一种永不退化的高维粒子滤波器，通过牛顿流平滑迁移粒子。
Newton-Flow Particle Filters based on Generalized Cramér Distance
- 用广义Cramér距离定义粒子集间差异，支持有序无关的可微计算
- 通过人工时间连续优化，实现从先验到后验密度的平稳粒子迁移
- 无需密度估计，仅需先验粒子与似然函数，可直接替代传统方法
我们提出一种适用于高维问题的递归粒子滤波器，其状态估计始终不会退化。状态由确定性的低偏差粒子集表示。重点在于测量更新步骤，利用似然函数表达观测及其不确定性。该似然通过人工时间上的同伦延拓逐步引入滤波过程。推导出粒子集之间广义Cramér距离的闭式表达，具备可微性且对粒子顺序不变。随后采用牛顿流在人工时间内持续最小化该距离，从而平滑地将粒子从先验密度移动至后验密度。新滤波器实现极为简单，效率极高，仅需一个先验粒子集和一个似然函数，无需从样本中估计密度，可作为经典方法的即插即用替代方案。
原文摘要 · Abstract (English)
We propose a recursive particle filter for high-dimensional problems that inherently never degenerates. The state estimate is represented by deterministic low-discrepancy particle sets. We focus on the measurement update step, where a likelihood function is used for representing the measurement and its uncertainty. This likelihood is progressively introduced into the filtering procedure by homotopy continuation over an artificial time. A generalized Cramér distance between particle sets is derived in closed form that is differentiable and invariant to particle order. A Newton flow then continually minimizes this distance over artificial time and thus smoothly moves particles from prior to posterior density. The new filter is surprisingly simple to implement and very efficient. It just requires a prior particle set and a likelihood function, never estimates densities from samples, and can be used as a plugin replacement for classic approaches.
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