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IMU Propagation as Preintegration

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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