Comparison and combination of EAKF and SIR-PF in the Bayesian filter framework

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• 作者：Zheqi Shen ; Xiangming Zhang ; Youmin Tang
• 关键词：data assimilation ; ensemble adjustment Kalman filter ; particle filter ; Bayesian estimation ; ensemble adjustment Kalman particle filter
• 刊名：Acta Oceanologica Sinica
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：35
• 期：3
• 页码：69-78
• 全文大小：1,141 KB
• 参考文献：Ambadan J T, Tang Youmin. 2011. Sigma-point particle filter for parameter estimation in a multiplicative noise environment. Journal of Advances in Modeling Earth Systems, 3(4): M12005CrossRef
  Anderson J L. 2001. An ensemble adjustment Kalman filter for data assimilation. Monthly Weather Review, 129(12): 2884–2903CrossRef
  Anderson J L, Anderson S L. 1999. A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts. Monthly Weather Review, 127(12): 2741–2758CrossRef
  Arulampalam M S, Maskell S, Gordon N, et al. 2002. A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, 50(2): 174–188CrossRef
  Bengtsson T, Snyder C, Nychka D. 2003. Toward a nonlinear ensemble filter for high-dimensional systems. Journal of Geophysical Research, 108(D24): 8775CrossRef
  Bishop C H, Etherton B J, Majumdar S J. 2001. Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Monthly Weather Review, 129(3): 420–436CrossRef
  Bocquet M, Pires C A, Wu Lin. 2010. Beyond gaussian statistical modeling in geophysical data assimilation. Monthly Weather Review, 138(8): 2997–3023CrossRef
  Botev Z I, Grotowski J F, Kroese D P. 2010. Kernel density estimation via diffusion. The Annals of Statistics, 38(5): 2916–2957CrossRef
  Burgers G, van Leeuwen P J, Evensen G. 1998. Analysis scheme in the ensemble Kalman filter. Monthly Weather Review, 126(6): 1719–1724CrossRef
  Cappé O, Godsill S J, Moulines E. 2007. An overview of existing methods and recent advances in sequential Monte Carlo. Proceedings of the IEEE, 95(5): 899–924CrossRef
  Chorin A J, Morzfeld M, Tu X. 2010. Implicit particle filters for data assimilation. Communications in Applied Mathematics and Computational Science, 5(2): 221–240CrossRef
  Crisan D, Doucet A. 2002. A survey of convergence results on particle filtering methods for practitioners. IEEE Transactions on Signal Processing, 50(3): 736–746CrossRef
  Doucet A, De Freitas N, Gordon N. 2001. Sequential Monte Carlo Methods in Practice. New York: SpringerCrossRef
  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 (1978–2012), 99(C5): 10143–10162CrossRef
  Frei M, Künsch H R. 2013. Bridging the ensemble Kalman and particle filters. Biometrika, 100(4): 781–800CrossRef
  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): 107–113CrossRef
  Han Guijun, Zhu Jiang, Zhou Guangqing. 2004. Salinity estimation using the T-S relation in the context of variational data assimilation. Journal of Geophysical Research: Oceans (1978–2012), 109(C3): C03018
  Houtekamer P L, Mitchell H L, Pellerin G, et al. 2005. Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations. Monthly Weather Review, 133(3): 604–620CrossRef
  Jazwinski A H. 1970. Stochastic Processes and Filtering Theory. New York: Academic Press, 1–376
  Kalman R E. 1960. A new approach to linear filtering and prediction problems. Journal of basic Engineering, 82(1): 35–45CrossRef
  Klinker E, Rabier F, Kelly G, et al. 2000. The ECMWF operational implementation of four-dimensional variational assimilation. III: Experimental results and diagnostics with operational configuration. Quarterly Journal of the Royal Meteorological Society, 126(564): 1191–1215CrossRef
  Knuth D E. 2013. Art of Computer Programming, Volume 4, Fascicle 4: Generating All Trees-History of Combinatorial Generation. Boston: Addison-Wesley
  Le Dimet F X, Talagrand O. 1986. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A, 38(2): 97–110CrossRef
  Le Gland F, Monbet V, Tran V-D. 2009. Large sample asymptotics for the ensemble Kalman filter. In: Crisan D, ed. The Oxford Handbook of Nonlinear Filtering. Oxford: Oxford University Press, 598–634
  Li Hong, Kalnay E, Miyoshi T, et al. 2009. Accounting for model errors in ensemble data assimilation. Monthly Weather Review, 137(10): 3407–3419CrossRef
  Lorenz E N. 1963. Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2): 130–141CrossRef
  Mahfouf J F, Rabier F. 2000. The ECMWF operational implementation of four-dimensional variational assimilation: II. Experimental results with improved physics. Quarterly Journal of the Royal Meteorological Society, 126(564): 1171–1190CrossRef
  Miller R N, Ghil M, Gauthiez F. 1994. Advanced data assimilation in strongly nonlinear dynamical systems. Journal of the Atmospheric Sciences, 51(8): 1037–1056CrossRef
  Morzfeld M, Chorin A J. 2012. Implicit particle filtering for models with partial noise, and an application to geomagnetic data assimilation. Nonlinear Processes in Geophysics, 19(3): 365–382CrossRef
  Musso C, Oudjane N, Le Gland F. 2001. Improving regularised particle filters. In: Doucet A, de Freitas N, Gordon N, eds. Sequential Monte Carlo Methods in Practice. New York: Springer, 247–271CrossRef
  Nakano S, Ueno G, Higuchi T. 2007. Merging particle filter for sequential data assimilation. Nonlinear Processes in Geophysics, 14(4): 395–408CrossRef
  Papadakis N, Mémin E, Cuzol A, et al. 2010. Data assimilation with the weighted ensemble Kalman filter. Tellus A, 62(5): 673–697
  Rabier F, Järvinen H, Klinker E, et al. 2000. The ECMWF operational implementation of four-dimensional variational assimilation: I. Experimental results with simplified physics. Quarterly Journal of the Royal Meteorological Society, 126(564): 1143–1170CrossRef
  Rezaie J, Eidsvik J. 2012. Shrinked (1-a) ensemble Kalman filter and a Gaussian mixture filter. Computational Geosciences, 16(3): 837–852CrossRef
  Shen Zheqi, Tang Youmin. 2015. A modified ensemble Kalman particle filter for non-Gaussian systems with nonlinear measurement functions. Journal of Advances in Modeling Earth Systems, 7(1): 50–66CrossRef
  Shu Yeqiang, Zhu Jiang, Wang Dongxiao, et al. 2009. Performance of four sea surface temperature assimilation schemes in the South China Sea. Continental Shelf Research, 29(11–12): 1489–1501CrossRef
  Shu Yeqiang, Zhu Jiang, Wang Dongxiao, et al. 2011. Assimilating remote sensing and in situ observations into a coastal model of northern South China Sea using ensemble Kalman filter. Continental Shelf Research, 31(6): S24–S36CrossRef
  Snyder C, Bengtsson T, Bickel P, et al. 2008. Obstacles to high-dimensional particle filtering. Monthly Weather Review, 136(12): 4629–4640CrossRef
  Tang Youmin, Ambandan J, Chen Dake. 2014. Nonlinear measurement function in the ensemble Kalman filter. Advances in Atmospheric Sciences, 31(3): 551–558CrossRef
  van Leeuwen P J. 2009. Particle filtering in geophysical systems. Monthly Weather Review, 137(12): 4089–4114CrossRef
  van Leeuwen P J. 2010. Nonlinear data assimilation in geosciences: an extremely efficient particle filter. Quarterly Journal of the Royal Meteorological Society, 136(653): 1991–1999CrossRef
  van Leeuwen P J. 2011. Efficient nonlinear data-assimilation in geophysical fluid dynamics. Computers & Fluids, 46(1): 52–58CrossRef
  Whitaker J S, Hamill T M. 2002. Ensemble data assimilation without perturbed observations. Monthly Weather Review, 130(7): 1913–1924CrossRef
  Zhang S, Anderson J L. 2003. Impact of spatially and temporally varying estimates of error covariance on assimilation in a simple atmospheric model. Tellus A, 55(2): 126–147CrossRef
  Zheng Fei, Zhu Jiang. 2008. Balanced multivariate model errors of an intermediate coupled model for ensemble Kalman filter data assimilation. Journal of Geophysical Research: Oceans (1978–2012), 113(C7): C07002CrossRef
  
• 作者单位：Zheqi Shen (1)
  Xiangming Zhang (1)
  Youmin Tang (1) (2)
  
  1. State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou, 310012, China
  2. Environmental Science and Engineering, University of Northern British Columbia, Prince George, V2N 4Z9, Canada
  
• 刊物主题：Oceanography; Climatology; Ecology; Engineering Fluid Dynamics; Marine & Freshwater Sciences; Environmental Chemistry;
• 出版者：Springer Berlin Heidelberg
• ISSN：1869-1099

文摘

Bayesian estimation theory provides a general approach for the state estimate of linear or nonlinear and Gaussian or non-Gaussian systems. In this study, we first explore two Bayesian-based methods: ensemble adjustment Kalman filter (EAKF) and sequential importance resampling particle filter (SIR-PF), using a well-known nonlinear and non-Gaussian model (Lorenz '63 model). The EAKF, which is a deterministic scheme of the ensemble Kalman filter (EnKF), performs better than the classical (stochastic) EnKF in a general framework. Comparison between the SIR-PF and the EAKF reveals that the former outperforms the latter if ensemble size is so large that can avoid the filter degeneracy, and vice versa. The impact of the probability density functions and effective ensemble sizes on assimilation performances are also explored. On the basis of comparisons between the SIR-PF and the EAKF, a mixture filter, called ensemble adjustment Kalman particle filter (EAKPF), is proposed to combine their both merits. Similar to the ensemble Kalman particle filter, which combines the stochastic EnKF and SIR-PF analysis schemes with a tuning parameter, the new mixture filter essentially provides a continuous interpolation between the EAKF and SIR-PF. The same Lorenz '63 model is used as a testbed, showing that the EAKPF is able to overcome filter degeneracy while maintaining the non-Gaussian nature, and performs better than the EAKF given limited ensemble size.