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针对非线性系统的状态估计问题, 提出了一种自调整平滑区间粒子滤波平滑算法. 该算法的显著特点是根据采样粒子观测值与系统状态观测值之间的偏差动态修正滤波平滑区间的长度, 有效抑制了传统的粒子滤波平滑算法中因区间长度固定可能造成粒子权重重新赋值带来误差增大的问题. 该算法的原理是依据粒子滤波器的工作机理, 把系统状态信息和热槽组成一个抽象的整体, 将粒子滤波平滑过程类比为观测信息和热槽交互的统计力学系统. 在无新的观测信息时, 整个系统遵循热力学第二定律, 即无论从任何初始状态出发, 整个力学系统的熵是非减的; 而当出现新的观测信息时, 粒子滤波器像麦克斯韦妖从新的观测信息中抽取能量传送给热槽, 使整个抽象系统的熵减少, 根据系统熵的递变规律变化对滤波平滑区间的长度加以动态修正, 优化粒子的权重赋值, 进而提高系统状态的估计精度. 利用matlab进行了仿真分析, 验证了该算法的有效性.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 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 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 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 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 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 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 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 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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