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A novel particle filter smoothing algorithm for non-linear state estimation is proposed. The key point of this algorithm is that the length of the interval of the particle filter smoothing can be dynamically computed by the difference between the particle and the signal observations, which effectively suppress the phenomenon of increasing error of the system state estimation caused by the particles' weight redistribution when using the fixed smoothing interval method. By considering the signal and the heat bath as an abstract universe based on the particle filter/resampling, a physical analogy is made between the particle filter and the abstract universe, which obeys the second law of thermodynamics. That is to say, when there is no new observation, no matter where the initial state is from, the entropy of the whole system will increase. However, with the coming of the observations this law can be violated. The particle filter behaves like a Maxwellian demon in this physical analogy, returning energy to the heat bath which thus causes entropy to decrease. This is possible due to the steady supply of new information. Then the length of the smoothing interval can be dynamically corrected based on the change of the entropy, so the weight assignments of the particles is optimized, and the performance of the particle filter can be improved. The estimation accuracy of the approach which is verified by simulations is better than the traditional smoothing methods with an affordable computation burden.
[1] Capp O, Godsill S J, Moulines E 2007 P. IEEE 95 899
[2] Liu X, Gao Q, Li X L 2014 Chin. Phys. B 23 010202
[3] Gordon N J, Salmond D J, Smith A F M 1993 IEEE Proc. F 140 107
[4] Zhu H, Zhang S N, Zhao H C 2014 Acta Phys. Sin. 63 058401 (in Chinese) [朱航, 张淑宁, 赵惠昌 2014 物理学报 63 058401]
[5] Zhang S N, Zhao H C, Xiong G, Guo C Y 2014 Acta Phys. Sin. 63 158401 (in Chinese) [张淑宁, 赵惠昌, 熊刚, 郭长勇 2014 物理学报 63 158401]
[6] Gning A, Ristic B, Mihaylova L 2012 IEEE T. Signal Proc. 60 2138
[7] Kitagawa G 1996 J. Comput. Graph. Statist. 5 415
[8] Doucet A, Godsill S J, Andrieu C 2000 Stat. Comput. 10 197
[9] Briers M, Doucet A, Maskell S 2010 Ann. I. Stat. Math. 62 61
[10] Doucet A, Freitas N D, Gordon N 2001 Sequential Monte Carlo Methods in Practice (New York: Springer-Verlag) pp177-195
[11] Liang J 2009 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese) [梁军 2009 博士学位论文 (哈尔滨: 哈尔滨工业大学)]
[12] Mitter S K, Newton N J 2003 SIAM J. Control Optim. 42 1813
[13] Newton N J 2006 SIAM J. Control Optim. 45 998
[14] Newton N J 2007 SIAM J. Control Optim. 46 1637
[15] Zhang D Z 2007 Acta Phys. Sin. 56 3152 (in Chinese) [张佃中 2007 物理学报 56 3152]
[16] Tomita Y, Omatu S, Sodea T 1980 Inform. Sci. 22 201
[17] Djuric P M, Kotecha J H, Zhang J Q, Huang Y F, Ghirmai T, Bugallo M F, Miguez J 2003 IEEE Signal Proc. Mag. 20 19
[18] Wang F S, Lu M Y, Zhao Q J, Yuan Z J 2014 Chin. J. Comput. 37 16 (in Chinese) [王法胜, 鲁明羽, 赵清杰, 袁泽剑 2014 计算机学报 37 16]
[19] Andrieu C, Doucet A, Holenstein R 2010 J. R. Stat. Soc. B 72 269
[20] 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]
[21] Pitt M K, Shephard N 1999 J. Am. Stat. Assoc. 94 590
[22] Li T C, Bolic M, Djuric P M 2015 IEEE Signal Proc. Mag. 32 70
[23] Brard J, Moral P D, Doucet A 2014 Electron. J. Probab. 19 1
[24] Hu X L, Schon T B, Ljung L 2011 IEEE T. Signal Proces. 59 3424
[25] Simth A F M, Gelfand A E 1992 Am. Stat. 46 84
[26] Kotecha J H, Djurić P A 2003 IEEE T. Signal Proc. 51 2602
[27] Doucet A, Johansen A M 2009 Oxford Handbook of Nonlinear Filter (Cambridge: Cambridge University Press) pp32-34
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[1] Capp O, Godsill S J, Moulines E 2007 P. IEEE 95 899
[2] Liu X, Gao Q, Li X L 2014 Chin. Phys. B 23 010202
[3] Gordon N J, Salmond D J, Smith A F M 1993 IEEE Proc. F 140 107
[4] Zhu H, Zhang S N, Zhao H C 2014 Acta Phys. Sin. 63 058401 (in Chinese) [朱航, 张淑宁, 赵惠昌 2014 物理学报 63 058401]
[5] Zhang S N, Zhao H C, Xiong G, Guo C Y 2014 Acta Phys. Sin. 63 158401 (in Chinese) [张淑宁, 赵惠昌, 熊刚, 郭长勇 2014 物理学报 63 158401]
[6] Gning A, Ristic B, Mihaylova L 2012 IEEE T. Signal Proc. 60 2138
[7] Kitagawa G 1996 J. Comput. Graph. Statist. 5 415
[8] Doucet A, Godsill S J, Andrieu C 2000 Stat. Comput. 10 197
[9] Briers M, Doucet A, Maskell S 2010 Ann. I. Stat. Math. 62 61
[10] Doucet A, Freitas N D, Gordon N 2001 Sequential Monte Carlo Methods in Practice (New York: Springer-Verlag) pp177-195
[11] Liang J 2009 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese) [梁军 2009 博士学位论文 (哈尔滨: 哈尔滨工业大学)]
[12] Mitter S K, Newton N J 2003 SIAM J. Control Optim. 42 1813
[13] Newton N J 2006 SIAM J. Control Optim. 45 998
[14] Newton N J 2007 SIAM J. Control Optim. 46 1637
[15] Zhang D Z 2007 Acta Phys. Sin. 56 3152 (in Chinese) [张佃中 2007 物理学报 56 3152]
[16] Tomita Y, Omatu S, Sodea T 1980 Inform. Sci. 22 201
[17] Djuric P M, Kotecha J H, Zhang J Q, Huang Y F, Ghirmai T, Bugallo M F, Miguez J 2003 IEEE Signal Proc. Mag. 20 19
[18] Wang F S, Lu M Y, Zhao Q J, Yuan Z J 2014 Chin. J. Comput. 37 16 (in Chinese) [王法胜, 鲁明羽, 赵清杰, 袁泽剑 2014 计算机学报 37 16]
[19] Andrieu C, Doucet A, Holenstein R 2010 J. R. Stat. Soc. B 72 269
[20] 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]
[21] Pitt M K, Shephard N 1999 J. Am. Stat. Assoc. 94 590
[22] Li T C, Bolic M, Djuric P M 2015 IEEE Signal Proc. Mag. 32 70
[23] Brard J, Moral P D, Doucet A 2014 Electron. J. Probab. 19 1
[24] Hu X L, Schon T B, Ljung L 2011 IEEE T. Signal Proces. 59 3424
[25] Simth A F M, Gelfand A E 1992 Am. Stat. 46 84
[26] Kotecha J H, Djurić P A 2003 IEEE T. Signal Proc. 51 2602
[27] Doucet A, Johansen A M 2009 Oxford Handbook of Nonlinear Filter (Cambridge: Cambridge University Press) pp32-34
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