Attitude estimation is a core problem in many mobile robotic systems, such as unmanned aerial and ground vehicles. The configuration space of these systems is properly modeled by exploiting the theory of Lie groups. In this article, we propose a second-order-optimal minimum-energy filter on the matrix Lie group TSE(2), the tangent bundle of the special Euclidean group SE(2), where the optimality is with respect to a cost function in the unknown input and output error measurements. In this article, the measurement equation consists of a global positioning system-like device with two antennas attached to the planar rigid body and an inertial measurement unit-like device. Even though the mathematics is quite complicated, the accuracy of the filter justifies this approach. Simulations show the effectiveness of the proposed filter.

中文翻译：

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平面刚体李群的二阶最优滤波器

姿态估计是许多移动机器人系统的核心问题，例如无人机和地面车辆。这些系统的配置空间通过利用李群理论进行了适当的建模。在本文中，我们在矩阵李群 TSE(2) 上提出了一个二阶最优最小能量滤波器，该矩阵是特殊欧几里得群 SE(2) 的切线丛，其中最优性是相对于成本函数未知的输入和输出误差测量。在本文中，测量方程包括一个全球定位系统类设备，两个天线连接到平面刚体和一个惯性测量单元类设备。尽管数学相当复杂，但过滤器的准确性证明了这种方法的合理性。仿真显示了所提出的滤波器的有效性。