Data Assimilation Meetings at Reading

Date Meeting type Speakers
23 October 2013 Visitor Speaker Shin'ya Nakano (Institute of Statistical Mathematics, Japan)
A filter algorithm combining ensemble transform Kalman filter and imortance sampling (pdf)
A hybrid algorithm that combines the ensemble transform Kalman filter (ETKF) with the importance sampling approach is proposed. Since the ETKF assumes a linear Gaussian observation model, the estimate obtained by the ETKF can be biased in cases with nonlinear or non-Gaussian observations. The particle filter (PF) is based on the importance sampling technique, and it is applicable to problems with nonlinear or non-Gaussian observations. However, it usually requires an unrealistically large sample size to achieve a good estimation, and thus it is computationally prohibitive. In the proposed hybrid algorithm, we obtain a proposal distribution similar to the posterior distribution by using the ETKF. We then draw a large number of samples from the proposal distribution, and these samples are weighted to approximate the posterior distribution according to the importance sampling principle. Since the importance sampling provides an estimate of the probability density function (PDF) without assuming linearity or Gaussianity, we can resolve the bias due to the nonlinear or non-Gaussian observations. Finally, in the next forecast step, we reduce the sample size to achieve computational efficiency on the basis of the Gaussian assumption while we use a relatively large number of samples in the importance sampling to consider the non-Gaussian features of the posterior PDF. The use of the ETKF is beneficial also in terms of the computational simplicity of generating a number of random samples from the proposal distribution and in weighting each of the samples.

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