外观
论文arXiv 2610.2049014 天前
迈向可认证的可观测性退化下状态估计
原文链接：Towards Certifiable State Estimation under Observability Degeneracy（arXiv 2610.20490 · 发布日期：2026-10-14）
Towards Certifiable State Estimation under Observability Degeneracy
针对感知退化下可认证状态估计失效问题，提出候选驱动对偶认证框架，并在退化测量鲁棒配准中验证。
核心要点
- 动机是严重物理感知退化会导致半定规划松弛秩扩张，使直接求解和谱舍入失效。
- 方法从上图视角证明代价紧性与乘子恢复保持，并结合解重映射的可观测性感知局部搜索。
- 提出闭式对偶乘子恢复方案，并给出由可观测 Hessian 最小非零特征值和残差泄漏参数化的安全阈值。
- 实验在退化测量下的鲁棒配准中验证该通用框架，摘要未说明开源信息。
验证范围与局限：验证范围为退化测量下的鲁棒配准。
英文摘要 (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.
作者：Baoshan Song
来源
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