We propose a framework for designing global observers for nonlinear systems with disturbances under geometric conditions based on orbital symmetries. Under some additional restrictions these orbital symmetry-based conditions boil down to geometric homogeneity (at infinity) conditions. Our observers are the result of the combination of a first filter, a state norm estimator, with a second filter adaptively tuned by the first and when compared with the existing literature have a completely novel structure, inherited by the orbital symmetry-based conditions. The observers exploit the geometric properties of orbital symmetries which are one-parameter groups of transformations capable of mapping the system state into neighbourhoods with parametrized width.

我们提出了一个框架，用于在基于轨道对称性的几何条件下为具有扰动的非线性系统设计全局观测器。在一些额外的限制下，这些基于轨道对称性的条件归结为几何均匀性（无穷大）条件。我们的观察者是第一个滤波器（状态范数估计器）与由第一个滤波器自适应调整的第二个滤波器相结合的结果，与现有文献相比，具有完全新颖的结构，由基于轨道对称性的条件继承。观察者利用轨道对称性的几何特性，轨道对称性是能够将系统状态映射到具有参数化宽度的邻域的单参数变换组。