New theory shows when pose graph optimization is certifiably globally optimal
zhenjun_zhao · x · 2026-10-19
An arXiv paper studies PGO, a foundational nonconvex problem in robotics state estimation with many potential local minima. The authors prove that when noise is below an explicit, a priori verifiable bound, the optimization landscape is benign: a local minimizer within a characterized basin of attraction is globally optimal, and is the unique local minimizer there.
Key results:
- A basin of attraction (BOA) around the global minimizer whose radius is explicitly controlled by noise.
- First-order-optimality-based criteria guaranteeing local = global optimum under a noise-controlled condition.
- Two regimes: an a posteriori condition (Theorem 4, valid over the whole feasible set) and an a priori condition (Theorem 5, checkable from the noise matrix alone).
Numerical simulations validate the theory across randomized cases.
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