This paper proposes a unified mathematical framework for inertial measurement unit (IMU) preintegration in inertial-aided navigation system in different frames under different motion condition. The navigation state is precisely discretized as three parts: local increment, global state, and global increment. The global increment can be calculated in different frames such as local geodetic navigation frame and earth-centered-earth-fixed frame. The local increment which is referred as the IMU preintegration can be calculated under different assumptions according to the motion of the agent and the grade of the IMU. Thus, it more accurate and more convenient for online state estimation of inertial-integrated navigation system under different environment. Furthermore, the covariance propagation based on left perturbation is proposed for the first time, which is independent of the inputs of the gyroscope and accelerometer. Finally, we show the monotonicity of the uncertainty for determinant optimality criteria and R\'enyi entropy optimality criteria.

翻译：本文建议了一个统一的数学框架,用于在不同的运动条件下将惯性测量单位(IMU)预先纳入不同框架的惯性辅助导航系统。导航状态被精确地分解为三个部分:局部递增、全球状态和全球递增。全球递增可按不同的框架计算,例如当地的大地测量导航框架和以地为中心、地势固定框架。称为IMU预化的本地递增可按照代理人的运动和IMU的等级在不同假设下计算。因此,对于不同环境中的惯性综合导航系统的在线状态估算来说,它更准确,更方便。此外,首次提出了以左扰动为基础的变异传播,这独立于陀螺仪和加速计的投入。最后,我们显示了确定性最佳性标准的不确定性和R\'enyi 最佳性标准的单一性。