A QCQP-Representable IMU Pre-Integration Factor for Certifiable State Estimation

Abstract: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.

8 pages, 3 figures, 3 tables. Submitted to IEEE International Conference on Robotics and Automation (ICRA) 2027

Robotics (cs.RO)

arXiv:2609.38048 [cs.RO]

(or arXiv:2609.38048v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.38048 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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