Large-scale kalman filtering using the limited memory BFGS method

H. Auvinen, J. M. Bardsley, H. Haario, T. Kauranne

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish
Pages (from-to)217-233
Number of pages17
JournalElectronic Transactions on Numerical Analysis
StatePublished - 2009


  • Bayesian estimation
  • Kalman filter
  • Large-scale optimization


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