论文标题
离散时间系统的模棱两可的滤波器设计
Equivariant Filter Design for Discrete-time systems
论文作者
论文摘要
许多非线性控制系统的运动学，尤其是在机器人领域中，承认了一种瞬时的lie群对称性，这在高性能观察者设计中很有用。最近提出的Eproiriant滤波器（EQF）利用了均衡性，以生成针对各种现实世界系统的高性能过滤器。但是，现有在eproiriant滤波器上的工作，并且总体上控制系统的等效性是基于连续的时间公式。在本文中，我们首先介绍离散时间系统的模棱两可的结构。然后，我们使用它来提出eproivariant过滤器的离散时间版本。该方法的一种新颖性是，对称群的几何形状自然在过滤器的重置步骤中作为平行传输。线性二阶运动学的初步结果具有单独的轴承和范围测量结果表明，离散的EQF显着胜过连续EQF的离散版本和经典离散EKF。
The kinematics of many nonlinear control systems, especially in the robotics field, admit a transitive Lie-group symmetry, which is useful in high performance observer design. The recently proposed equivariant filter (EqF) exploits equivariance to generate high performance filters for a wide range of real-world systems. However, existing work on the equivariant filter, and equivariance of control systems in general, is based on a continuous-time formulation. In this paper, we first present the equivariant structure of a discrete-time system. We then use this to propose a discrete-time version of the equivariant filter. A novelty of the approach is that the geometry of the symmetry group naturally appears as parallel transport in the reset step of the filter. Preliminary results for linear second order kinematics with separate bearing and range measurements indicate that the discrete EqF significantly outperforms both a discretized version of the continuous EqF and a classical discrete EKF.
