Particle filters are a frequent choice for inference tasks in nonlinear and
non-Gaussian state-space models. They can either be used for state inference by
approximating the filtering distribution or for parameter inference by
approximating the marginal data (observation) likelihood. A good proposal
distribution and a good resampling scheme are crucial to obtain low variance
estimates. However, traditional methods like multinomial resampling introduce
nondifferentiability in PF-based loss functions for parameter estimation,
prohibiting gradient-based learning tasks. This work proposes a differentiable
resampling scheme by deterministic sampling from an empirical cumulative
distribution function. We evaluate our method on parameter inference tasks and
proposal learning.

提出了一种可微分的重采样方案，通过从经验累积分布函数进行确定性采样，用于粒子滤波器的参数推断和提议学习任务。

利用最优放置重采样的可微粒子滤波

Differentiable Particle Filtering using Optimal Placement Resampling

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.

通过提出一种基于确定性域的重复中值遍历策略，我们在重采样中实现了较低的方差，相比其他重采样方法，快速而准确地逼近了非线性情况下的隐藏马尔可夫模型。