  In this work, we propose a novel method for performing inertial aided
navigation, by using deep neural networks (DNNs). To date, most DNN inertial
navigation methods focus on the task of inertial odometry, by taking gyroscope
and accelerometer readings as input and regressing for integrated IMU poses
(i.e., position and orientation). While this design has been successfully
applied on a number of applications, it is not of theoretical performance
guarantee unless patterned motion is involved. This inevitably leads to
significantly reduced accuracy and robustness in certain use cases. To solve
this problem, we design a framework to compute observable IMU integration terms
using DNNs, followed by the numerical pose integration and sensor fusion to
achieve the performance gain. Specifically, we perform detailed analysis on the
motion terms in IMU kinematic equations, propose a dedicated network design,
loss functions, and training strategies for the IMU data processing, and
conduct extensive experiments. The results show that our method is generally
applicable and outperforms both traditional and DNN methods by wide margins.
