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Front. Inform. Technol. Electron. Eng.  2015, Vol. 16 Issue (11): 969-984    DOI: 10.1631/FITEE.1500199
    
粒子滤波重采样：同分布原则、一种新方法以及综合对比
Tian-cheng Li, Gabriel Villarrubia, Shu-dong Sun, Juan M. Corchado, Javier Bajo
1BISITE Group, Faculty of Science, University of Salamanca, C/Espejo s/n, Salamanca 37008, Spain; 2School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China; 3Department of Artificial Intelligence, Technical University of Madrid, Calle Ramiro de Maeztu 7, Madrid 28040, Spain; 4Osaka Institute of Technology, Asahi-ku Ohmiya, Osaka 535-8585, Japan
Resampling methods for particle filtering: identical distribution, a new method, and comparable study
Tian-cheng Li, Gabriel Villarrubia, Shu-dong Sun, Juan M. Corchado, Javier Bajo
1BISITE Group, Faculty of Science, University of Salamanca, C/Espejo s/n, Salamanca 37008, Spain; 2School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China; 3Department of Artificial Intelligence, Technical University of Madrid, Calle Ramiro de Maeztu 7, Madrid 28040, Spain; 4Osaka Institute of Technology, Asahi-ku Ohmiya, Osaka 535-8585, Japan
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摘要： 目的：重采样方法是粒子滤波设计的重要环节，也是避免或克服“权值退化”和“多样性匮乏”这一对粒子滤波难点问题的关键。当前研究领域已有几十余种重采样方法，然而尚缺乏一个基础性的重采样设计原则以及对这些方法的综合性能对比。针对于此，本文提出重采样“同分布”设计原则，并在此基础上，提出一种能够最大程度满足同分布原则的最优重采样方法。本文希望所提出的重采样同分布原则以及新方法有利于进一步的新方法设计或已有方法的工程选用。
创新点：理论上严格定义了同分布原则作为重采样方法设计的普遍性原则，给出三种同分布测度方法；提出了一种最小采样方差（MSV: minimum sampling variance）最优重采样方法，在满足渐近无偏性的前提下获得最小采样方差。
方法：给出三种“重采样同分布”测度方法：Kullback-Leibler偏差,Kolmogorov-Smirnov统计和采样方差（sampling variance）。所提出的最小采样方差重采样放宽了无偏性条件，仅满足渐近无偏，但获得了最小采样方差（参见定理2-4论证以及仿真性能对比）。
结论：重采样前后粒子的概率分布应该统计上一致（即“同分布”）是重采样方法设计的一个重要原则。明确这一基本原则有利于规范化重采样新方法的设计与工程选用。所提出的MSV重采样新方法渐近无偏，并具有最小采样方差的优异理论特性，即最优地满足同分布原则。算法性能分析表明：大多数无偏或者渐近无偏重采样方法在滤波精度上差异较小，但是在采样方差、计算效率方面差异较大。另一方面，基于一些特殊规则或者问题模型设计的重采样方法可能具有特别优势。
关键词： 粒子滤波;  重采样;  统计同分布;  采样方差    
Abstract: Resampling is a critical procedure that is of both theoretical and practical significance for efficient implementation of the particle filter. To gain an insight of the resampling process and the filter, this paper contributes in three further respects as a sequel to the tutorial (Li et al., 2015). First, identical distribution (ID) is established as a general principle for the resampling design, which requires the distribution of particles before and after resampling to be statistically identical. Three consistent metrics including the (symmetrical) Kullback-Leibler divergence, Kolmogorov-Smirnov statistic, and the sampling variance are introduced for assessment of the ID attribute of resampling, and a corresponding, qualitative ID analysis of representative resampling methods is given. Second, a novel resampling scheme that obtains the optimal ID attribute in the sense of minimum sampling variance is proposed. Third, more than a dozen typical resampling methods are compared via simulations in terms of sample size variation, sampling variance, computing speed, and estimation accuracy. These form a more comprehensive understanding of the algorithm, providing solid guidelines for either selection of existing resampling methods or new implementations.
Key words: Particle filter    Resampling    Kullback-Leibler divergence    Kolmogorov-Smirnov statistic
收稿日期: 2015-06-24 出版日期: 2015-11-04
CLC:  TN713  
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Tian-cheng Li
Gabriel Villarrubia
Shu-dong Sun
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Javier Bajo

引用本文:

Tian-cheng Li, Gabriel Villarrubia, Shu-dong Sun, Juan M. Corchado, Javier Bajo. Resampling methods for particle filtering: identical distribution, a new method, and comparable study. Front. Inform. Technol. Electron. Eng., 2015, 16(11): 969-984.

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http://www.zjujournals.com/xueshu/fitee/CN/10.1631/FITEE.1500199    或    http://www.zjujournals.com/xueshu/fitee/CN/Y2015/V16/I11/969

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