摘要：AbstractIt 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 robotics applications such as inertial navigation or simultaneous localization and mapping (SLAM). 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. The EqF specializes to the Invariant Extended Kalman Filter (IEKF) in the case where the observed system is group affine or invariant.
关键词：KeywordsEquivariant Systems TheoryNonlinear ObserversEquivariant Filter (EqF)
