李群上的非线性对称保持观测器
Non-linear Symmetry-preserving Observer on Lie Groups
摘要：
在本文中，我们给出了一个几何框架的有限维李群具有某些特定的对称性系统的观察器的设计。设计和误差（真实和估计状态之间）方程是显式和内在的。我们还考虑了一种特殊的情况：李群上的左不变系统具有右等变输出。该理论给出了一类观测器，使得差错方程是自治的。观测器局部收敛于任何轨迹，全局行为与轨迹无关，这使人想起线性平稳的情况。
英文摘要：
In this paper we give a geometrical framework for the design of observers on finite-dimensional Lie groups for systems which possess some specific symmetries. The design and the error (between true and estimated state) equation are explicit and intrinsic. We consider also a particular case: left-invariant systems on Lie groups with right equivariant output. The theory yields a class of observers such that error equation is autonomous. The observers converge locally around any trajectory, and the global behavior is independent from the trajectory, which reminds of the linear stationary case.
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