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Owing to the fact that standard particle filter and ensemble Kalman filter can not efficiently represent the posterior probability density function (PDF), an improved particle filter is proposed. In this algorithm, an innovation step is introduced after the prediction step, and the analyses of non-observation time and observation time are treated separately. The numerical simulations of a low- and a high-dimensional systems show that this new particle filter can follow the true state of a highly nonlinear non-Gaussian system very well.
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Keywords:
- assimilation /
- nonlinear /
- particle filter /
- ensemble Kalman filter
[1] Zou X L 2009 Data Assimilation-Theory and Application(Vol.1)(Beijing China Meteorological Press) p43 (in Chinese)[邹晓蕾 2009 资料同化-理论与应用}(上册)(北京：气象出版社) 第43页]
[2] Evensen G 1994 J. Geophys. Res. 99 10143
[3] Evensen G, Van Leeuwen P J 2000 Mon Wea. Rev. 128 1852
[4] Houtekamer P L, Mitchell H L 2001 Mon Wea. Rev.129 123
[5] Lorenc A C 2003 Q. J. R. Meteorol. Soc. 129 3183
[6] Julier S, Uhlmann J, Durrant W 2000 IEEE Transactions on AutomatedControl, Technical Notes and Correspondence 45 477
[7] Liu C S, Xiao Q N, Wang B 2008 Mon Wea. Rev.136 3363
[8] Navon I M, Zou X, Derber J 1992 Mon Wea. Rev.120 1433
[9] Cao X Q, Huang S X, Zhang W M 2008 Acta Phys. sin. 57 1984(in Chinese)[曹小群, 黄思训, 杜华栋 2008 物理学报 57 1984]
[10] Michail D V, Dan C, Manfred O 2011 Physica D (in Press)
[11] Pitt M, Shephard N 1999 J. Amer. Statist. Assoc. 94 590
[12] Musso C, Oudjane N, LeGland F 2001 “Sequential Monte CarloMethods in Practice (New York: Springer-Verlag) pp247–271
[13] Arulampalam M S, Maskell S, Gordon N, Clapp T 2002 IEEETransactions On Signal Processing 50 174
[14] Cheng S Y, Zhang J Y 2008 Acta Electronica Sinica 36 500 (in Chinese)[程水英, 张剑云 2008 电子学报 36 500]
[15] Du Z C, Tang B, Li K 2006 Acta Phys. Sin. 55 999 (in Chinese)[杜正聪, 唐斌, 李可 2006 物理学报 55 999]
[16] Kotceha J H, Djuric P M 2003 IEEE Transactions On Signal Processing 51 2592
[17] Kotceha J H, Djuric P M 2003 IEEE Transactions On Signal Processing 51 2602
[18] VanderMerwe R, Wan E 2003 Proceedings of the IEEE InternationalConference on Acoustics Speech and Signal Processing(ICASSP) 6 701
[19] Eyink G L, Kim S 2006 J. Stat. Phys. 123 1071
[20] VanLeeuwen P J 2009 Mon Wea. Rev.137 4089
[21] Li X R, Jilkov V P 2003 IEEE Trans. AES 39 1333
[22] Bar S. Y, Li X R, Kirubarajan T 2001 Estimation with Applicationsto Tracking and Navigation: Theory, Algorithms, and Software(New York: John Wiley & Sons) pp373–374
[23] Doucet A, Freitas N D, Gordon N 2001 Sequential Mente CarloMethods in Practice(New York Springer-Verlag) pp25–26
[24] VanLeeuwen P J 2010 Q. J. R. Meteorol. Soc. 136 1991
[25] Nakano S, Ueno G, Higuchi T 2007 Nonlin. Processes Geophys.14 395
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[1] Zou X L 2009 Data Assimilation-Theory and Application(Vol.1)(Beijing China Meteorological Press) p43 (in Chinese)[邹晓蕾 2009 资料同化-理论与应用}(上册)(北京：气象出版社) 第43页]
[2] Evensen G 1994 J. Geophys. Res. 99 10143
[3] Evensen G, Van Leeuwen P J 2000 Mon Wea. Rev. 128 1852
[4] Houtekamer P L, Mitchell H L 2001 Mon Wea. Rev.129 123
[5] Lorenc A C 2003 Q. J. R. Meteorol. Soc. 129 3183
[6] Julier S, Uhlmann J, Durrant W 2000 IEEE Transactions on AutomatedControl, Technical Notes and Correspondence 45 477
[7] Liu C S, Xiao Q N, Wang B 2008 Mon Wea. Rev.136 3363
[8] Navon I M, Zou X, Derber J 1992 Mon Wea. Rev.120 1433
[9] Cao X Q, Huang S X, Zhang W M 2008 Acta Phys. sin. 57 1984(in Chinese)[曹小群, 黄思训, 杜华栋 2008 物理学报 57 1984]
[10] Michail D V, Dan C, Manfred O 2011 Physica D (in Press)
[11] Pitt M, Shephard N 1999 J. Amer. Statist. Assoc. 94 590
[12] Musso C, Oudjane N, LeGland F 2001 “Sequential Monte CarloMethods in Practice (New York: Springer-Verlag) pp247–271
[13] Arulampalam M S, Maskell S, Gordon N, Clapp T 2002 IEEETransactions On Signal Processing 50 174
[14] Cheng S Y, Zhang J Y 2008 Acta Electronica Sinica 36 500 (in Chinese)[程水英, 张剑云 2008 电子学报 36 500]
[15] Du Z C, Tang B, Li K 2006 Acta Phys. Sin. 55 999 (in Chinese)[杜正聪, 唐斌, 李可 2006 物理学报 55 999]
[16] Kotceha J H, Djuric P M 2003 IEEE Transactions On Signal Processing 51 2592
[17] Kotceha J H, Djuric P M 2003 IEEE Transactions On Signal Processing 51 2602
[18] VanderMerwe R, Wan E 2003 Proceedings of the IEEE InternationalConference on Acoustics Speech and Signal Processing(ICASSP) 6 701
[19] Eyink G L, Kim S 2006 J. Stat. Phys. 123 1071
[20] VanLeeuwen P J 2009 Mon Wea. Rev.137 4089
[21] Li X R, Jilkov V P 2003 IEEE Trans. AES 39 1333
[22] Bar S. Y, Li X R, Kirubarajan T 2001 Estimation with Applicationsto Tracking and Navigation: Theory, Algorithms, and Software(New York: John Wiley & Sons) pp373–374
[23] Doucet A, Freitas N D, Gordon N 2001 Sequential Mente CarloMethods in Practice(New York Springer-Verlag) pp25–26
[24] VanLeeuwen P J 2010 Q. J. R. Meteorol. Soc. 136 1991
[25] Nakano S, Ueno G, Higuchi T 2007 Nonlin. Processes Geophys.14 395
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