Abstract
This paper presents an improved approach based on the equivalent-weights particle filter (EWPF) that uses the proposal density to effectively improve the traditional particle filter. The proposed approach uses historical data to calculate statistical observations instead of the future observations used in the EWPF’s proposal density and draws on the localization scheme used in the localized PF (LPF) to construct the localized EWPF. The new approach is called the statistical observation localized EWPF (LEWPF-Sobs); it uses statistical observations that are better adapted to the requirements of real-time assimilation and the localization function is used to calculate weights to reduce the effect of missing observations on the weights. This approach not only retains the advantages of the EWPF, but also improves the assimilation quality when using sparse observations. Numerical experiments performed with the Lorenz 96 model show that the statistical observation EWPF is better than the EWPF and EAKF when the model uses standard distribution observations. Comparisons of the statistical observation localized EWPF and LPF reveal the advantages of the new method, with fewer particles giving better results. In particular, the new improved filter performs better than the traditional algorithms when the observation network contains densely spaced measurements associated with model state nonlinearities.
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Acknowledgements
Thanks go to Mengbin Zhu for his comments and suggestions at the early version of this manuscript. Conversations with Ting Zhao, Rixu Hao, Dequan Yang and Hengde Zhao led to modifications of many for the first version of the manuscript. And Harbin Engineering University and China Scholar Council (awarded to Deng Xiong for two and half years’ study abroad at GFDL/UW-Madison/Ohio State University Visiting Program).
Funding
The National Basic Research Program of China under contract Nos 2017YFC1404100, 2017YFC1404103 and 2017YFC1404104; the National Natural Science Foundation of China under contract No. 41676088.
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Zhao, Y., Yang, S., Jia, R. et al. The statistical observation localized equivalent-weights particle filter in a simple nonlinear model. Acta Oceanol. Sin. 41, 80–90 (2022). https://doi.org/10.1007/s13131-021-1876-1
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DOI: https://doi.org/10.1007/s13131-021-1876-1