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.

准确的不确定性估计是实现多传感器系统（如视觉或激光雷达惯性测距）中获得最佳信息融合的基础。本研究基于学习方法，以数据驱动的方式构建与传播协方差，减小了惯性测距在漂移速率上的误差，为惯性测距领域的先进发展奠定了基础。