Towards Certifiable State Estimation under Observability Degeneracy

Key points

• 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.1
• 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.1
• 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.1
• 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.1

Sources (1)

• [1]Towards Certifiable State Estimation under Observability Degeneracy
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 14, 05:03 PM

  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.

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