An Efficient Closed-Form Solution to Full Visual-Inertial State Initialization

Abstract

In this letter, we present a closed-form initialization method that recovers the full visual–inertial state without nonlinear optimization. Unlike previous approaches that rely on iterative solvers, our formulation yields analytical, easy-to-implement, and numerically stable solutions for reliable start-up. Our method builds on small-rotation and constant-velocity approximations, which keep the formulation compact while preserving the essential coupling between motion and inertial measurements. We further propose an observability-driven, two-stage initialization scheme that balances accuracy with initialization latency. Extensive experiments on the EuRoC dataset validate our assumptions: our method achieves <inline-formula><tex-math notation="LaTeX">$10-20\%$</tex-math></inline-formula> lower initialization error than optimization-based approaches, while using <inline-formula><tex-math notation="LaTeX">$4\times$</tex-math></inline-formula> shorter initialization windows and reducing computational cost by <inline-formula><tex-math notation="LaTeX">$5\times$</tex-math></inline-formula>.