Certifiable Alignment of GNSS and Local Frames via Lagrangian Duality | IPNL — Intelligent Positioning and Navigation Laboratory

Baoshan Song, Matthew Giamou, Penggao Yan, Chunxi Xia, Li-Ta Hsu

IEEE Robotics and Automation Letters (2026)

journal Q1

Pipeline: the non-convex alignment problem is relaxed via rank-1 relaxation into a quadratic dual problem; after an observability check the dual is solved and rank tightness certifies whether the global optimum was found.

Key idea. Aligning the global GNSS frame with a local odometry/SLAM frame is a non-convex problem that local solvers can get silently wrong. The method applies a rank-1 relaxation and Lagrangian duality, checks observability (asking for more measurements when the problem is under-determined), and uses the rank tightness of the dual solution to certify when the recovered alignment is the global optimum.

Why it matters. Frame alignment underpins any fusion of GNSS with locally consistent navigation. A certificate of global optimality replaces “hope the solver converged” with a checkable guarantee. (IEEE Robotics and Automation Letters, 2026, Q1.)