Volume 35, pp. 217-233, 2009.
Large-scale Kalman filtering using the limited memory BFGS method
H. Auvinen, J. M. Bardsley, H. Haario, and T. Kauranne
Abstract
The standard formulations of the Kalman filter (KF) and extended
Kalman filter (EKF) require the storage and multiplication of
matrices of size , where is the size of the state
space, and the inversion of matrices of size , where
is the size of the observation space. Thus when both and
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. The methodology is
then tested on two examples: the first is large-scale and linear,
and the second is small scale and nonlinear. Our results indicate
that the resulting methods, which we will denote LBFGS-KF and
LBFGS-EKF, yield results that are comparable with those obtained
using KF and EKF, respectively, and can be used on much larger
scale problems.
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Key words
Kalman filter, Bayesian estimation, large-scale optimization
AMS subject classifications
65K10, 15A29
ETNA articles which cite this article
Vol. 39 (2012), pp. 271-285 Antti Solonen, Heikki Haario, Janne Hakkarainen, Harri Auvinen, Idrissa Amour and Tuomo Kauranne:
Variational ensemble Kalman filtering using limited memory BFGS
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