We propose a method for optimal Bayesian filtering with deterministic particles. In order to avoid particle degeneration, the filter step is not performed at once. Instead, the particles progressively flow from prior to posterior. This is achieved by splitting the filter step into a series of sub-steps. In each sub-step, optimal resampling is done by a map that replaces non-equally weighted particles with equally weighted ones. Inversions of the maps or monotonicity constraints are not required, greatly simplifying the procedure. The parameters of the mapping network are optimized w.r.t.\ to a particle set distance. This distance is differentiable, and compares non-equally and equally weighted particles. Composition of the map sequence provides a final mapping from prior to posterior particles. Radial basis function neural networks are used as maps. It is important that no intermediate continuous density representation is required. The entire flow works directly with particle representations. This avoids costly density estimation.

翻译：我们提出一种基于确定性粒子的最优贝叶斯滤波方法。为避免粒子退化，滤波步骤不一次性完成，而是使粒子从先验分布渐进流动至后验分布。该方法通过将滤波步骤分解为一系列子步骤实现：每个子步骤中，通过映射将非等权粒子替换为等权粒子以实现最优重采样。该过程无需映射求逆或单调性约束，大幅简化了操作流程。映射网络参数针对粒子集距离进行优化——该距离具有可微性，能比较非等权与等权粒子。映射序列的复合运算可形成从先验粒子到后验粒子的最终映射。采用径向基函数神经网络作为映射函数，且无需任何中间连续密度表示，整个流动过程直接基于粒子表示，从而避免了昂贵的密度估计。