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arXiv · 2610.20490

Towards Certifiable State Estimation under Observability Degeneracy

Baoshan Song
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Abstract

Certifiable optimization provides global optimality guarantees for non-convex state estimation in robotics. However, under severe physical sensing degeneracy, convex Semidefinite Programming relaxations solved via Interior-Point Methods suffer from rank expansion, rendering direct semidefinite solving and spectral rounding algebraically invalid. In this paper, we establish a universal candidate-driven dual certification framework that resolves this challenge without incurring rank expansion. First, from an epigraph perspective, we prove that while sensing degeneracy expands the primal optimal set into a flat equi-cost face, cost tightness and multiplier recovery remain strictly intact, enabling global verification without direct semidefinite solving. Second, we propose an observability-aware local search using solution remapping, coupled with a closed-form dual multiplier recovery scheme that executes in sub-microsecond latency. Third, we derive a model-specific adaptive dual safety threshold parameterized by the minimum non-zero eigenvalue of the observable Hessian and uneradicated residual leakage, preventing false rejections of optimal candidates under weak observability. We validate our universal framework with robust registration under degenerate measurements.

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Baoshan Song. 2026-10-14. Towards Certifiable State Estimation under Observability Degeneracy. https://arxiv.org/abs/2610.20490

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