发表机构
INRIA Rhone Alpes（法国国家信息与自动化研究所罗讷-阿尔卑斯分所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出UID诱导规范形，统一解决未知输入解耦与重构问题，并实现仅用三点特征和单轴陀螺仪的最小结构运动递归状态估计。
AI 中文摘要
本文建立了由未知输入驱动的非线性系统状态估计问题的首个通用结构解。基于非线性未知输入可观测性理论，我们证明每个此类系统都允许一个结构等价表示，称为UID诱导规范形。所提出的表示将未知输入携带的信息分解为两个互补部分：与可观测动态结构解耦的未知输入方向，以及完全表示影响可观测动态的未知输入信息的可观测量。因此，UID诱导规范形为未知输入解耦和未知输入重构提供了统一的结构解，无需对未知输入作任何模型或随机假设。该框架的实际意义通过一个先前未探索的最小结构运动配置得到展示。所提出的表示使得仅从三个点特征和单轴陀螺仪进行递归状态估计成为可能，从而能够恢复三维结构和相机运动，直至一个未知的全局尺度因子。真实世界数据的实验验证了所提出的框架，并证明了这种最小传感配置的可行性。
英文摘要
This paper establishes the first general structural solution to the problem of state estimation for nonlinear systems driven by unknown inputs. Building upon nonlinear unknown-input observability theory, we show that every such system admits a structurally equivalent representation, referred to as the UID-induced normal form. The proposed representation decomposes the information carried by the unknown inputs into two complementary components: unknown-input directions that are structurally decoupled from the observable dynamics and observable quantities that completely represent the unknown-input information affecting the observable dynamics. As a consequence, the UID-induced normal form provides a unified structural solution to unknown-input decoupling and unknown-input reconstruction, without requiring any model or stochastic assumption on the unknown inputs. The practical significance of the proposed framework is demonstrated through a previously unexplored minimal Structure-from-Motion configuration. The proposed representation enables recursive state estimation from only three point features and a single-axis gyroscope, allowing the recovery of the three-dimensional structure and camera motion up to an unknown global scale factor. Experiments on real-world data validate the proposed framework and demonstrate the feasibility of this minimal sensing configuration.
