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：惯性里程计的精确不确定性估计是多传感器系统（如视觉或激光雷达惯性里程计）实现最优融合的基础。现有研究常简化惯性测量不确定性的假设，假定固定的协方差参数和基于经验的IMU传感器模型。然而，传感器的固有限制和非线性特性难以捕捉。此外，不确定性会随传感器速率和运动模态变化，导致不同IMU间的差异。为解决这些问题，我们提出一种基于学习的方法，既能封装IMU固有的非线性特性，又能以数据驱动方式确保协方差的精确传播。我们扩展了PyPose库，使其支持流形上带协方差传播的可微分批量式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和跨越262公里的直升机大规模数据集上进行了评估。在这些数据集上，惯性里程计的漂移率降低了2.2至4倍。我们的方法为惯性里程计的进阶发展奠定了基础。