009__35__a2/}
}
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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/