Title: Global Observer Design for a Class of Linear Observed Systems on Groups Show Chinese title

Title: 一类群上线性观测系统的全局观测器设计

Abstract: Linear observed systems on groups encode the geometry of a variety of practical state estimation problems. In this paper, we propose a unified observer framework for a class of linear observed systems by restricting a bi-invariant system on a Lie group to its normal subgroup. This structural property powerfully enables a system immersion of the original system into a linear time-varying system. Leveraging the immersion, an observer is constructed by first designing a Kalman-like observer for the immersed system and then reconstructing the group-valued state via optimization. Under a rank condition, global exponential stability (GES) is achieved provided one global optimum of the reconstruction optimization is found, reflecting the topological difficulties inherent to the non-Euclidean state space. Semi-global stability is guaranteed when input biases are jointly estimated. The theory is applied to the GES observer design for two-frame systems, capable of modeling a family of navigation problems. Two non-trivial examples are provided to illustrate implementation details. Show Chinese abstract

Abstract: 线性观测系统在群上编码了各种实际状态估计问题的几何结构。 在本文中，我们通过将一个双不变系统限制在其正规子群上，提出了一类线性观测系统的统一观测器框架。 这种结构特性强有力地使得原系统能够浸入到一个时变线性系统中。 利用这种浸入，首先为浸入系统设计一个类似卡尔曼的观测器，然后通过优化重构群值状态。 在秩条件满足的情况下，只要找到重构优化的一个全局最优解，就可以实现全局指数稳定（GES），这反映了非欧几里得状态空间固有的拓扑困难。 当输入偏差被联合估计时，保证半全局稳定性。 该理论应用于两帧系统的GES观测器设计，能够对一类导航问题进行建模。 提供了两个非平凡的例子来说明实现细节。