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 Cram\'er-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.

翻译：本文结合别名方法与系统化采样概念，后者是粒子滤波中常用于高效低方差重采样的技术。所提出的方法能够实现离散分布的极快速采样：抽取k个样本的速度比基于累积分布函数的二分搜索或多数库中使用的反演方法快一个数量级。通过改进的Cramér-Von Mises拟合优度统计量评估经验分布函数，结果表明该方法相较于多项式采样具有显著优势。由于连续分布常可通过离散分布近似，本方法可作为生成粒子滤波建议分布（如机器人运动模型）随机样本的通用高效方案。