TY - JOUR

T1 - Large-scale kalman filtering using the limited memory BFGS method

AU - Auvinen, H.

AU - Bardsley, J. M.

AU - Haario, H.

AU - Kauranne, T.

PY - 2009

Y1 - 2009

N2 - The standard formulations of the Kalman filter (KF) and extended Kalman filter (EKF) require the storage and multiplication of matrices of size n × n, where n is the size of the state space, and the inversion of matrices of size m × 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. 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.

AB - The standard formulations of the Kalman filter (KF) and extended Kalman filter (EKF) require the storage and multiplication of matrices of size n × n, where n is the size of the state space, and the inversion of matrices of size m × 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. 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.

KW - Bayesian estimation

KW - Kalman filter

KW - Large-scale optimization

UR - http://www.scopus.com/inward/record.url?scp=76049105699&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:76049105699

SN - 1068-9613

VL - 35

SP - 217

EP - 233

JO - Electronic Transactions on Numerical Analysis

JF - Electronic Transactions on Numerical Analysis

ER -