On a nonlinear Kalman filter with simplified divided difference approximation

Xiaodong Luo, Ibrahim Hoteit, Irene M. Moroz

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We present a new ensemble-based approach that handles nonlinearity based on a simplified divided difference approximation through Stirling's interpolation formula, which is hence called the simplified divided difference filter (sDDF). The sDDF uses Stirling's interpolation formula to evaluate the statistics of the background ensemble during the prediction step, while at the filtering step the sDDF employs the formulae in an ensemble square root filter (EnSRF) to update the background to the analysis. In this sense, the sDDF is a hybrid of Stirling's interpolation formula and the EnSRF method, while the computational cost of the sDDF is less than that of the EnSRF. Numerical comparison between the sDDF and the EnSRF, with the ensemble transform Kalman filter (ETKF) as the representative, is conducted. The experiment results suggest that the sDDF outperforms the ETKF with a relatively large ensemble size, and thus is a good candidate for data assimilation in systems with moderate dimensions. © 2011 Elsevier B.V. All rights reserved.
Original languageEnglish (US)
Pages (from-to)671-680
Number of pages10
JournalPhysica D: Nonlinear Phenomena
Volume241
Issue number6
DOIs
StatePublished - Mar 2012

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

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