论文标题
谎言组运动系统的模棱两可的滤波器设计
Equivariant Filter Design for Kinematic Systems on Lie Groups
论文作者
论文摘要
众所周知，在高性能和强大的观察者的设计中，可以利用Lie组系统上的系统的不变性和贬值属性。本文提出了一个分析框架，该框架允许将谎言组上的任何运动系统自然地嵌入到模棱两可的运动学系统中。该框架使我们能够表征不变系统，组仿射系统和模棱两可系统之间的属性和关系。我们提出了一种新的滤波器设计，即eproivariant滤波器（EQF），该设计利用了系统嵌入的模棱两可的属性，可以应用于Lie组上的任何运动系统。
It is known that invariance and equivariance properties for systems on Lie groups can be exploited in the design of high performance and robust observers and filters for real-world robotic systems. This paper proposes an analysis framework that allows any kinematic system on a Lie group to be embedded in a natural manner into an equivariant kinematic system. This framework allows us to characterise the properties of, and relationships between, invariant systems, group affine systems, and equivariant systems. We propose a new filter design, the Equivariant Filter (EqF), that exploits the equivariance properties of the system embedding and can be applied to any kinematic system on a Lie group.
