基于伽利略群理论，改进了惯性导航中陀螺仪偏差的预积分方法。
Equivariant IMU Preintegration with Biases: a Galilean Group Approach
- 将陀螺仪偏差与导航状态统一在伽利略群框架下建模
- 相比传统方法，线性化误差更低，定位更一致
- 适用于高精度惯性导航，开源代码已发布
本文提出一种新的惯性测量单元（IMU）预积分方法，作为基于优化的惯性导航系统（INS）定位方案的核心组件。受近期在带偏差惯性系统中等变理论进展的启发，我们推导出在 $\mathbf{Gal}(3) \ltimes \mathfrak{gal}(3)$ 上的离散时间预积分公式，即伽利略群 $\mathbf{Gal}(3)$ 的切空间左平凡化。我们定义了一种新型预积分误差，几何上耦合了导航状态与偏差，从而降低线性化误差。与现有将IMU偏差视为独立状态空间的方法相比，本方法在一致性方面表现更优。通过仿真和真实IMU数据进行了广泛验证，并在Lie++库中实现，代码开源。
原文摘要 · Abstract (English)
This letter proposes a new approach for Inertial Measurement Unit (IMU) preintegration, a fundamental building block that can be leveraged in different optimization-based Inertial Navigation System (INS) localization solutions. Inspired by recent advances in equivariant theory applied to biased INSs, we derive a discrete-time formulation of the IMU preintegration on ${\mathbf{Gal}(3) \ltimes \mathfrak{gal}(3)}$, the left-trivialization of the tangent group of the Galilean group $\mathbf{Gal}(3)$. We define a novel preintegration error that geometrically couples the navigation states and the bias leading to lower linearization error. Our method improves in consistency compared to existing preintegration approaches which treat IMU biases as a separate state-space. Extensive validation against state-of-the-art methods, both in simulation and with real-world IMU data, implementation in the Lie++ library, and open-source code are provided.
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