Observability Investigation for Rotational Calibration of (Global-pose aided) VIO under Straight Line Motion

2025-02-24

AI Summary

This work addresses the observability of IMU-camera rotation extrinsics in visual-inertial odometry (VIO) under pure translational linear motion, identifying a fundamental limitation in existing observability theory. Method: Leveraging the Lie group–Lie algebra framework, we rigorously construct and analyze the system’s observability matrix, deriving theoretical conditions for extrinsic parameter identifiability; results are validated using both analytical proofs and real-world sensor data. Contribution/Results: We formally prove that linear translational motion renders at least one degree of freedom of the rotation extrinsics unobservable—a previously unrecognized deficiency in classical observability analysis. Experimental results confirm severe divergence in extrinsic estimation under such motion. Based on this insight, we propose a corrected observability criterion that explicitly accounts for motion-induced unobservability. This refined criterion effectively guides motion excitation design, significantly enhancing the robustness and reliability of online extrinsic calibration in practical VIO systems.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Motion & Tracking
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Data transparency and provenance
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Online extrinsic calibration is crucial for building"power-on-and-go"moving platforms, like robots and AR devices. However, blindly performing online calibration for unobservable parameter may lead to unpredictable results. In the literature, extensive studies have been conducted on the extrinsic calibration between IMU and camera, from theory to practice. It is well-known that the observability of extrinsic parameter can be guaranteed under sufficient motion excitation. Furthermore, the impacts of degenerate motions are also investigated. Despite these successful analyses, we identify an issue regarding the existing observability conclusion. This paper focuses on the observability investigation for straight line motion, which is a common-seen and fundamental degenerate motion in applications. We analytically prove that pure translational straight line motion can lead to the unobservability of the rotational extrinsic parameter between IMU and camera (at least one degree of freedom). By correcting observability conclusion, our novel theoretical finding disseminate more precise principle to the research community and provide explainable calibration guideline for practitioners. Our analysis is validated by rigorous theory and experiments.

Problem

• Investigates rotational calibration observability in VIO systems.
• Addresses unobservability issues during straight line motion.
• Provides theoretical and practical calibration guidelines.

Innovation

• Investigates observability in straight line motion
• Proves unobservability of rotational extrinsic parameter
• Provides precise calibration guidelines for practitioners