A resampling scheme provides a way to switch low-weight particles for sequential Monte Carlo with higher-weight particles representing the objective distribution. The less the variance of the weight distribution is, the more concentrated the effective particles are, and the quicker and more accurate it is to approximate the hidden Markov model, especially for the nonlinear case. We propose a repetitive deterministic domain with median ergodicity for resampling and have achieved the lowest variances compared to the other resampling methods. As the size of the deterministic domain $M\ll N$ (the size of population), given a feasible size of particles, our algorithm is faster than the state of the art, which is verified by theoretical deduction and experiments of a hidden Markov model in both the linear and non-linear cases.

翻译：重采样方案提供了一种方法，用于将低权重粒子替换为能更好代表目标分布的高权重粒子，从而在顺序蒙特卡洛中实现粒子转换。权重分布的方差越小，有效粒子的集中程度越高，对隐马尔可夫模型（尤其是非线性情况）的近似就越快速和准确。我们提出了一种具有中位数遍历性的重复确定性区域用于重采样，并实现了相较于其他重采样方法的最低方差。当确定性区域大小$M\ll N$（种群大小）时，在给定可行粒子规模下，我们的算法比当前最优方法更快，这一结论通过线性与非线性隐马尔可夫模型的理论推导和实验得到了验证。