The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems
The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems
复制标题
DOI：
10.1016/j.automatica.2021.109752
复制
发表时间：
2021-09
期刊：
影响因子：
--
通讯作者：
Nathan J. Kong;J. Payne;George Council;Aaron M. Johnson
中科院分区：
文献类型：
--
作者：
Nathan J. Kong;J. Payne;George Council;Aaron M. Johnson
许多状态估计和控制算法需要了解概率分布如何在动态系统中传播。然而，尽管混合动力系统在许多领域变得越来越重要，但在利用关于概率分布如何通过混合转变映射的知识方面的工作还很少。在这里，我们利用利用跃迁矩阵(灵敏度方程的一阶更新)的传播定律来创建Salted Kalman Filter(SKF)，这是Kalman Filter和Extended Kalman Filter对混合动力系统的自然扩展。除了混合事件，SKF是一个标准的卡尔曼过滤器。当混合事件发生时，突变矩阵起到与系统动力学类似的作用，随后导致对预测和更新步骤的离散修改。通过减少状态估计的均方误差，特别是在混合过渡事件之后，SKF的性能优于朴素的变分更新-重置映射的雅可比。与混合粒子过滤器相比，粒子过滤器仅在使用大量粒子时才在均方误差方面优于SKF，这可能是因为对混合过渡附近的分裂分布进行了更准确的计算。
Many state estimation and control algorithms require knowledge of how probability distributions propagate through dynamical systems. However, despite hybrid dynamical systems becoming increasingly important in many fields, there has been little work on utilizing the knowledge of how probability distributions map through hybrid transitions. Here, we make use of a propagation law that employs the saltation matrix (a first-order update to the sensitivity equation) to create the Salted Kalman Filter (SKF), a natural extension of the Kalman Filter and Extended Kalman Filter to hybrid dynamical systems. Away from hybrid events, the SKF is a standard Kalman filter. When a hybrid event occurs, the saltation matrix plays an analogous role as that of the system dynamics, subsequently inducing a discrete modification to both the prediction and update steps. The SKF outperforms a naive variational update – the Jacobian of the reset map – by having a reduced mean squared error in state estimation, especially immediately after a hybrid transition event. Compared against a hybrid particle filter, the particle filter outperforms the SKF in mean squared error only when a large number of particles are used, likely due to a more accurate accounting of the split distribution near a hybrid transition.