基于空间分布和时间序列分析的粒子滤波算法
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摘要
针对粒子滤波存在的粒子贫化问题,提出了一种改进的重采样粒子滤波算法.在重采样步骤中基于采样粒子集的空间分布引入时间序列分析,选取相关度最高的粒子进行传递,避免了只关注采样粒子权值的传统重采样算法中仅复制大权值粒子而任意丢弃小权值粒子的缺陷,因此能够消弱粒子贫化现象,提高算法的估计精度.在理论上利用两样本Kolmogorov-Smimov检验原理证明了改进算法重采样后的粒子集和采样前的粒子集来自同一总体.仿真结果表明,尤其是在初始采样粒子数目较小时,该算法在非线性系统状态估计中的精度优于传统的粒子滤波算法.
In order to solve the problem of sample particles impoverishment,an improved resampling particle filter is presented.It is based on the space distribution and time series analysis.The most important particle that has higher temporal correlation between the particle's path and observation path in particle propagating is chosen.It can avoid the problem in the traditional resampling algorithm that only the particle's weights are considered,and the low weighed particles have the risk to be thrown away.Thus the problem of particles impoverishment is weakened and the estimate accuracy is improved.By the two-sample Kolmogorov-Smirnov Test,a proof is given that the particles that are resampled by the improved algorithm and the original particles belong to the same distribution.The proposed approach,verified by simulations,indicates that its accuracy is better than traditional methods for the nonlinear system state estimation,especially when the number of initial sampling particles is small.
In order to solve the problem of sample particles impoverishment,an improved resampling particle filter is presented.It is based on the space distribution and time series analysis.The most important particle that has higher temporal correlation between the particle's path and observation path in particle propagating is chosen.It can avoid the problem in the traditional resampling algorithm that only the particle's weights are considered,and the low weighed particles have the risk to be thrown away.Thus the problem of particles impoverishment is weakened and the estimate accuracy is improved.By the two-sample Kolmogorov-Smirnov Test,a proof is given that the particles that are resampled by the improved algorithm and the original particles belong to the same distribution.The proposed approach,verified by simulations,indicates that its accuracy is better than traditional methods for the nonlinear system state estimation,especially when the number of initial sampling particles is small.
引文
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[8]叶有时,刘淑芬,孙强,刘鸿瑾,刘波,杨桦,吴一帆.改进粒子滤波算法在深空红外小目标跟踪中的应用[J].电子学报,2015,43(8):1506-1512.Ye You-shi,Liu Shu-fen,Sun Qiang,Liu Hong-jin,Liu Bo,Yang Hua,Wu Yi-fan.Application of improved particle filter algorithm in deep space infrared small target tracking[J].Acta Electronica Sinica,2015,43(8):1506-1512.(in Chinese)
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[11]Xu B,Zhu J,Xu H.An ant stochastic decision based particle filter and its convergence[J].Signal Processing,2010,90(9):2731-2748.
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[18]Berard J,Moral P D,Doucet A.A lognormal central limit theorem for particle approximations of normalizing constants[J].Bectronic Journal of Probability,2013,19:1-28.
[19]Hu X L,Schon T,Ljung L.A general convergence result for particle filtering[J].IEEE Transactions on Signal Processing,2011,59(7):3424-3429.
[20]Beskos A,Jasra A.On the stability of sequential monte carlo methods in high dimensions[J].Annals of Applied Probability An Official Journal of the Institute of Mathematical Statistics,2014,24(4):1396-1445.
[21]Durbin J,Koopman S J.Time Series Analysis by State Space Methods[M].Oxford:Oxford University Press,2012.187-188.
[22]Benesty P J,Chen J,Huang Y,et al.Pearson Correlation Coefficient[M].Berlin Heidelberg:Springer Berlin Heidelberg,2009.1-4.
[23]Gibbons J D,Chakraborti S.Nonparametric statistical inference[J].Journal of the Royal Statistical Society,2011,149(35):977-979.
[24]Pitt M K,Shephard N.Filtering via simulation:auxiliary particle filters[J].Journal of the American Statistical Association,1999,94(446):590-599.
[25]田梦楚,薄煜明,陈志敏,吴盘龙,赵高鹏.萤火虫算法智能优化粒子滤波[J].自动化学报,2016,42(1):89-97.TIAN Meng-chu,BO Yu-ming,CHEN Zhi-min,Wu Panlong,ZHAO Gao-peng.Firefly algorithm intelligence optimized particle filter[J].Acta Automatica Sinica,2016,42(1):89-97.(in Chinese)
[2]Djuric P M,Kotecha J H,Zhang J,et al.Particle filtering[J].Signal Processing Magazine IEEE,2003,20(5):19-38.
[3]夏楠,邱天爽,李景春,李书芳.一种卡尔曼滤波与粒子滤波相结合的非线性滤波算法[J].电子学报,2013,41(1):148-152.XIA Nan,QIU Tian-shuang,LI Jing-chun,LI Shu-fang.A nonlinear filtering algorithm combining the kalman filter and the particle fiIter[J].Acta Electronica Sinica,2013,41(1):148-152.(in Chinese)
[4]张宏欣,周穗华,冯士民.高斯粒子流滤波器[J].电子学报,2016,44(4):795-803.ZHANG Hong-xin,ZHOU Sui-hua,FENG Shi-min.Gaussian particle flow filter[J].Acta Electronica Sinica,2016,44(4):795-803.(in Chinese)
[5]Gordon N J,Salmond D J.Smith A F M.Novel approach to nonlinear/nongaussian bayesian state estimation[J].IEE Proceedings-F,1993,140(2):107-113.
[6]吴孙勇,廖桂生,杨志伟.基于粒子滤波的宽带信号波达方向估计[J].电子学报,2011,39(6):1353-1357.WU Sun-yong,LIAO Gui-sheng,ANG Zhi-wei.Direction of arrival estimation of wideband signal based on particle filters[J].Acta Electronica Sinica,2011,39(6):1353-1357.(in Chinese)
[7]张玲霞,刘志仓,王辉,齐会云,胡旦.非线性系统故障诊断的粒子滤波算法[J].电子学报,2015,43(3):615-619.Zhang Ling-xia,Liu Zhi-cang,Wang Hui,Qi Hui-yun,Hu Dan.Particle filter method for diagnosis in nonlinear system[J].Acta Electronica Sinica,2015,43(3):615-619.(in Chinese)
[8]叶有时,刘淑芬,孙强,刘鸿瑾,刘波,杨桦,吴一帆.改进粒子滤波算法在深空红外小目标跟踪中的应用[J].电子学报,2015,43(8):1506-1512.Ye You-shi,Liu Shu-fen,Sun Qiang,Liu Hong-jin,Liu Bo,Yang Hua,Wu Yi-fan.Application of improved particle filter algorithm in deep space infrared small target tracking[J].Acta Electronica Sinica,2015,43(8):1506-1512.(in Chinese)
[9]Li T C,Sun S D,Sattar T P,Corchado J M.Fight sample degeneracy and impoverishment in particle filters:a review of intelligent approaches[J].Expert Systems with Applications,2014,41(8):3944-3954.
[10]Park S,Hwand J P,Kim E,Kang H J.A new evolutionary particle filter for the prevention of sample impoverishment[J].IEEE Transactions on Evolutionary Computation,2009,13(4):801-809.
[11]Xu B,Zhu J,Xu H.An ant stochastic decision based particle filter and its convergence[J].Signal Processing,2010,90(9):2731-2748.
[12]Christophe A,Arnaud D.Roman H.Particle Markov chain Monte Carlo methods[J].Journal of the Royal Statistical Society,2010,72(3):269-342.
[13]Musso C,Oudjane N,Gland F.Improving regularized particle filters[A].Doucet A,Godsill S,Andrieu C.Sequential Monte Carlo Methods in Practice[M].New York:Springer-Verlag,2001.247-273.
[14]Li T C,Bolic M,Djuric P M.Resampling methods for Particle Filtering[J].IEEE Signal Processing Magazine,2015,32(3):70-86.
[15]Li T,Sattar T P,Sun S.Deterministic resampling:unbiased sampling to avoid sample impoverishment in particle filters[J].Signal Processing,2012,92(7):1637-1645.
[16]Liu J S,Chen R.Sequential monte carlo methods for dynamical systems[J].Journal of American Statistical Association,1998,93(443):1032-1044.
[17]Doucet A,Johansen A M.A Tutorial on Particle Filtering and Smoothing:Fifteen Years Later[M].Handbook of Nonlinear Filtering.Oxford:Oxford University Press,2009.1-41.
[18]Berard J,Moral P D,Doucet A.A lognormal central limit theorem for particle approximations of normalizing constants[J].Bectronic Journal of Probability,2013,19:1-28.
[19]Hu X L,Schon T,Ljung L.A general convergence result for particle filtering[J].IEEE Transactions on Signal Processing,2011,59(7):3424-3429.
[20]Beskos A,Jasra A.On the stability of sequential monte carlo methods in high dimensions[J].Annals of Applied Probability An Official Journal of the Institute of Mathematical Statistics,2014,24(4):1396-1445.
[21]Durbin J,Koopman S J.Time Series Analysis by State Space Methods[M].Oxford:Oxford University Press,2012.187-188.
[22]Benesty P J,Chen J,Huang Y,et al.Pearson Correlation Coefficient[M].Berlin Heidelberg:Springer Berlin Heidelberg,2009.1-4.
[23]Gibbons J D,Chakraborti S.Nonparametric statistical inference[J].Journal of the Royal Statistical Society,2011,149(35):977-979.
[24]Pitt M K,Shephard N.Filtering via simulation:auxiliary particle filters[J].Journal of the American Statistical Association,1999,94(446):590-599.
[25]田梦楚,薄煜明,陈志敏,吴盘龙,赵高鹏.萤火虫算法智能优化粒子滤波[J].自动化学报,2016,42(1):89-97.TIAN Meng-chu,BO Yu-ming,CHEN Zhi-min,Wu Panlong,ZHAO Gao-peng.Firefly algorithm intelligence optimized particle filter[J].Acta Automatica Sinica,2016,42(1):89-97.(in Chinese)