论文标题
非线性过滤算法的贝叶斯定律的最佳运输公式
An Optimal Transport Formulation of Bayes' Law for Nonlinear Filtering Algorithms
论文作者
论文摘要
本文使用最佳运输理论介绍了贝叶法律的各种表示。差异表示是根据（状态，观察）的联合分布与其独立耦合之间的最佳运输。通过在传输图上施加某些结构，使用变异问题的解决方案用于构建一个将先前的分布传输到观测信号的任何值的Brenier型图。新的公式用于用于离散时间过滤问题的集合卡尔曼滤波器（ENKF）的最佳传输形式，并提出了使用输入凸神经网络的ENKF向非高斯设置的新型扩展。最后，所提出的方法用于在连续时限内得出反馈粒子填充物（FPF）的最佳传输形式，该形式构成其第一个变化构建，而无需使用非线性滤波方程或贝叶斯定律明确而无明确。
This paper presents a variational representation of the Bayes' law using optimal transportation theory. The variational representation is in terms of the optimal transportation between the joint distribution of the (state, observation) and their independent coupling. By imposing certain structure on the transport map, the solution to the variational problem is used to construct a Brenier-type map that transports the prior distribution to the posterior distribution for any value of the observation signal. The new formulation is used to derive the optimal transport form of the Ensemble Kalman filter (EnKF) for the discrete-time filtering problem and propose a novel extension of EnKF to the non-Gaussian setting utilizing input convex neural networks. Finally, the proposed methodology is used to derive the optimal transport form of the feedback particle filler (FPF) in the continuous-time limit, which constitutes its first variational construction without explicitly using the nonlinear filtering equation or Bayes' law.
