将别名法与系统采样结合，实现高效低方差离散分布采样。
Systematic Alias Sampling: an efficient and low-variance way to sample from a discrete distribution
- 融合别名法与系统采样，提升采样效率。
- 采样速度比传统方法快一个数量级，且分布更接近真实。
- 适合机器人运动模型等需要高效随机采样的场景。
本文将别名法与系统采样相结合，一种常用于粒子滤波中高效低方差重采样的方法。所提方法可实现从离散分布中极快速的采样：生成k个样本的速度比基于累积分布函数的二分查找或多数库中使用的反演方法快一个数量级。通过修正的Cramér-Von Mises拟合优度统计量评估生成的经验分布函数，结果显示该方法在拟合性上显著优于多项式采样。由于连续分布常可近似为离散形式，该方法可作为通用高效的随机采样手段，适用于粒子滤波中的提案分布，如机器人运动模型。
原文摘要 · Abstract (English)
In this paper we combine the Alias method with the concept of systematic sampling, a method commonly used in particle filters for efficient low-variance resampling. The proposed method allows very fast sampling from a discrete distribution: drawing k samples is up to an order of magnitude faster than binary search from the cumulative distribution function (cdf) or inversion methods used in many libraries. The produced empirical distribution function is evaluated using a modified Cramér-Von Mises goodness-of-fit statistic, showing that the method compares very favourably to multinomial sampling. As continuous distributions can often be approximated with discrete ones, the proposed method can be used as a very general way to efficiently produce random samples for particle filter proposal distributions, e.g. for motion models in robotics.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。