论文标题
具有非线性状态平等约束的最佳基于运输的过滤
Optimal Transport Based Filtering with Nonlinear State Equality Constraints
论文作者
论文摘要
在这项工作中，我们提出了一个框架，以解决使用贝叶斯过滤的状态依赖性非线性相等限制状态估计的问题。该框架是专门用于使用最佳传输理论的贝叶斯过滤的线性近似。作为该框架的一部分，我们介绍了三个传统上使用的非线性相等性约束算法以及最佳基于基于运输的过滤器的算法：相等约束的最佳运输过滤器，预测的最佳运输滤波器和测量值仪的最佳运输过滤器。如果非线性平等约束代表任意凸流歧管，我们表明，最佳传输过滤器的重采样步骤可以从该歧管上定义的任何概率分布函数生成用于过滤的初始样品。我们使用建议的框架显示数值结果。
In this work we propose a framework to address the issue of state dependent nonlinear equality-constrained state estimation using Bayesian filtering. This framework is constructed specifically for a linear approximation of Bayesian filtering that uses the theory of Optimal Transport. As a part of this framework, we present three traditionally-used nonlinear equality constraint-preserving algorithms coupled with the Optimal Transport based filter: the equality-constrained Optimal Transport filter, the projected Optimal Transport filter, and the measurement-augmented Optimal Transport filter. In cases where the nonlinear equality-constraints represent an arbitrary convex manifold, we show that the re-sampling step of Optimal Transport filter, can generate initial samples for filtering, from any probability distribution function defined on this manifold. We show numerical results using our proposed framework.
