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。

AirIMU：学习惯性里程计的不确定性传播

AirIMU: Learning Uncertainty Propagation for Inertial Odometry

Predictive maintenance plays a critical role in ensuring the uninterrupted
operation of industrial systems and mitigating the potential risks associated
with system failures. This study focuses on sensor-based condition monitoring
and explores the application of deep learning techniques using a hydraulic
system testbed dataset. Our investigation involves comparing the performance of
three models: a baseline model employing conventional methods, a single CNN
model with early sensor fusion, and a two-lane CNN model (2L-CNN) with late
sensor fusion. The baseline model achieves an impressive test error rate of 1%
by employing late sensor fusion, where feature extraction is performed
individually for each sensor. However, the CNN model encounters challenges due
to the diverse sensor characteristics, resulting in an error rate of 20.5%. To
further investigate this issue, we conduct separate training for each sensor
and observe variations in accuracy. Additionally, we evaluate the performance
of the 2L-CNN model, which demonstrates significant improvement by reducing the
error rate by 33% when considering the combination of the least and most
optimal sensors. This study underscores the importance of effectively
addressing the complexities posed by multi-sensor systems in sensor-based
condition monitoring.

通过使用一个液压系统测试数据集，本研究聚焦于传感器基于的状态监测，并探索了使用深度学习技术的应用。我们比较了三种模型的性能：一个使用常规方法的基准模型，一个具有早期传感器融合的单一卷积神经网络模型，以及一个具有晚期传感器融合的双路卷积神经网络模型 (2L-CNN)。基准模型通过晚期传感器融合取得了令人印象深刻的 1% 测试误差率，其中对每个传感器进行了单独的特征提取。然而，由于传感器特征的多样性，卷积神经网络模型遇到了挑战，导致了 20.5% 的误差率。为了进一步调查这个问题，我们对每个传感器进行了单独的训练，并观察到了准确性的变化。此外，我们还评估了 2L-CNN 模型的性能，在考虑最不理想和最理想传感器的组合时，错误率降低了 33%。本研究强调了在传感器基于的状态监测中有效应对多传感器系统的复杂性的重要性。