The statistical observation localized equivalent-weights particle filter in a simple nonlinear model

Yuxin Zhao; Shuo Yang; Renfeng Jia; Di Zhou; Xiong Deng; Chang Liu; Xinrong Wu

doi:10.1007/s13131-021-1876-1

Volume 41 Issue 2

Feb. 2022

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Article Navigation > Acta Oceanologica Sinica > 2022 > 41(2): 80-90

Yuxin Zhao, Shuo Yang, Renfeng Jia, Di Zhou, Xiong Deng, Chang Liu, Xinrong Wu. The statistical observation localized equivalent-weights particle filter in a simple nonlinear model[J]. Acta Oceanologica Sinica, 2022, 41(2): 80-90. doi: 10.1007/s13131-021-1876-1

Citation:

Yuxin Zhao, Shuo Yang, Renfeng Jia, Di Zhou, Xiong Deng, Chang Liu, Xinrong Wu. The statistical observation localized equivalent-weights particle filter in a simple nonlinear model[J]. Acta Oceanologica Sinica, 2022, 41(2): 80-90. doi: 10.1007/s13131-021-1876-1

Citation:

Yuxin Zhao, Shuo Yang, Renfeng Jia, Di Zhou, Xiong Deng, Chang Liu, Xinrong Wu. The statistical observation localized equivalent-weights particle filter in a simple nonlinear model[J]. Acta Oceanologica Sinica, 2022, 41(2): 80-90. doi: 10.1007/s13131-021-1876-1

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The statistical observation localized equivalent-weights particle filter in a simple nonlinear model

doi: 10.1007/s13131-021-1876-1

1.
College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China
2.
Harbin Marine Boiler & Turbine Research Institute, Harbin 150078, China
3.
China Ship Development and Design Center, Wuhan 430064, China
4.
Key Laboratory of Marine Environmental Information Technology, National Marine Data and Information Service, State Oceanic Administration, Tianjin 300171, China

Funds: 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.

More Information

Corresponding author: E-mail: xiongdeng407@hrbeu.edu.cn
Received Date: 2021-03-20
Accepted Date: 2021-06-05

Available Online: 2021-12-02

Publish Date: 2022-02-01

Abstract

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.
- data assimilation,
- particle filter,
- equivalent weights particle filter,
- localization methods

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References(27)

References

[1]	Ades M, Van Leeuwen P J. 2013. An exploration of the equivalent weights particle filter. Quarterly Journal of the Royal Meteorological Society, 139(672): 820–840. doi: 10.1002/qj.1995
[2]	Ades M, Van Leeuwen P J. 2015. The equivalent-weights particle filter in a high-dimensional system. Quarterly Journal of the Royal Meteorological Society, 141(687): 484–503. doi: 10.1002/qj.2370
[3]	Chen Yan, Zhang Weimin, Wang Pingqiang. 2020. An application of the localized weighted ensemble Kalman filter for ocean data assimilation. Quarterly Journal of the Royal Meteorological Society, 146(732): 3029–3047. doi: 10.1002/qj.3824
[4]	Chorin A J, Tu Xuemin. 2009. Implicit sampling for particle filters. Proceedings of the National Academy of Sciences of the United States of America, 106(41): 17249–17254. doi: 10.1073/pnas.0909196106
[5]	De Freitas N, Andrieu C, Højen-Sørensen P, et al. 2001. Sequential monte Carlo methods for neural networks. In: Doucet A, De Freitas N, Gordon N, eds. Sequential Monte Carlo Methods in Practice. New York, NY, USA: Springer, 359–379
[6]	Evensen G. 1994. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. Journal of Geophysical Research: Oceans, 99(C5): 10143–10162. doi: 10.1029/94JC00572
[7]	Gaspari G, Cohn S E. 1999. Construction of correlation functions in two and three dimensions. Quarterly Journal of the Royal Meteorological Society, 125(554): 723–757. doi: 10.1002/qj.49712555417
[8]	Gordon N J, Salmond D J, Smith A F M. 1993. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings F (Radar and Signal Processing), 140(2): 107–113. doi: 10.1049/ip-f-2.1993.0015
[9]	Houtekamer P L, Mitchell H L. 1998. Data assimilation using an ensemble Kalman filter technique. Monthly Weather Review, 126(3): 796–811. doi: 10.1175/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2
[10]	Law K, Stuart A, Zygalakis K. 2015. Data Assimilation: A Mathematical Introduction. Cham, Switzerland: Springer
[11]	Lei Jing, Bickel P. 2011. A moment matching ensemble filter for nonlinear non-Gaussian data assimilation. Monthly Weather Review, 139(12): 3964–3973. doi: 10.1175/2011MWR3553.1
[12]	Lorenz E N. 1995. Predictability: a problem partly solved. In: Proceedings Seminar on Predictability. Reading, UK: ECMWF
[13]	Nakano S, Ueno G, Higuchi T. 2007. Merging particle filter for sequential data assimilation. Nonlinear Processes in Geophysics, 14(4): 395–408. doi: 10.5194/npg-14-395-2007
[14]	Poterjoy J. 2016. A localized particle filter for high-dimensional nonlinear systems. Monthly Weather Review, 144(1): 59–76. doi: 10.1175/MWR-D-15-0163.1
[15]	Poterjoy J, Anderson J L. 2016. Efficient assimilation of simulated observations in a high-dimensional geophysical system using a localized particle filter. Monthly Weather Review, 144(5): 2007–2020. doi: 10.1175/MWR-D-15-0322.1
[16]	Robert S, Leuenberger D, Künsch H R. 2018. A local ensemble transform Kalman particle filter for convective-scale data assimilation. Quarterly Journal of the Royal Meteorological Society, 144(713): 1279–1296. doi: 10.1002/qj.3116
[17]	Shen Zheqi, Tang Youmin, Li Xiaojing. 2017. A new formulation of vector weights in localized particle filter. Quarterly Journal of the Royal Meteorological Society, 143(709): 3269–3278. doi: 10.1002/qj.3180
[18]	Shen Zheqi, Zhang Xiangming, Tang Youmin. 2016. Comparison and combination of EAKF and SIR-PF in the Bayesian filter framework. Acta Oceanologica Sinica, 35(3): 69–78. doi: 10.1007/s13131-015-0757-x
[19]	Stordal A S, Karlsen H A, Nævdal G, et al. 2011. Bridging the ensemble Kalman filter and particle filters: the adaptive Gaussian mixture filter. Computational Geosciences, 15(2): 293–305. doi: 10.1007/s10596-010-9207-1
[20]	Van Leeuwen P J. 2010. Nonlinear data assimilation in geosciences: an extremely efficient particle filter. Quarterly Journal of the Royal Meteorological Society, 136(653): 1991–1999. doi: 10.1002/qj.699
[21]	Van Leeuwen P J. 2011. Efficient nonlinear data-assimilation in geophysical fluid dynamics. Computers & Fluids, 46(1): 52–58
[22]	Van Leeuwen P J. 2015. Aspects of particle filtering in high-dimensional spaces. In: First International Conference on Dynamic Data-Driven Environmental Systems Science. Cambridge, UK: Springer, 251–262
[23]	Van Leeuwen P J, Evensen G. 1996. Data assimilation and inverse methods in terms of a probabilistic formulation. Monthly Weather Review, 124(12): 2898–2913. doi: 10.1175/1520-0493(1996)124<2898:DAAIMI>2.0.CO;2
[24]	Van Leeuwen P J, Künsch H R, Nerger L, et al. 2019. Particle filters for high-dimensional geoscience applications: a review. Quarterly Journal of the Royal Meteorological Society, 145(723): 2335–2365. doi: 10.1002/qj.3551
[25]	Whitaker J S, Hamill T M. 2012. Evaluating methods to account for system errors in ensemble data assimilation. Monthly Weather Review, 140(9): 3078–3089. doi: 10.1175/MWR-D-11-00276.1
[26]	Zhang S. 2011. A study of impacts of coupled model initial shocks and state–parameter optimization on climate predictions using a simple pycnocline prediction model. Journal of Climate, 24(23): 6210–6226. doi: 10.1175/JCLI-D-10-05003.1
[27]	Zhu Mengbin, Van Leeuwen P J, Amezcua J. 2016. Implicit equal‐weights particle filter. Quarterly Journal of the Royal Meteorological Society, 142(698): 1904–1919. doi: 10.1002/qj.2784