Accurate uncertainty estimation for inertial odometry is the foundation to achieve optimal fusion in multi-sensor systems, such as visual or LiDAR inertial odometry. Prior studies often simplify the assumptions regarding the uncertainty of inertial measurements, presuming fixed covariance parameters and empirical IMU sensor models. However, the inherent physical limitations and non-linear characteristics of sensors are difficult to capture. Moreover, uncertainty may fluctuate based on sensor rates and motion modalities, leading to variations across different IMUs. To address these challenges, we formulate a learning-based method that not only encapsulate the non-linearities inherent to IMUs but also ensure the accurate propagation of covariance in a data-driven manner. We extend the PyPose library to enable differentiable batched IMU integration with covariance propagation on manifolds, leading to significant runtime speedup. To demonstrate our method's adaptability, we evaluate it on several benchmarks as well as a large-scale helicopter dataset spanning over 262 kilometers. The drift rate of the inertial odometry on these datasets is reduced by a factor of between 2.2 and 4 times. Our method lays the groundwork for advanced developments in inertial odometry.

翻译：精确估计惯性里程计的不确定性是实现多传感器系统（如视觉或激光雷达惯性里程计）最优融合的基础。以往研究常简化惯性测量不确定性的假设，预设固定协方差参数和经验性IMU传感器模型。然而，传感器固有的物理限制和非线性特征难以捕捉。此外，不确定性可能因传感器速率和运动模态而波动，导致不同IMU之间存在差异。为应对这些挑战，我们提出一种基于学习的方法，不仅封装IMU固有的非线性特性，还确保以数据驱动方式精确传播协方差。我们扩展了PyPose库，使其支持在流形上带协方差传播的可微批处理IMU积分，从而显著提升运行速度。为展示方法的适应性，我们在多个基准测试以及覆盖262公里的大规模直升机数据集上进行评估。这些数据集上的惯性里程计漂移率降低了2.2倍到4倍。我们的方法为惯性里程计的先进发展奠定了基础。