Structural Foundations of Nonlinear Systems with Unknown Inputs: The UID-Induced Normal Form and Minimal-Sensing Structure-from-Motion

Abstract: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.

Optimization and Control (math.OC); Computer Vision and Pattern Recognition (cs.CV); Robotics (cs.RO)

arXiv:2610.05939 [math.OC]

(or arXiv:2610.05939v1 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2610.05939 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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