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.

中文翻译：

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李群运动系统的等变滤波器设计

众所周知，李群上系统的不变性和等方差性可用于为现实世界的机器人系统设计高性能和鲁棒的观测器和滤波器。本文提出了一个分析框架，允许李群上的任何运动系统以自然的方式嵌入到等变运动系统中。该框架使我们能够表征不变系统、群仿射系统和等变系统的特性和它们之间的关系。我们提出了一种新的滤波器设计，即等变滤波器 (EqF)，它利用了系统嵌入的等方差特性，可以应用于李群上的任何运动系统。