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 advancements in equivariant theory applied to biased INSs, we derive a discrete-time formulation of the IMU preintegration on $\mathbf{G}(3) \ltimes \mathfrak{g}(3)$, the tangent group of the inhomogeneous Galilean group $\mathbf{G}(3)$. 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-sourcing of the code are provided.

翻译：本通讯提出了一种新的惯性测量单元（IMU）预积分方法，该方法可作为不同基于优化的惯性导航系统（INS）定位解决方案的基础模块。受近期应用于含偏置INS的等变理论进展的启发，我们在非齐次伽利略群 $\mathbf{G}(3)$ 的切群 $\mathbf{G}(3) \ltimes \mathfrak{g}(3)$ 上推导了IMU预积分的离散时间公式。我们定义了一种新颖的预积分误差，该误差在几何上耦合了导航状态与偏置，从而降低了线性化误差。与将IMU偏置视为独立状态空间的现有预积分方法相比，我们的方法在一致性方面有所改进。本文提供了针对最先进方法的广泛验证（包括仿真和真实世界IMU数据）、在Lie++库中的实现以及代码的开源。