Sampling-free linear Bayesian updating of model state and parameters using a square root approach

Oliver Pajonk*, Bojana V. Rosić, Hermann G. Matthies

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

18 Citations (Scopus)
3 Downloads (Pure)


We present a sampling-free implementation of a linear Bayesian filter based on a square root formulation. It employs spectral series expansions of the involved random variables, one such example being Wiener's polynomial chaos. The method is compared to several related methods, as well as a full Bayesian update, on a simple scalar example. Additionally it is applied to a combined state and parameter estimation problem for a chaotic system, the well-known Lorenz-63 model. There, we compare it to the ensemble square root filter (EnSRF), which is essentially a probabilistic implementation of the same underlying estimator. The spectral method is found to be more robust than the probabilistic one, especially for variance estimation. This is to be expected due to the sampling-free implementation.

Original languageEnglish
Pages (from-to)70-83
Number of pages14
JournalComputers and Geosciences
Publication statusPublished - 1 Jun 2013
Externally publishedYes


  • Bayesian estimation
  • Inverse problem
  • Kalman filter
  • Lorenz-63
  • Polynomial chaos expansion
  • White noise analysis


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