IMU预积分与传播本质相同，可互相转换。
IMU Propagation as Preintegration
- 用现有传播代码封装即可实现预积分
- 在随机数据上与GTSAM结果高度一致
- 适合开发/调试惯性系统的研究者
IMU预积分广泛应用于基于因子图的视觉-惯性、激光雷达-惯性及雷达-惯性状态估计中，但通常被视为与常规IMU传播分离的特殊实现。本文表明，预积分与传播是同一底层计算的不同表现形式。我们提出一种不依赖约定的视角：通过封装已有IMU传播过程，可获得预积分测量、偏差雅可比和协方差；反之，预积分模块也可恢复状态转移矩阵与传播协方差。该视角简化了传播代码复用，支持不同误差状态定义间的转换，并提供预积分实现的一致性验证方法。在随机IMU序列上的实验表明，基于RK4的传播实现与GTSAM的切线和流形预积分模块在恢复的雅可比、协方差和转移矩阵方面高度一致。
原文摘要 · Abstract (English)
IMU preintegration is widely used in factor-graph-based visual--inertial, lidar--inertial, and radar--inertial state estimation, yet it is often treated as a specialized implementation separate from conventional IMU propagation. This note shows that IMU preintegration and propagation are equivalent realizations of the same underlying computation. We present a convention-agnostic view in which the preintegrated measurement, bias Jacobians, and covariance can be obtained by wrapping an existing IMU propagation routine, while a preintegration module can conversely recover state-transition matrices and propagated covariances. This perspective simplifies the reuse of existing propagation code, supports translation across different error-state definitions, and provides practical consistency checks for preintegration implementations. Experiments with random IMU sequences demonstrate close agreement between an RK4-based propagation implementation and GTSAM's tangent and manifold preintegration modules in the recovered Jacobians, covariances, and transition matrices.
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