发表机构
Northeastern University（东北大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出首个QCQP可表示的IMU预积分因子，基于Cayley映射和冗余约束实现紧松弛，应用于可认证GNSS-IMU平滑，达到验证的全局最优。
AI 中文摘要
我们提出了一种QCQP可表示的IMU预积分因子，使得预积分惯性测量能够实现可认证估计。据我们所知，这是首个直接将IMU预积分纳入可认证估计的工作。惯性传感是机器人学中常见且可靠的模态，将其纳入可认证估计拓宽了该方法的实际应用范围。主要挑战在于获得所需的代数结构以及足够紧的凸松弛。标准IMU预积分依赖于指数映射，而指数映射不允许精确的多项式表示。此外，获得QCQP公式需要辅助提升变量，而标准的半定规划（SDP）松弛可能较松。我们通过基于Cayley映射推导IMU预积分因子，并引入一组显式的冗余约束来收紧所得松弛，从而解决了这些问题。为验证所提出的因子，我们将其应用于可认证的GNSS-IMU平滑问题，并在合成数据和真实世界数据上进行了评估。结果表明，所提出的公式产生了紧的松弛，并将所得估计问题求解至验证的全局最优性。
英文摘要
We propose a QCQP-representable IMU pre-integration factor that enables certifiable estimation with pre-integrated inertial measurements. To the best of our knowledge, this is the first work to directly incorporate IMU pre-integration into certifiable estimation. Inertial sensing is a common and reliable modality in robotics, and incorporating it broadens the practical scope of certifiable estimation. The main challenges are obtaining the required algebraic structure and a sufficiently tight convex relaxation. Standard IMU pre-integration relies on the exponential map, which does not admit an exact polynomial representation. Moreover, obtaining a QCQP formulation requires auxiliary lifting variables, for which the standard semidefinite programming (SDP) relaxation can be loose. We address these issues by deriving an IMU pre-integration factor based on the Cayley map and an explicit set of redundant constraints that tighten the resulting relaxation. To validate the proposed factor, we apply it to certifiable GNSS-IMU smoothing and evaluate it on synthetic and real-world data. The results show that the proposed formulation yields tight relaxations and solves the resulting estimation problems to verified global optimality.
Comments8 pages, 3 figures, 3 tables. Submitted to IEEE International Conference on Robotics and Automation (ICRA) 2027
