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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.

This paper provides a further extension to the tutorial Li et al., 2015. First, an identical distribution (ID) principle for re-sampling design is proposed, together with three metrics to evaluate the ID attribute. Next, a new re-sampling method which can achieve the optimal sampling variance is presented. Last, the effectiveness of the proposed method is verified by comparison with conventional re-sampling methods. This paper is well-written and provides great insight into the re-sampling procedure of the particle filter. It will be a good guidance for the researchers working on particle filter.

粒子滤波重采样：同分布原则、一种新方法以及综合对比

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