🤖 AI Summary
This work addresses the longstanding disconnect between IMU preintegration and propagation, which has hindered code reuse, complicated error-state transformations, and impeded consistency verification. For the first time, we establish their mathematical equivalence and propose a unified framework that is agnostic to error-state conventions. By encapsulating any IMU propagation routine—such as RK4—the framework automatically generates corresponding preintegrated measurements, bias Jacobians, and covariances, and vice versa. This formulation enables seamless migration across different error-state definitions and incorporates a built-in mechanism for consistency validation. Experiments demonstrate that an RK4-based propagation implementation achieves high agreement with GTSAM’s tangent-space and manifold preintegration modules in terms of Jacobians, covariances, and state transition matrices, confirming the correctness and practical utility of the proposed approach.
📝 Abstract
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.